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((boolean nonempty-type-decl nil booleans nil)
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nil)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
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(>= const-decl "bool" reals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil))
nil))
(log_nat_TCC3 0
(log_nat_TCC3-1 nil 3321008812
("" (skeep) (("" (rewrite "expt_x0") (("" (assert) nil nil)) nil))
nil)
((expt_x0 formula-decl nil exponentiation nil)
(number nonempty-type-decl nil numbers nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
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(real_pred const-decl "[number_field -> boolean]" reals 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)
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(bool nonempty-type-eq-decl nil booleans nil)
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(above nonempty-type-eq-decl nil integers nil)
(posint_exp application-judgement "posint" exponentiation nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
nil))
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(("" (skosimp*)
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nil))
nil))
nil))
nil))
nil))
nil))
nil)
((real_times_real_is_real application-judgement "real" reals nil)
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real_props nil)
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(mult_divides1 application-judgement "(divides(n))" divides nil)
(posint_times_posint_is_posint application-judgement "posint"
integers nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
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(boolean nonempty-type-decl nil booleans nil)
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nil)
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(< const-decl "bool" reals nil)
(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)
(> const-decl "bool" reals nil)
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(= const-decl "[T, T -> boolean]" equalities nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
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(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(^ const-decl "real" exponentiation nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(posint_exp application-judgement "posint" exponentiation nil))
nil))
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(log_nat_TCC5-1 nil 3321008812
("" (skosimp :preds? t)
(("" (typepred "floor(x!1/p!1)")
(("" (case "x!1/p!1 < floor(x!1)")
(("1" (assert) (("1" (cross-mult 2) nil nil)) nil)
("2" (typepred "floor(x!1)")
(("2" (cross-mult 1)
(("2" (case "1 + floor(x!1) < floor(x!1) * p!1")
(("1" (assert) nil nil)
("2" (move-terms 1 l 2)
(("2" (factor 1)
(("2" (div-by 1 "(p!1 - 1)")
(("2" (case "1 / (p!1 - 1) < 1")
(("1" (case "1 <= floor(x!1)")
(("1" (assert) nil nil) ("2" (assert) nil nil))
nil)
("2" (cross-mult 1) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
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(< const-decl "bool" reals nil)
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(integer nonempty-type-from-decl nil integers nil)
(<= const-decl "bool" reals nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(times_div_cancel2 formula-decl nil extra_real_props nil)
(both_sides_div_pos_lt1 formula-decl nil real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(div_mult_pos_lt1 formula-decl nil real_props nil)
(real_gt_is_strict_total_order name-judgement
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(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_plus_int_is_int application-judgement "int" integers 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)
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(nonneg_real nonempty-type-eq-decl nil real_types nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(posint_times_posint_is_posint application-judgement "posint"
integers nil)
(div_mult_pos_ge1 formula-decl nil real_props 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)
(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)
(>= const-decl "bool" reals nil) (> const-decl "bool" 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)
(above nonempty-type-eq-decl nil integers nil))
nil))
(log_nat_TCC6 0
(log_nat_TCC6-2 nil 3399807171
("" (skosimp :preds? t)
(("" (lemma "floor_lt_floor_int")
(("" (inst?) (("" (assert) nil nil)) nil)) nil))
nil)
((floor_lt_floor_int formula-decl nil prelude_aux nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
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nil)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(above nonempty-type-eq-decl nil integers nil))
nil)
(log_nat_TCC6-1 nil 3321008812
("" (skosimp :preds? t)
(("" (split)
(("1" (beta)
(("1" (typepred "v!1(x!1 / p!1, p!1)`2")
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("2" (cross-mult) (("2" (assert) nil nil)) nil))
nil))
nil)
("2" (beta)
(("2" (typepred "v!1(x!1 / p!1, p!1)`2")
(("1" (cross-mult -3)
(("1" (rewrite "expt_plus")
(("1" (rewrite "expt_x1") (("1" (assert) nil nil)) nil))
nil))
nil)
("2" (cross-mult) (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil)
nil nil))
(log_nat_bounds_TCC1 0
(log_nat_bounds_TCC1-1 nil 3321012239 ("" (subtype-tcc) nil nil)
((posint_exp application-judgement "posint" exponentiation nil))
nil))
(log_nat_bounds_TCC2 0
(log_nat_bounds_TCC2-1 nil 3321012239 ("" (subtype-tcc) nil nil)
((^ const-decl "real" exponentiation nil)
(posint_exp application-judgement "posint" exponentiation nil))
nil))
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(("" (beta)
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nzreal nonempty-type-eq-decl nil reals nil)
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integers nil)
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real_props nil)
(both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
nil)
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real_props nil)
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rationals nil)
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(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(posint nonempty-type-eq-decl nil integers nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
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(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers nil)
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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)
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(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(/= const-decl "boolean" notequal nil)
(^ const-decl "real" exponentiation nil)
(log_nat def-decl "[n: nat, {y | y < p AND x = p ^ n * y}]" log_nat
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shostak))
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(("" (hide 2)
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(posint_times_posint_is_posint application-judgement "posint"
integers nil)
(both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
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nil)
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real_props nil)
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"(strict_total_order?[real])" real_props nil)
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real_props nil)
(real_times_real_is_real application-judgement "real" reals nil)
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(log_nat def-decl "[n: nat, {y | y < p AND x = p ^ n * y}]" log_nat
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(^ const-decl "real" exponentiation nil)
(/= const-decl "boolean" notequal nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(< const-decl "bool" reals nil)
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(nat nonempty-type-eq-decl nil naturalnumbers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(>= const-decl "bool" reals nil)
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(> 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)
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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
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(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
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shostak))
(log_nat_itaux_TCC1 0
(log_nat_itaux_TCC1-1 nil 3544887262 ("" (subtype-tcc) nil nil) nil
nil))
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(NOT const-decl "[bool -> bool]" booleans nil)
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(>= const-decl "bool" reals nil) (> const-decl "bool" reals nil)
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(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(/= const-decl "boolean" notequal nil)
(^ const-decl "real" exponentiation nil)
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"(strict_total_order?[real])" real_props nil)
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(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posint_exp application-judgement "posint" exponentiation nil))
nil))
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(log_nat_itaux_TCC3-1 nil 3544887262
("" (skeep :preds? t) (("" (assert) nil nil)) nil)
((real_lt_is_strict_total_order name-judgement
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"(strict_total_order?[real])" real_props nil)
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real_props nil)
(posint_exp application-judgement "posint" exponentiation nil))
nil))
(log_nat_itaux_TCC4 0
(log_nat_itaux_TCC4-1 nil 3544887262
("" (skeep :preds? t)
(("" (grind-reals)
(("" (rewrite "expt_plus")
(("" (rewrite "expt_x1") (("" (assert) nil nil)) nil)) nil))
nil))
nil)
((real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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"(strict_total_order?[real])" real_props nil)
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"(strict_total_order?[real])" real_props nil)
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real_props nil)
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(> const-decl "bool" reals nil)
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(/= const-decl "boolean" notequal nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
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(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)
(expt_plus formula-decl nil exponentiation nil)
(posint_exp application-judgement "posint" exponentiation nil))
nil))
(log_nat_itaux_TCC5 0
(log_nat_itaux_TCC5-1 nil 3544887262
("" (skeep :preds? t)
(("" (lemma "log_nat_TCC6")
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nil)
((log_nat_TCC6 termination-tcc nil log_nat nil)
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(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)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(expt def-decl "real" exponentiation nil)
(^ const-decl "real" exponentiation nil)
(posnat_expt application-judgement "posnat" exponentiation nil))
nil))
(least_pow_2_ge_TCC4 0
(least_pow_2_ge_TCC4-1 nil 3609934857
("" (skeep) (("" (cross-mult 3) (("" (assert) nil nil)) nil)) nil)
((posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types 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)
(div_mult_pos_ge1 formula-decl nil real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil))
nil))
(least_pow_2_ge_TCC5 0
(least_pow_2_ge_TCC5-1 nil 3609934857
("" (skeep)
(("" (skeep)
(("" (rewrite "log_nat_id")
(("" (assert)
(("" (splash)
(("1" (skeep)
(("1" (lemma "log_nat_bounds")
(("1" (inst?)
(("1" (assert)
(("1" (replace -4 :dir rl)
(("1" (flatten)
(("1" (case "NOT xp > 2^(-n-1)")
(("1" (lemma "expt_inverse")
(("1" (inst - "n+1" "2")
(("1"
(replaces -1)
(("1"
(cross-mult -2)
(("1" (cross-mult 1) nil nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2" (case "2^(-n-1)>2^i")
(("1" (assert) nil nil)
("2"
(assert)
(("2"
(lemma "both_sides_expt_gt1_lt")
(("2"
(inst - "2" "i" "-n-1")
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2" (lemma "log_nat_bounds")
(("2" (inst?)
(("2" (assert)
(("2" (replace -2 :dir rl)
(("2" (assert)
(("2" (flatten)
(("2" (lemma "expt_inverse")
(("2" (inst - "n" "2")
(("2"
(replaces -1)
(("2"
(cross-mult -1)
(("2" (cross-mult 1) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((minus_int_is_int application-judgement "int" integers nil)
(posrat_exp application-judgement "posrat" exponentiation nil)
(nnrat_exp application-judgement "nnrat" exponentiation nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(div_mult_pos_le2 formula-decl nil real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(div_mult_pos_lt1 formula-decl nil real_props nil)
(div_mult_pos_gt2 formula-decl nil extra_real_props nil)
(expt_inverse formula-decl nil exponentiation nil)
(both_sides_expt_gt1_lt formula-decl nil exponentiation 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)
(log_nat_bounds formula-decl nil log_nat nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(< const-decl "bool" reals nil) (<= const-decl "bool" reals nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(^ const-decl "real" exponentiation nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(>= const-decl "bool" reals 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)
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.43 Sekunden
(vorverarbeitet)
¤
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