|
(axpy
(FcanonicBounded2 0
(FcanonicBounded2-1 nil 3320508538
("" (skeep)
(("" (typepred "x1") (("" (rewrite "FcanonicBounded") nil nil))
nil))
nil)
((b formal-const-decl "Format" axpy nil)
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(float type-eq-decl nil float nil)
(Format type-eq-decl nil float nil)
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(> const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number nonempty-type-decl nil numbers nil)
(above nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(FcanonicBounded formula-decl nil float nil))
nil))
(MinOrMax_Rlt 0
(MinOrMax_Rlt-1 nil 3320496512
("" (skeep)
(("" (expand "MinOrMax?")
(("" (split)
(("1" (rewrite "RoundedModeUlp" :subst ("b" "b" "P" "isMin?"))
(("1" (rewrite "isMin_RoundedMode") nil nil)) nil)
("2" (rewrite "RoundedModeUlp" :subst ("b" "b" "P" "isMax?"))
(("2" (rewrite "isMax_RoundedMode") nil nil)) nil))
nil))
nil))
nil)
((MinOrMax? const-decl "bool" axpy nil)
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(float type-eq-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
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(number_field nonempty-type-from-decl nil number_fields nil)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(radix formal-const-decl "above(1)" axpy nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(isMin_RoundedMode formula-decl nil float nil)
(real_minus_real_is_real application-judgement "real" reals nil))
shostak))
(MinOrMax_Fopp_TCC1 0
(MinOrMax_Fopp_TCC1-1 nil 3320496511
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((FoppBounded formula-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Format type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(float type-eq-decl nil float nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(radix formal-const-decl "above(1)" axpy nil))
nil))
(MinOrMax_Fopp 0
(MinOrMax_Fopp-1 nil 3320496618
("" (skeep)
(("" (expand "MinOrMax?")
(("" (split)
(("1" (skosimp*) (("1" (rewrite "MinOppMax") nil nil)) nil)
("2" (skosimp*) (("2" (rewrite "MaxOppMin") nil nil)) nil))
nil))
nil))
nil)
((MinOrMax? const-decl "bool" axpy nil)
(MaxOppMin formula-decl nil float nil)
(radix formal-const-decl "above(1)" axpy nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(float type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(Format type-eq-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(MinOppMax formula-decl nil float nil))
shostak))
(MinOrMax1_TCC1 0
(MinOrMax1_TCC1-1 nil 3320496511
("" (skeep)
(("" (rewrite "FcanonicBounded")
(("" (rewrite "FpredCanonic") nil nil)) nil))
nil)
((FcanonicBounded formula-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Format type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(float type-eq-decl nil float nil)
(Fpred const-decl "float" float nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(radix formal-const-decl "above(1)" axpy nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(FpredCanonic formula-decl nil float nil))
nil))
(MinOrMax1_TCC2 0
(MinOrMax1_TCC2-1 nil 3320504768
("" (skeep) (("" (rewrite "FcanonicBounded") nil nil)) nil)
((FcanonicBounded formula-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Format type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(float type-eq-decl nil float nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(radix formal-const-decl "above(1)" axpy nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(MinOrMax1 0
(MinOrMax1-1 nil 3320504301
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(("" (case "z <= FtoR(f)")
(("1" (expand "abs" -4)
(("1" (grind-reals)
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(("1" (skosimp*)
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(("1" (split)
(("1" (replace -1 1 :dir rl)
(("1"
(case-replace
"FtoR(f!1)=FtoR(Fnormalize(b)(f!1))")
(("1" (rewrite "FsuccProp")
(("1"
(trans-ineq 1 "z" :strict 1)
(("1"
(trans-ineq
1
" FtoR[radix](f)-Fulp(b)(Fpred(b)(f))"
:strict
2)
(("1"
(rewrite "FpredDiff" :dir rl)
(("1" (assert) nil nil))
nil)
("2" (assert) nil nil))
nil))
nil)
("2" (rewrite "FpredCanonic") nil nil))
nil)
("2" (assert) nil nil))
nil))
nil)
("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(("2" (expand "abs" -4)
(("2" (grind-reals)
(("2" (expand "MinOrMax?")
(("2" (skosimp*)
(("2" (hide 2)
(("2" (expand "isMin?")
(("2" (skosimp*)
(("2"
(lemma "FpredFsucc" :subst ("f" "f" "b" "b"))
(("2" (split)
(("1" (replace -1 1 :dir rl)
(("1"
(case-replace
"FtoR(f!1)=FtoR(Fnormalize(b)(f!1))")
(("1"
(rewrite "FpredProp")
(("1"
(trans-ineq 1 "z" :strict 2)
(("1"
(trans-ineq
1
"FtoR(f)+Fulp(b)(Fpred(b)(f))"
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1)
(("1" (assert) nil nil)
("2"
(trans-ineq
1
"FtoR(f)+Fulp(b)(f)")
(("1"
(assert)
(("1"
(rewrite "FulpFpred1")
nil
nil))
nil)
("2"
(rewrite "FsuccDiff" :dir rl)
(("2" (assert) nil nil))
nil)
("3"
(skosimp*)
(("3"
(rewrite "FcanonicBounded")
nil
nil))
nil)
("4"
(rewrite "FcanonicBounded")
nil
nil))
nil))
nil))
nil)
("2"
(rewrite "FsuccCanonic")
nil
nil))
nil)
("2" (assert) nil nil))
nil))
nil)
("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((FtoR const-decl "real" float nil)
(float type-eq-decl nil float nil)
(radix formal-const-decl "above(1)" axpy nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
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(bool nonempty-type-eq-decl nil booleans nil)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(isMax? const-decl "bool" float nil)
(FsuccFpred formula-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Format type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(Fpred const-decl "float" float nil)
(FsuccProp formula-decl nil float nil)
(Fulp const-decl "real" float nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(FpredDiff formula-decl nil float nil)
(< const-decl "bool" reals nil)
(FpredCanonic formula-decl nil float nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(Fbounded? const-decl "bool" float nil)
(Fcanonic? const-decl "bool" float nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(Fnormalize def-decl
"{x: (Fcanonic?(b)) | FtoR(x) = FtoR(f):: real AND Fexp(x) <= Fexp(f)}"
float nil)
(MinOrMax? const-decl "bool" axpy nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(FsuccCanonic formula-decl nil float nil)
(both_sides_plus_le1 formula-decl nil real_props nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(FulpFpred1 formula-decl nil float nil)
(FsuccDiff formula-decl nil float nil)
(FcanonicBounded formula-decl nil float nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(FpredProp formula-decl nil float nil)
(Fsucc const-decl "float" float nil)
(FpredFsucc formula-decl nil float nil)
(isMin? const-decl "bool" float nil)
(minus_real_is_real application-judgement "real" reals nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_minus_real_is_real application-judgement "real" reals nil))
shostak))
(MinOrMax2_TCC1 0
(MinOrMax2_TCC1-1 nil 3320505812
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((FcanonicBounded formula-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Format type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(float type-eq-decl nil float nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(radix formal-const-decl "above(1)" axpy nil))
nil))
(MinOrMax2 0
(MinOrMax2-1 nil 3320505496
("" (skeep)
(("" (expand* "MinOrMax?" "isMin?")
(("" (skosimp*)
(("" (split)
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("2" (skosimp*)
(("2" (hide 2)
(("2" (lemma "FpredFsucc" :subst ("f" "f" "b" "b"))
(("2"
(case-replace "FtoR(f!1)=FtoR(Fnormalize(b)(f!1))")
(("1" (split)
(("1" (replace -1 1 :dir rl)
(("1" (rewrite "FpredProp")
(("1" (hide 2 -1 -2)
(("1" (trans-ineq 1 "z" :strict 2)
(("1" (expand "abs" -4)
(("1"
(trans-ineq
1
"FtoR(f)+Fulp(b)(f)"
:strict
1)
(("1" (assert) nil nil)
("2"
(rewrite "FsuccDiff" :dir rl)
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (rewrite "FsuccCanonic") nil nil))
nil))
nil)
("2" (propax) nil nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(FtoR const-decl "real" float nil)
(Fbounded? const-decl "bool" float nil)
(Fcanonic? const-decl "bool" float nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(<= const-decl "bool" reals nil)
(Fnormalize def-decl
"{x: (Fcanonic?(b)) | FtoR(x) = FtoR(f):: real AND Fexp(x) <= Fexp(f)}"
float nil)
(FsuccCanonic formula-decl nil float nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(FsuccDiff formula-decl nil float nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(Fulp const-decl "real" float nil) (< const-decl "bool" reals nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(FpredProp formula-decl nil float nil)
(Fsucc const-decl "float" float nil)
(FpredFsucc formula-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Format type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(float type-eq-decl nil float nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(radix formal-const-decl "above(1)" axpy nil)
(real_minus_real_is_real application-judgement "real" reals nil))
shostak))
(MinOrMax3_TCC1 0
(MinOrMax3_TCC1-1 nil 3320506118
("" (skeep) (("" (rewrite "FcanonicBounded") nil nil)) nil)
((FcanonicBounded formula-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Format type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(float type-eq-decl nil float nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(radix formal-const-decl "above(1)" axpy nil))
nil))
(MinOrMax3 0
(MinOrMax3-1 nil 3320505840
("" (skeep)
(("" (case "z <= FtoR(f)")
(("1" (expand "abs" -4)
(("1" (grind-reals)
(("1" (expand* "MinOrMax?" "isMax?")
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(("1" (split)
(("1" (replace -1 1 :dir rl)
(("1"
(case-replace
"FtoR(f!1)=FtoR(Fnormalize(b)(f!1))")
(("1" (rewrite "FsuccProp")
(("1" (hide 2 -1 -2)
(("1" (trans-ineq 1 "z" :strict 1)
(("1"
(trans-ineq
1
"FtoR[radix](f) -Fulp(b)(f)"
:strict
2)
(("1"
(rewrite "FulpCanonic")
(("1"
(case-replace
"f=(# Fnum:=0, Fexp:=-dExp(b) #)")
(("1"
(hide-all-but 1)
(("1"
(expand* "Fpred" "FtoR")
(("1"
(grind-reals)
(("1"
(lemma "radix_less_vNum")
(("1"
(inst -1 "b")
(("1"
(hide 1)
(("1"
(grind-reals)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(rewrite
"FcanonicUnique"
:subst
("b"
"b"
"p"
"f"
"q"
"(# Fnum := 0, Fexp := -dExp(b) #)"))
(("1"
(rewrite -3 :dir rl)
(("1"
(expand "FtoR" 1)
(("1" (assert) nil nil))
nil))
nil)
("2"
(hide-all-but 1)
(("2"
(expand*
"Fcanonic?"
"Fsubnormal?"
"Fbounded?")
(("2"
(grind-reals)
(("2"
(expand "abs")
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil)
("2" (rewrite "FpredCanonic") nil nil))
nil)
("2" (assert) nil nil))
nil))
nil)
("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (flip-ineq 1)
(("2" (expand* "MinOrMax?" "isMin?")
(("2" (skosimp*)
(("2" (split)
(("1" (assert) nil nil)
("2" (skosimp*)
(("2" (expand "abs" -5)
(("2" (grind-reals)
(("2" (hide 2)
(("2"
(lemma "FpredFsucc" :subst ("f" "f" "b" "b"))
(("2" (split)
(("1" (replace -1 1 :dir rl)
(("1"
(case-replace
"FtoR(f!1)=FtoR(Fnormalize(b)(f!1))")
(("1"
(rewrite "FpredProp")
(("1"
(hide -1 -2 2)
(("1"
(trans-ineq 1 "z" :strict 2)
(("1"
(trans-ineq
1
"FtoR(f)+Fulp(b)(f)"
:strict
1)
(("1" (assert) nil nil)
("2"
(rewrite "FulpCanonic")
(("2"
(case-replace
"f=(# Fnum:=0, Fexp:=-dExp(b) #)")
(("1"
(hide-all-but 1)
(("1"
(expand* "Fsucc" "FtoR")
(("1"
(grind-reals)
(("1"
(hide 1)
(("1"
(lemma
"radix_less_vNum")
(("1"
(inst?)
(("1"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(rewrite
"FcanonicUnique"
:subst
("b"
"b"
"p"
"f"
"q"
"(# Fnum := 0, Fexp := -dExp(b) #)"))
(("1"
(rewrite -4 :dir rl)
(("1"
(expand "FtoR" 1)
(("1"
(assert)
nil
nil))
nil))
nil)
("2"
(hide-all-but 1)
(("2"
(expand*
"Fcanonic?"
"Fsubnormal?"
"Fbounded?")
(("2"
(expand "abs")
(("2"
(grind-reals)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(rewrite "FsuccCanonic")
nil
nil))
nil)
("2" (assert) nil nil))
nil))
nil)
("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((FtoR const-decl "real" float nil)
(float type-eq-decl nil float nil)
(radix formal-const-decl "above(1)" axpy nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(int nonempty-type-eq-decl nil integers nil)
(<= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(FsuccFpred formula-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Format type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(Fpred const-decl "float" float nil)
(FsuccProp formula-decl nil float nil)
(< const-decl "bool" reals nil)
(FulpCanonic formula-decl nil float nil)
(posrat_exp application-judgement "posrat" exponentiation nil)
(nnrat_exp application-judgement "nnrat" exponentiation nil)
(FcanonicUnique formula-decl nil float nil)
(nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(zero_times1 formula-decl nil real_props nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(Fsubnormal? const-decl "bool" float nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(times_div2 formula-decl nil real_props nil)
(nzrat_times_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(minus_nzint_is_nzint application-judgement "nzint" integers nil)
(nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(div_mult_pos_le1 formula-decl nil real_props nil)
(posrat_times_posrat_is_posrat application-judgement "posrat"
rationals nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(radix_less_vNum formula-decl nil float nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(minus_int_is_int application-judgement "int" integers nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(Fulp const-decl "real" float nil)
(FpredCanonic formula-decl nil float nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(Fbounded? const-decl "bool" float nil)
(Fcanonic? const-decl "bool" float nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(Fnormalize def-decl
"{x: (Fcanonic?(b)) | FtoR(x) = FtoR(f):: real AND Fexp(x) <= Fexp(f)}"
float nil)
(MinOrMax? const-decl "bool" axpy nil)
(isMax? const-decl "bool" float nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(isMin? const-decl "bool" float nil)
(FsuccCanonic formula-decl nil float nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(div_mult_pos_le2 formula-decl nil real_props nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(FpredProp formula-decl nil float nil)
(Fsucc const-decl "float" float nil)
(FpredFsucc formula-decl nil float nil)
(minus_real_is_real application-judgement "real" reals nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_minus_real_is_real application-judgement "real" reals nil))
shostak))
(RoundLe_TCC1 0
(RoundLe_TCC1-1 nil 3320498426
("" (skeep) (("" (rewrite "FcanonicBounded") nil nil)) nil)
((FcanonicBounded formula-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Format type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(float type-eq-decl nil float nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(radix formal-const-decl "above(1)" axpy nil))
nil))
(RoundLe_TCC2 0
(RoundLe_TCC2-1 nil 3320498426
("" (skeep)
(("" (expand* "FtoR" "abs") (("" (grind-reals) nil nil)) nil)) nil)
((abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(FtoR const-decl "real" float nil)
(nonzero_times1 formula-decl nil real_props nil)
(nonzero_times2 formula-decl nil real_props nil)
(rat_times_rat_is_rat application-judgement "rat" rationals nil)
(nnrat_exp application-judgement "nnrat" exponentiation nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(minus_int_is_int application-judgement "int" integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
nil))
(RoundLe_TCC3 0
(RoundLe_TCC3-1 nil 3320498426
("" (skosimp*) (("" (field -3) (("" (grind) nil nil)) nil)) nil)
((rat_minus_rat_is_rat application-judgement "rat" rationals nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers nil)
(/= const-decl "boolean" notequal nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(int nonempty-type-eq-decl nil integers nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(radix formal-const-decl "above(1)" axpy nil)
(float type-eq-decl nil float nil)
(nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(both_sides_times1_imp formula-decl nil extra_real_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(bijective? const-decl "bool" functions nil)
(id const-decl "(bijective?[T, T])" identity nil)
(TRUE const-decl "bool" booleans nil)
(rat_times_rat_is_rat application-judgement "rat" rationals nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(minus_int_is_int application-judgement "int" integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(RoundLe 0
(RoundLe-1 nil 3320498427
("" (assert)
(("" (skeep)
(("" (assert)
(("" (case "0 < abs(Fnum(f))")
(("1" (case "0 < 1 - 1 / (2 * abs(Fnum(f)))")
(("1" (mult-by 2 "(1 - 1 / (2 * abs(Fnum(f))))")
(("1"
(case-replace
" abs(FtoR[radix](f)) * (1 - 1 / (2 * abs(Fnum(f)))) =
abs(FtoR(f))-Fulp(b)(f)/2")
(("1" (move-terms 2 l 2)
(("1" (move-terms 2 r 1)
(("1" (trans-ineq 2 "abs(FtoR(f)-z)")
(("1" (expand "abs" 1)
(("1" (grind-reals) nil nil)) nil)
("2" (rewrite "ClosestUlp")
(("2" (rewrite "FcanonicBounded") nil nil))
nil))
nil))
nil))
nil)
("2" (hide 2 3)
(("2" (field 1)
(("2" (rewrite "FulpCanonic")
(("2" (expand "FtoR" 1)
(("2" (rewrite "abs_mult")
(("2" (expand "abs" 1 2)
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (case "1 <= abs(Fnum(f))")
(("1" (field 1) nil nil)
("2" (hide-all-but (-1 1)) (("2" (grind) nil nil)) nil))
nil))
nil)
("2" (hide-all-but (1 2))
(("2" (expand* "abs" "FtoR") (("2" (grind-reals) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((float type-eq-decl nil float nil)
(radix formal-const-decl "above(1)" axpy nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(int nonempty-type-eq-decl nil integers nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
nil)
(minus_int_is_int application-judgement "int" integers nil)
(both_sides_times_pos_le1 formula-decl nil real_props nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(FtoR const-decl "real" float nil)
(f skolem-const-decl "float[radix]" axpy nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(div_cancel2 formula-decl nil real_props nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(FulpCanonic formula-decl nil float nil)
(posrat_exp application-judgement "posrat" exponentiation nil)
(nnrat_exp application-judgement "nnrat" exponentiation nil)
(^ const-decl "real" exponentiation nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(abs_mult formula-decl nil real_props nil)
(rat_abs_is_nonneg application-judgement "{r: nonneg_rat | r >= q}"
real_defs nil)
(nzrat_abs_is_pos application-judgement "{r: posrat | r >= q}"
real_defs nil)
(nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(minus_nzint_is_nzint application-judgement "nzint" integers nil)
(minus_even_is_even application-judgement "even_int" integers nil)
(rat_times_rat_is_rat application-judgement "rat" rationals nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(TRUE const-decl "bool" booleans nil)
(id const-decl "(bijective?[T, T])" identity nil)
(bijective? const-decl "bool" functions nil)
(both_sides_times1 formula-decl nil real_props nil)
(rat nonempty-type-eq-decl nil rationals nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(<= const-decl "bool" reals nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(times_div1 formula-decl nil real_props nil)
(both_sides_times2 formula-decl nil real_props nil)
(cross_mult formula-decl nil real_props nil)
(minus_real_is_real application-judgement "real" reals nil)
(FcanonicBounded formula-decl nil float nil)
(ClosestUlp formula-decl nil float nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Format type-eq-decl nil float nil)
(Fbounded? const-decl "bool" float nil)
(Fulp const-decl "real" float nil)
(b formal-const-decl "Format" axpy nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nonzero_times2 formula-decl nil real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(rat_minus_rat_is_rat application-judgement "rat" rationals nil))
shostak))
(RoundGe_TCC1 0
(RoundGe_TCC1-1 nil 3320499635
("" (skeep) (("" (field -3) nil nil)) nil)
((int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(rat_plus_rat_is_rat application-judgement "rat" rationals nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers nil)
(/= const-decl "boolean" notequal nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(int nonempty-type-eq-decl nil integers nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(radix formal-const-decl "above(1)" axpy nil)
(float type-eq-decl nil float nil))
nil))
(RoundGe 0
(RoundGe-1 nil 3320499635
("" (skeep)
(("" (case "0 < abs(Fnum(f))")
(("1" (case "0 < 1 + 1 / (2 * abs(Fnum(f)))")
(("1" (mult-by 2 "(1 + 1 / (2 * abs(Fnum(f))))")
(("1" (assert)
(("1"
(case-replace
" abs(FtoR[radix](f)) * (1 / (2 * abs(Fnum(f)))) =
Fulp(b)(f)/2")
(("1" (move-terms 2 r 1)
(("1" (trans-ineq 2 "abs(FtoR(f)-z)")
(("1" (hide-all-but 1)
(("1" (expand "abs") (("1" (grind-reals) nil nil))
nil))
nil)
("2" (rewrite "ClosestUlp")
(("2" (rewrite "FcanonicBounded") nil nil)) nil))
nil))
nil)
("2" (field 1)
(("2" (rewrite "FulpCanonic")
(("2" (hide-all-but 1)
(("2" (expand* "abs" "FtoR")
(("2" (grind-reals) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (field 1) nil nil))
nil)
("2" (hide-all-but (1 2))
(("2" (expand* "abs" "FtoR") (("2" (grind-reals) nil nil))
nil))
nil))
nil))
nil)
((float type-eq-decl nil float nil)
(radix formal-const-decl "above(1)" axpy nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(int nonempty-type-eq-decl nil integers nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(both_sides_times_pos_le1 formula-decl nil real_props nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(FtoR const-decl "real" float nil)
(f skolem-const-decl "float[radix]" axpy nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(div_cancel2 formula-decl nil real_props nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(b formal-const-decl "Format" axpy nil)
(Fulp const-decl "real" float nil)
(Fbounded? const-decl "bool" float nil)
(Format type-eq-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(minus_real_is_real application-judgement "real" reals nil)
(FcanonicBounded formula-decl nil float nil)
(ClosestUlp formula-decl nil float nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(<= const-decl "bool" reals nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(FulpCanonic formula-decl nil float nil)
(posrat_exp application-judgement "posrat" exponentiation nil)
(nnrat_exp application-judgement "nnrat" exponentiation nil)
(neg_times_lt formula-decl nil real_props nil)
(minus_rat_is_rat application-judgement "rat" rationals nil)
(rat_times_rat_is_rat application-judgement "rat" rationals nil)
(minus_int_is_int application-judgement "int" integers nil)
(TRUE const-decl "bool" booleans nil)
(id const-decl "(bijective?[T, T])" identity nil)
(bijective? const-decl "bool" functions nil)
(both_sides_times1 formula-decl nil real_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(real_times_real_is_real application-judgement "real" reals nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(rat_plus_rat_is_rat application-judgement "rat" rationals nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nonzero_times2 formula-decl nil real_props nil))
shostak))
(ExactSum_Near_TCC1 0
(ExactSum_Near_TCC1-1 nil 3320510642 ("" (subtype-tcc) nil nil)
((real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(nat_exp application-judgement "nat" exponentiation nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(zero_hat formula-decl nil exponent_props "reals/")
(radix formal-const-decl "above(1)" axpy nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(vNum const-decl "posnat" float nil)
(Fbounded? const-decl "bool" float nil)
(FtoR const-decl "real" float nil)
(Closest? const-decl "bool" float nil)
(/= const-decl "boolean" notequal nil)
(nnrat_exp application-judgement "nnrat" exponentiation nil)
(posrat_exp application-judgement "posrat" exponentiation nil)
(rat_times_rat_is_rat application-judgement "rat" rationals nil)
(rat_minus_rat_is_rat application-judgement "rat" rationals nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(ExactSum_Near 0
(ExactSum_Near-1 nil 3320510940
("" (skeep)
(("" (lemma "errorBoundedPlus")
(("" (inst -1 "b" "f" "p" "q")
(("" (split)
(("1" (skosimp*)
(("1" (case "FtoR(e!1)=0")
(("1" (assert) nil nil)
("2" (hide 2)
(("2" (typepred "e!1")
(("2" (expand "Fbounded?" -1)
(("2" (flatten)
(("2" (expand "FtoR" 1)
(("2" (case "abs(Fnum(e!1)) < 1")
(("1" (grind-reals) nil nil)
("2" (hide 2)
(("2" (mult-by 1 "radix ^ (-dExp(b))")
(("2"
(trans-ineq
1
"abs(FtoR[radix](f) - (FtoR[radix](p) + FtoR[radix](q)))"
:strict
2)
(("1"
(trans-ineq 1 "abs(FtoR(e!1))")
(("1"
(expand "FtoR" 1)
(("1"
(rewrite "abs_mult")
(("1"
(expand "abs" 1 3)
(("1"
(grind-reals)
(("1"
(rewrite "Exp_increq_1")
nil
nil))
nil))
nil))
nil))
nil)
("2"
(rewrite -3)
(("2"
(expand "abs" 1)
(("2" (grind-reals) nil nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (propax) nil nil) ("3" (propax) nil nil)
("4" (propax) nil nil) ("5" (propax) nil nil))
nil))
nil))
nil))
nil)
((radix formal-const-decl "above(1)" axpy nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(errorBoundedPlus formula-decl nil float nil)
(Fbounded? const-decl "bool" float nil)
(FtoR const-decl "real" float nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(int_min application-judgement "{k: int | k <= i AND k <= j}"
real_defs nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nnrat_exp application-judgement "nnrat" exponentiation nil)
(posrat_exp application-judgement "posrat" exponentiation nil)
(minus_int_is_int application-judgement "int" integers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(rat_times_rat_is_rat application-judgement "rat" rationals nil)
(nonzero_times2 formula-decl nil real_props nil)
(both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(/= const-decl "boolean" notequal nil)
(^ const-decl "real" exponentiation nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(posrat_times_posrat_is_posrat application-judgement "posrat"
rationals nil)
(nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(abs_mult formula-decl nil real_props nil)
(nzrat_abs_is_pos application-judgement "{r: posrat | r >= q}"
real_defs nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(both_sides_times_pos_le2 formula-decl nil real_props nil)
(Exp_increq_1 formula-decl nil float nil)
(min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
(<= const-decl "bool" reals nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(float type-eq-decl nil float nil)
(b formal-const-decl "Format" axpy nil)
(Format type-eq-decl nil float nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.80 Sekunden
(vorverarbeitet)
¤
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