|
(sigma_bijection_nat
(series_bijection_TCC1 0
(series_bijection_TCC1-1 nil 3323008883
("" (skosimp) (("" (assert) nil nil)) nil)
((posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
shostak))
(series_bijection 0
(series_bijection-1 nil 3323009119
("" (skosimp*)
(("" (expand "series")
((""
(lemma "sigma_bijection[below[n!1+1]]"
("low" "0" "high" "n!1"))
(("1" (expand "o")
(("1" (expand "extend")
(("1"
(inst - "LAMBDA (x: nat):
IF x < 1 + n!1 THEN a!1(x) ELSE a!1(0) ENDIF")
(("1" (expand "restrict")
(("1" (inst - "phi!1")
(("1" (expand "restrict")
(("1"
(case "forall (m:nat): m <= n!1 => sigma[subrange_T[below[n!1 + 1]](0, n!1)]
(0, m,
LAMBDA (s_1: subrange_T[below[n!1 + 1]](0, n!1)): a!1(s_1)) = sigma(0, m, a!1)")
(("1" (inst - "n!1")
(("1" (assert)
(("1" (replace -1)
(("1" (replace -2 1)
(("1"
(hide -1 -2)
(("1"
(case
"forall (m:nat): m <= n!1 => sigma[subrange_T[below[n!1 + 1]](0, n!1)]
(0, m,
LAMBDA (x_1: subrange_T[below[n!1 + 1]](0, n!1)):
IF phi!1(x_1) < 1 + n!1 THEN a!1(phi!1(x_1))
ELSE a!1(0)
ENDIF)
=
sigma(0, m,
LAMBDA (x: nat):
IF x < 1 + n!1 THEN a!1(phi!1(x)) ELSE a!1(0) ENDIF)")
(("1"
(inst - "n!1")
(("1" (assert) nil nil))
nil)
("2"
(hide 2)
(("2"
(induct "m")
(("1"
(assert)
(("1"
(expand "sigma")
(("1"
(assert)
(("1"
(typepred "phi!1(0)")
(("1"
(assert)
(("1"
(expand "sigma")
(("1"
(propax)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(skosimp*)
(("2"
(assert)
(("2"
(expand "sigma" 1)
(("2"
(typepred
"phi!1(1 + j!1)")
(("2" (assert) nil nil))
nil))
nil))
nil))
nil)
("3"
(hide 2)
(("3" (grind) nil nil))
nil)
("4"
(hide 2)
(("4" (grind) nil nil))
nil)
("5"
(hide 2)
(("5" (grind) nil nil))
nil))
nil))
nil)
("3"
(hide-all-but 1)
(("3"
(skosimp*)
(("3" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide -1 2)
(("2" (induct "m")
(("1" (assert)
(("1" (expand "sigma")
(("1"
(expand "sigma")
(("1" (propax) nil nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (assert)
(("2"
(expand "sigma" 1)
(("2" (propax) nil nil))
nil))
nil))
nil)
("3" (hide 2)
(("3" (skosimp*) (("3" (assert) nil nil))
nil))
nil)
("4" (hide 2) (("4" (grind) nil nil)) nil)
("5" (hide 2) (("5" (grind) nil nil)) nil))
nil))
nil)
("3" (hide -1 2) (("3" (grind) nil nil)) nil)
("4" (hide -1 2) (("4" (grind) nil nil)) nil)
("5" (hide -1 2) (("5" (grind) nil nil)) nil))
nil))
nil)
("2" (hide 2)
(("2" (typepred "phi!1")
(("2" (expand "bijective?")
(("2" (flatten)
(("2" (split)
(("1" (hide -2)
(("1"
(expand "injective?")
(("1"
(skosimp)
(("1" (assert) nil nil))
nil))
nil))
nil)
("2" (hide -1)
(("2"
(expand "restrict")
(("2"
(expand "surjective?")
(("2"
(typepred "phi!1")
(("2"
(expand "bijective?")
(("2"
(flatten)
(("2"
(hide-all-but (-1 1))
(("2"
(expand "injective?")
(("2"
(skosimp*)
(("2"
(inst - "x1!1" "x2!1")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (expand "restrict")
(("3"
(expand "surjective?")
(("3"
(skosimp)
(("3"
(inst - "y!1")
(("3"
(skosimp)
(("3" (inst + "x!1") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide 2) (("2" (grind) nil nil)) nil))
nil))
nil))
nil)
((series const-decl "sequence[real]" series "series/")
(O const-decl "T3" function_props nil)
(sequence type-eq-decl nil sequences nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(restrict const-decl "R" restrict nil)
(restrict_of_inj_is_inj application-judgement "(injective?[S, R])"
restrict nil)
(n!1 skolem-const-decl "nat" sigma_bijection_nat nil)
(subrange_T type-eq-decl nil sigma_bijection nil)
(bijective? const-decl "bool" functions nil)
(phi!1 skolem-const-decl
"(bijective?[below[1 + n!1], below[1 + n!1]])" sigma_bijection_nat
nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(T_low type-eq-decl nil sigma "reals/")
(T_high type-eq-decl nil sigma "reals/")
(sigma def-decl "real" sigma "reals/")
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(pred type-eq-decl nil defined_types nil)
(nat_induction formula-decl nil naturalnumbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(sigma_0_neg formula-decl nil sigma_nat "reals/")
(real_plus_real_is_real application-judgement "real" reals nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(surjective? const-decl "bool" functions nil)
(injective? const-decl "bool" functions nil)
(extend const-decl "R" extend nil)
(integer nonempty-type-from-decl nil integers nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(<= const-decl "bool" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(sigma_bijection formula-decl nil sigma_bijection 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)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(< const-decl "bool" reals nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(below type-eq-decl nil nat_types nil))
shostak)))
¤ Dauer der Verarbeitung: 0.25 Sekunden
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