Impressum float.prf

Sprache: Lisp

(float (vNum_TCC1 0
 (vNum_TCC1-1 nil 3321636413 ("" (subtype-tcc) nil nil)
 ((/= const-decl "boolean" notequal nil)) nil))
 (radix_div_vNum 0
 (radix_div_vNum-1 nil 3319366647
 ("" (judgement-tcc)
 ((""
 (case-replace
 "expt(radix, Prec(b!1)) / radix=expt(radix, Prec(b!1)-1)")
 (("1" (grind-reals) nil nil)
 ("2" (hide 2)
 (("2" (rewrite "expt_minus_aux")
 (("2" (rewrite "expt_x1_aux") nil nil)) nil))
 nil))
 nil))
 nil)
 ((int_minus_int_is_int application-judgement "int" integers
 nil)
 (number nonempty-type-decl nil numbers nil)
 (boolean nonempty-type-decl nil booleans nil)
 (= const-decl "[T, T -> boolean]" equalities nil)
 (number_field_pred const-decl "[number -> boolean]"
 number_fields nil)
 (numfield nonempty-type-eq-decl nil number_fields nil)
 (number_field nonempty-type-from-decl nil 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)
 (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)
 (expt def-decl "real" exponentiation nil)
 (> const-decl "bool" reals nil)
 (above nonempty-type-eq-decl nil integers nil)
 (radix formal-const-decl "above(1)" float nil)
 (Format type-eq-decl nil float nil)
 (- const-decl "[numfield, numfield -> numfield]"
 number_fields nil)
 (nzreal nonempty-type-eq-decl nil reals nil)
 (expt_minus_aux formula-decl nil exponentiation nil)
 (expt_x1_aux formula-decl nil exponentiation nil)
 (posnat_expt application-judgement "posnat" exponentiation
 nil)
 (^ const-decl "real" exponentiation nil)
 (real_ge_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (posrat_div_posrat_is_posrat application-judgement "posrat"
 rationals nil)
 (posint_exp application-judgement "posint" exponentiation
 nil)
 (vNum const-decl "posnat" float nil))
 nil))
 (radix_less_vNum 0
 (radix_less_vNum-1 nil 3319366647
 ("" (judgement-tcc)
 (("" (lemma "both_sides_expt_gt1_ge_aux")
 (("" (inst -1 "radix" "Prec(b!1)-1" "0")
 (("" (grind-reals)
 (("" (rewrite "expt_x1_aux" -1) (("" (assert) nil nil))
 nil))
 nil))
 nil))
 nil))
 nil)
 ((both_sides_expt_gt1_ge_aux formula-decl nil exponentiation
 nil)
 (int_plus_int_is_int application-judgement "int" integers
 nil)
 (nnint_plus_posint_is_posint application-judgement "posint"
 integers nil)
 (even_plus_odd_is_odd application-judgement "odd_int"
 integers nil)
 (expt_x1_aux formula-decl nil exponentiation nil)
 (Format type-eq-decl nil float nil)
 (- const-decl "[numfield, numfield -> numfield]"
 number_fields nil)
 (numfield nonempty-type-eq-decl nil number_fields nil)
 (nat nonempty-type-eq-decl nil naturalnumbers nil)
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 (above nonempty-type-eq-decl nil integers 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)
 (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)
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 (number_field_pred const-decl "[number -> boolean]"
 number_fields nil)
 (boolean nonempty-type-decl nil booleans nil)
 (number nonempty-type-decl nil numbers nil)
 (int_minus_int_is_int application-judgement "int" integers
 nil)
 (real_gt_is_strict_total_order name-judgement
 "(strict_total_order?[real])" real_props nil)
 (posnat_expt application-judgement "posnat" exponentiation
 nil)
 (^ const-decl "real" exponentiation nil)
 (real_ge_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (posint_exp application-judgement "posint" exponentiation
 nil)
 (real_le_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (vNum const-decl "posnat" float nil))
 nil))
 (FtoR_TCC1 0
 (FtoR_TCC1-1 nil 3318615387 ("" (subtype-tcc) nil nil)
 ((/= const-decl "boolean" notequal nil)) nil))
 (float_int_def 0
 (float_int_def-1 nil 3544780855 ("" (grind) nil nil)
 ((float_int const-decl "float" float nil)
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 (^ const-decl "real" exponentiation nil)
 (FtoR const-decl "real" float nil))
 shostak))
 (Fplus_TCC1 0
 (Fplus_TCC1-1 nil 3319889173 ("" (subtype-tcc) nil nil)
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 (int_min application-judgement "{k: int | k <= i AND k <= j}"
 real_defs nil))
 nil))
 (Fplus_TCC2 0
 (Fplus_TCC2-1 nil 3319889173 ("" (subtype-tcc) nil nil)
 ((/= const-decl "boolean" notequal nil)
 (int_min application-judgement "{k: int | k <= i AND k <= j}"
 real_defs nil))
 nil))
 (Fplus_TCC3 0
 (Fplus_TCC3-1 nil 3319889173 ("" (subtype-tcc) nil nil)
 ((^ const-decl "real" exponentiation nil)
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 nil)
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 nil)
 (real_gt_is_strict_total_order name-judgement
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 real_props nil)
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 real_defs nil)
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 (posrat_exp application-judgement "posrat" exponentiation
 nil)
 (rat_times_rat_is_rat application-judgement "rat" rationals
 nil)
 (rat_plus_rat_is_rat application-judgement "rat" rationals
 nil))
 nil))
 (Fminus_TCC1 0
 (Fminus_TCC1-1 nil 3319889173 ("" (subtype-tcc) nil nil)
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 nil)
 (posnat_expt application-judgement "posnat" exponentiation
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 (real_gt_is_strict_total_order name-judgement
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 real_props nil)
 (int_min application-judgement "{k: int | k <= i AND k <= j}"
 real_defs 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))
 nil))
 (sum_float_commutes 0
 (sum_float_commutes-1 nil 3545039871 ("" (grind) nil 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)
 (posnat_expt application-judgement "posnat" exponentiation
 nil)
 (int_minus_int_is_int application-judgement "int" integers
 nil)
 (real_gt_is_strict_total_order name-judgement
 "(strict_total_order?[real])" real_props nil)
 (expt def-decl "real" exponentiation nil)
 (min const-decl "{p: real | p <= m AND p <= n}" real_defs
 nil)
 (^ const-decl "real" exponentiation nil)
 (Fplus const-decl "float" float nil)
 (+ const-decl "float" float nil))
 shostak))
 (mult_float_commutes 0
 (mult_float_commutes-1 nil 3545039902 ("" (grind) nil nil)
 ((Fmult const-decl "float" float nil)
 (* const-decl "float" float nil))
 shostak))
 (FexptCorrect_TCC1 0
 (FexptCorrect_TCC1-1 nil 3545396627 ("" (subtype-tcc) nil nil)
 ((nnrat_exp application-judgement "nnrat" exponentiation nil)
 (posrat_exp application-judgement "posrat" exponentiation
 nil)
 (FtoR const-decl "real" float nil))
 nil))
 (FexptCorrect 0
 (FexptCorrect-1 nil 3545396632
 ("" (skeep)
 (("" (expand "^")
 (("" (expand "Fexpt")
 (("" (expand "FtoR")
 (("" (lemma "mult_expt")
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 nil))
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 nil))
 nil)
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 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)
 (= const-decl "[T, T -> boolean]" equalities nil)
 (boolean nonempty-type-decl nil booleans nil)
 (number nonempty-type-decl nil numbers nil)
 (rat_times_rat_is_rat application-judgement "rat" rationals
 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)
 (posnat_expt application-judgement "posnat" exponentiation
 nil)
 (posrat_div_posrat_is_posrat application-judgement "posrat"
 rationals nil)
 (real_ge_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
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 nil)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (int_expt application-judgement "int" exponentiation nil)
 (nzreal_exp application-judgement "nzreal" exponentiation
 nil)
 (nnrat_times_nnrat_is_nnrat application-judgement
 "nonneg_rat" rationals nil)
 (nnint_times_nnint_is_nnint application-judgement
 "nonneg_int" integers nil)
 (nat_expt application-judgement "nat" exponentiation nil)
 (int_minus_int_is_int application-judgement "int" integers
 nil)
 (expt_times formula-decl nil exponentiation nil)
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 (OR const-decl "[bool, bool -> bool]" booleans nil)
 (> const-decl "bool" reals nil)
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 (f skolem-const-decl "float" float nil)
 (float type-eq-decl nil float nil)
 (/= const-decl "boolean" notequal nil)
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 (mult_expt formula-decl nil exponentiation nil)
 (Fexpt const-decl "float" float nil))
 nil))
 (sigma_TCC1 0
 (sigma_TCC1-1 nil 3544869888 ("" (subtype-tcc) nil nil)
 ((boolean nonempty-type-decl nil booleans nil)
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 nil)
 (real_gt_is_strict_total_order name-judgement
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 real_props nil))
 nil))
 (sigma_TCC2 0
 (sigma_TCC2-1 nil 3544869888 ("" (termination-tcc) nil nil) nil
 nil))
 (FDivInt_TCC1 0
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 shostak))
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 (owre "fix" 3399983082
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 (field)
 (("1"
 (mult-by
 -1
 "ln(radix)")
 (("1"
 (field
 -1)
 nil
 nil)
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 (hide
 -1
 -2
 2)
 (("2"
 (case
 "ln(radix) > 0")
 (("1"
 (split)
 (("1"
 (grind-reals)
 nil
 nil)
 ("2"
 (propax)
 nil
 nil))
 nil)
 ("2"
 (hide
 2)
 (("2"
 (lemma
 "ln_strict_increasing")
 (("2"
 (expand
 "strict_increasing?")
 (("2"
 (inst
 -1
 "1"
 "radix")
 (("2"
 (grind-reals)
 nil
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
 ("2"
 (hide
 -1
 -2
 2)
 (("2"
 (case
 "x>0")
 (("1"
 (grind-reals)
 nil
 nil)
 ("2"
 (hide
 2)
 (("2"
 (grind-reals)
 nil
 nil))
 nil))
 nil))
 nil))
 nil)
 ("2"
 (hide
 2)
 (("2"
 (grind-reals)
 nil
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
 ("2"
 (hide -1 -2 2)
 (("2"
 (rewrite "hathat_int")
 nil
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
 ("2" (case "0 <= x * radix ^ (-AA)")
 (("1"
 (hide -2 -3 2)
 (("1" (grind-reals) nil nil))
 nil)
 ("2"
 (hide -1 -2 2 3)
 (("2" (grind-reals) nil nil))
 nil))
 nil))
 nil)
 ("2"
 (case "-dExp(b) <= ln(x * radix / vNum(b)) / ln(radix)")
 (("1" (grind-reals) nil nil)
 ("2" (hide -2 2)
 (("2"
 (mult-by 1 "ln(radix)" +)
 (("1"
 (wrap-formula 1 "exp")
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 (case-replace
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 (rewrite "exp_ln")
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 (div-by 1 "radix")
 (("1"
 (mult-by 1 "vNum(b)")
 (("1"
 (case-replace
 " radix ^ (-dExp(b)) / radix=radix ^ (-dExp(b) - 1)")
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 (field)
 (("1"
 (rewrite "hathat_int")
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 (hide -1 -2 -4)
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 (case-replace
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 (("1"
 (hide -2 2)
 (("1"
 (grind-reals)
 nil
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
 ("2"
 (hide 2 -1 -2)
 (("2"
 (lemma "expt_plus")
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 (inst
 -1
 "-dExp(b)"
 "-1"
 "radix")
 (("2"
 (grind-reals)
 (("2"
 (expand "^" 1 2)
 (("2"
 (grind-reals)
 (("2"
 (rewrite
 "expt_x1_aux")
 nil
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
 ("2"
 (hide -1 2)
 (("2"
 (expand "^^")
 (("2" (propax) nil nil))
 nil))
 nil))
 nil)
 ("2"
 (lemma "ln_increasing")
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 (expand "increasing?")
 (("2"
 (lemma "ln_exp")
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 nil))
 nil))
 nil))
 nil)
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 (hide 2 -1)
 (("2"
 (case "ln(radix) > 0")
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 (split)
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 ("2" (propax) nil nil))
 nil)
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 (hide 2)
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 (lemma "ln_strict_increasing")
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 (expand "strict_increasing?")
 (("2"
 (inst -1 "1" "radix")
 (("2"
 (grind-reals)
 nil
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
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 (cancel-by 1 "radix")
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 (hide -1 1)
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 (("1"
 (case
 "integer_pred(vNum(b) / radix)")
 (("1"
 (hide -3 -4)
 (("1"
 (lemma "div_simple")
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 (inst -1 "vNum(b)" "radix")
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 (case
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 (skosimp*)
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 (case-replace
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 nil
 nil)
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 (grind-reals)
 nil
 nil))
 nil))
 nil))
 nil)
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 (hide -3 2)
 (("2"
 (assert)
 nil
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
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 (assert)
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 (hide-all-but 1)
 (("2"
 (rewrite "radix_div_vNum")
 nil
 nil))
 nil))
 nil))
 nil)
 ("2"
 (hide 2)
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 (case
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 (hide
 -1
 -2
 -3
 2)
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 (div-by
 1
 "-ln(radix)"
 -)
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 (field)
 nil
 nil)
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 (case
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 (assert)
 nil
 nil)
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 (hide
 -1
 2
 3)
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 (lemma
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 (expand
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 (inst
 -1
 "1"
 "radix")
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 (grind-reals)
 nil
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 nil))
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 nil))
 nil))
 nil))
 nil))
 nil))
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 (hide -1 -2 2)
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 (rewrite
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 nil
 nil))
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 nil))
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 (hide -1 -2 2)
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 (rewrite "hathatln")
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 nil))
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 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
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 nil))
 nil))
 nil)
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 (RND_aux_alt_TCC1-1 nil 3544343150
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 nil)
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 nil))
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 (("" (decompose-equality)
 (("" (expand "RND_aux")
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 (("" (rewrite "FpredCanonic")
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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)
 (real_lt_is_strict_total_order name-judgement
 "(strict_total_order?[real])" real_props nil)
 (/= const-decl "boolean" notequal nil))
 nil))
 (Exp_incr_1 0
 (Exp_incr_1-1 nil 3318763991
 ("" (skeep)
 (("" (use "both_sides_expt_gt1_lt")
 (("1" (assert) nil nil) ("2" (assert) nil nil)) nil))
 nil)
 ((both_sides_expt_gt1_lt formula-decl nil exponentiation nil)
 (posreal nonempty-type-eq-decl nil real_types nil)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (>= const-decl "bool" reals 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)
 (bool nonempty-type-eq-decl nil booleans 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)
 (radix formal-const-decl "above(1)" float 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)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (posrat_exp application-judgement "posrat" exponentiation
 nil))
 shostak))
 (Exp_incr_2 0
 (Exp_incr_2-1 nil 3318865674
 ("" (skeep)
 (("" (use " both_sides_expt_gt1_lt")
 (("1" (assert) nil nil) ("2" (assert) nil nil)) nil))
 nil)
 ((both_sides_expt_gt1_lt formula-decl nil exponentiation nil)
 (posreal nonempty-type-eq-decl nil real_types nil)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (>= const-decl "bool" reals 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)
 (bool nonempty-type-eq-decl nil booleans 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)
 (radix formal-const-decl "above(1)" float 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)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (posrat_exp application-judgement "posrat" exponentiation
 nil))
 shostak))
 (Exp_increq_1_TCC1 0
 (Exp_increq_1_TCC1-1 nil 3318783146 ("" (subtype-tcc) nil 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)
 (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)
 (real_le_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (/= const-decl "boolean" notequal nil))
 nil))
 (Exp_increq_1 0
 (Exp_increq_1-1 nil 3318865769
 ("" (skeep)
 (("" (use "both_sides_expt_gt1_le")
 (("1" (assert) nil nil) ("2" (assert) nil nil)) nil))
 nil)
 ((both_sides_expt_gt1_le formula-decl nil exponentiation nil)
 (posreal nonempty-type-eq-decl nil real_types nil)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (>= const-decl "bool" reals 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)
 (bool nonempty-type-eq-decl nil booleans 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)
 (radix formal-const-decl "above(1)" float nil)
 (real_gt_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)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (posrat_exp application-judgement "posrat" exponentiation
 nil))
 shostak))
 (Exp_increq_2 0
 (Exp_increq_2-1 nil 3318865818
 ("" (skeep)
 (("" (use "both_sides_expt_gt1_le")
 (("1" (assert) nil nil) ("2" (assert) nil nil)) nil))
 nil)
 ((both_sides_expt_gt1_le formula-decl nil exponentiation nil)
 (posreal nonempty-type-eq-decl nil real_types nil)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (>= const-decl "bool" reals 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)
 (bool nonempty-type-eq-decl nil booleans 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)
 (radix formal-const-decl "above(1)" float nil)
 (real_gt_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)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (posrat_exp application-judgement "posrat" exponentiation
 nil))
 shostak))
 (Exp_1 0
 (Exp_1-1 nil 3318698220
 ("" (skeep)
 (("" (case "0 <= e1")
 (("1" (case "e1 <= 0")
 (("1" (grind) nil nil)
 ("2" (rewrite "Exp_increq_2")
 (("2" (rewrite "expt_x0") (("2" (assert) nil nil))
 nil))
 nil))
 nil)
 ("2" (rewrite "Exp_increq_2")
 (("2" (rewrite "expt_x0") (("2" (assert) nil nil)) nil))
 nil))
 nil))
 nil)
 ((int nonempty-type-eq-decl nil integers nil)
 (integer_pred const-decl "[rational -> boolean]" integers
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 (real_pred const-decl "[number_field -> boolean]" reals nil)
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 (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_x0 formula-decl nil exponentiation nil)
 (posint_exp application-judgement "posint" exponentiation
 nil)
 (Exp_increq_2 formula-decl nil float nil)
 (expt def-decl "real" exponentiation nil)
 (^ const-decl "real" exponentiation nil)
 (real_ge_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (posrat_div_posrat_is_posrat application-judgement "posrat"
 rationals nil)
 (posnat_expt application-judgement "posnat" exponentiation
 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))
 shostak))
 (EqExpEq 0
 (EqExpEq-1 nil 3318696278
 ("" (skeep)
 (("" (case "e1 <= e2")
 (("1" (case "e2 <= e1")
 (("1" (grind) nil nil)
 ("2" (rewrite "Exp_increq_2") nil nil))
 nil)
 ("2" (rewrite "Exp_increq_2") nil nil))
 nil))
 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)
 (<= 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)
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 (expt def-decl "real" exponentiation nil)
 (^ const-decl "real" exponentiation nil)
 (minus_int_is_int application-judgement "int" integers nil)
 (real_ge_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (posrat_div_posrat_is_posrat application-judgement "posrat"
 rationals nil)
 (posnat_expt application-judgement "posnat" exponentiation
 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))
 shostak))
 (expt_odd_TCC1 0
 (expt_odd_TCC1-1 nil 3319544683 ("" (subtype-tcc) nil nil)
 ((/= const-decl "boolean" notequal nil)) nil))
 (expt_odd 0
 (expt_odd-1 nil 3319544683
 ("" (induct "n")
 (("1" (grind-reals) (("1" (rewrite "expt_x1") nil nil)) nil)
 ("2" (rewrite "expt_x1") (("2" (grind-reals) nil nil)) nil)
 ("3" (skeep)
 (("3" (split 1)
 (("1" (skosimp*)
 (("1" (rewrite "expt_plus")
 (("1" (rewrite "expt_x1")
 (("1" (grind-reals)
 (("1" (rewrite "odd_times_odd_is_odd") nil nil))
 nil))
 nil))
 nil))
 nil)
 ("2" (skosimp*)
 (("2" (rewrite "expt_plus")
 (("2" (rewrite "expt_x1")
 (("2" (lemma "even_or_odd")
 (("2" (inst -1 "radix")
 (("2" (flatten)
 (("2" (case "even?(radix)")
 (("1" (hide -2 -3 1)
 (("1"
 (lemma "even_iff_not_odd")
 (("1"
 (inst -1 "(radix ^ (1 + j)) * radix")
 (("1"
 (flatten)
 (("1"
 (case
 "even?((radix ^ (1 + j)) * radix)")
 (("1" (assert) nil nil)
 ("2"
 (rewrite
 "int_times_even_is_even")
 nil
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
 ("2" (assert) nil nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
 ((even_or_odd formula-decl nil naturalnumbers nil)
 (* const-decl "[numfield, numfield -> numfield]"
 number_fields nil)
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 (even_iff_not_odd formula-decl nil naturalnumbers nil)
 (even? const-decl "bool" integers nil)
 (posint_plus_nnint_is_posint application-judgement "posint"
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 (odd_times_odd_is_odd judgement-tcc nil integers nil)
 (odd_int nonempty-type-eq-decl nil integers nil)
 (posint_times_posint_is_posint application-judgement "posint"
 integers nil)
 (mult_divides1 application-judgement "(divides(n))" divides
 nil)
 (mult_divides2 application-judgement "(divides(m))" divides
 nil)
 (int_minus_int_is_int application-judgement "int" integers
 nil)
 (expt_plus formula-decl nil exponentiation nil)
 (nzreal nonempty-type-eq-decl nil reals nil)
 (even_plus_odd_is_odd application-judgement "odd_int"
 integers nil)
 (expt_x1 formula-decl nil exponentiation nil)
 (nat_induction formula-decl nil naturalnumbers nil)
 (+ const-decl "[numfield, numfield -> numfield]"
 number_fields nil)
 (numfield nonempty-type-eq-decl nil number_fields nil)
 (^ const-decl "real" exponentiation nil)
 (/= const-decl "boolean" notequal nil)
 (OR const-decl "[bool, bool -> bool]" booleans nil)
 (radix formal-const-decl "above(1)" float nil)
 (above nonempty-type-eq-decl nil integers nil)
 (> const-decl "bool" reals nil)
 (odd? const-decl "bool" integers nil)
 (IFF const-decl "[bool, bool -> bool]" booleans nil)
 (pred type-eq-decl nil defined_types nil)
 (nat nonempty-type-eq-decl nil naturalnumbers 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)
 (nnint_plus_posint_is_posint application-judgement "posint"
 integers nil)
 (posint_exp application-judgement "posint" exponentiation
 nil))
 shostak))
 (expt_even 0
 (expt_even-1 nil 3319562624
 ("" (induct "n")
 (("1" (grind-reals) (("1" (rewrite "expt_x1") nil nil)) nil)
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 ("3" (skeep)
 (("3" (rewrite 1 "expt_plus")
 (("1"
 (rewrite "expt_plus" :subst
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 (("1" (rewrite "expt_x1")
 (("1" (split 1)
 (("1" (skosimp*)
 (("1" (split -2)
 (("1" (rewrite "even_times_int_is_even") nil
 nil)
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 nil))
 nil)
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 (("2" (case-replace "1+j=j+1")
 (("1" (hide -1)
 (("1"
 (case-replace
 "even?((radix ^ (j + 1)) * radix)=NOT odd?((radix ^ (1 + j)) * radix)")
 (("1"
 (case-replace
 "even?(radix)=NOT odd?(radix)")
 (("1"
 (rewrite "odd_times_odd_is_odd")
 (("1"
 (lemma
 "odd_or_even_int"
 :subst
 ("x" "radix ^ (1 + j)"))
 (("1" (assert) nil nil))
 nil))
 nil)
 ("2"
 (lemma
 "even_iff_not_odd"
 :subst
 ("x" "radix"))
 (("2" (grind-reals) nil nil))
 nil))
 nil)
 ("2" (case-replace "1+j=j+1")
 (("1"
 (lemma
 "even_iff_not_odd"
 :subst
 ("x" "((radix ^ (j + 1)) * radix)"))
 (("1" (grind-reals) nil nil))
 nil)
 ("2" (assert) nil nil))
 nil))
 nil))
 nil)
 ("2" (assert) nil nil))
 nil))
 nil))
 nil))
 nil))
 nil)
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 (("2" (hide 2)
 (("2" (case-replace "even?(radix)=NOT odd?(radix)")
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 (case-replace
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 (("1"
 (case-replace
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 (("1" (case-replace "2+j=1+(1+j)")
 (("1" (rewrite "expt_plus")
 (("1"
 (rewrite "expt_x1")
 (("1"
 (rewrite "odd_times_odd_is_odd")
 nil
 nil))
 nil))
 nil)
 ("2" (assert) nil nil))
 nil)
 ("2"
 (lemma "even_iff_not_odd" :subst
 ("x" "radix ^ (2 + j)"))
 (("2" (grind-reals) nil nil)) nil))
 nil)
 ("2" (assert) nil nil))
 nil)
 ("2"
 (lemma "even_iff_not_odd" :subst
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 (("2" (grind-reals) nil nil)) nil))
 nil)
 ("2"
 (lemma "even_iff_not_odd" :subst ("x" "radix"))
 (("2" (grind-reals) nil nil)) nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil)
 ((nzreal nonempty-type-eq-decl nil reals nil)
 (expt_plus formula-decl nil exponentiation 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)
 (odd_or_even_int formula-decl nil naturalnumbers nil)
 (odd_times_odd_is_odd judgement-tcc nil integers nil)
 (odd_int nonempty-type-eq-decl nil integers nil)
 (even_iff_not_odd formula-decl nil naturalnumbers nil)
 (* const-decl "[numfield, numfield -> numfield]"
 number_fields nil)
 (NOT const-decl "[bool -> bool]" booleans nil)
 (odd? const-decl "bool" integers nil)
 (real_ge_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (= const-decl "[T, T -> boolean]" equalities nil)
 (even_int nonempty-type-eq-decl nil integers nil)
 (even_times_int_is_even judgement-tcc nil integers nil)
 (int_minus_int_is_int application-judgement "int" integers
 nil)
 (posint_plus_nnint_is_posint application-judgement "posint"
 integers nil)
 (even_plus_odd_is_odd application-judgement "odd_int"
 integers nil)
 (expt_x1 formula-decl nil exponentiation nil)
 (nat_induction formula-decl nil naturalnumbers nil)
 (+ const-decl "[numfield, numfield -> numfield]"
 number_fields nil)
 (numfield nonempty-type-eq-decl nil number_fields nil)
 (^ const-decl "real" exponentiation nil)
 (/= const-decl "boolean" notequal nil)
 (OR const-decl "[bool, bool -> bool]" booleans nil)
 (radix formal-const-decl "above(1)" float nil)
 (above nonempty-type-eq-decl nil integers nil)
 (> const-decl "bool" reals nil)
 (even? const-decl "bool" integers nil)
 (IFF const-decl "[bool, bool -> bool]" booleans nil)
 (pred type-eq-decl nil defined_types nil)
 (nat nonempty-type-eq-decl nil naturalnumbers 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)
 (nnint_plus_posint_is_posint application-judgement "posint"
 integers nil)
 (posint_exp application-judgement "posint" exponentiation
 nil))
 shostak))
 (FoppCorrect 0
 (FoppCorrect-1 nil 3319368570
 ("" (skeep)
 (("" (expand* "FtoR" "Fopp") (("" (grind-reals) nil nil))
 nil))
 nil)
 ((Fopp const-decl "float" float nil)
 (FtoR const-decl "real" float nil)
 (rat_times_rat_is_rat application-judgement "rat" rationals
 nil)
 (minus_int_is_int application-judgement "int" integers nil)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (minus_rat_is_rat application-judgement "rat" rationals nil))
 shostak))
 (FoppFopp 0
 (FoppFopp-1 nil 3545043329
 ("" (grind) (("" (decompose-equality) nil nil)) 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)
 (- const-decl "[numfield -> numfield]" number_fields nil)
 (numfield nonempty-type-eq-decl nil number_fields nil)
 (minus_int_is_int application-judgement "int" integers nil)
 (Fopp const-decl "float" float nil))
 shostak))
 (Fopp_mult_left 0
 (Fopp_mult_left-1 nil 3545043536
 ("" (skeep) (("" (grind) nil nil)) nil)
 ((minus_int_is_int application-judgement "int" integers nil)
 (mult_divides1 application-judgement "(divides(n))" divides
 nil)
 (mult_divides2 application-judgement "(divides(m))" divides
 nil)
 (int_plus_int_is_int application-judgement "int" integers
 nil)
 (* const-decl "float" float nil)
 (Fmult const-decl "float" float nil)
 (- const-decl "float" float nil)
 (Fopp const-decl "float" float nil))
 shostak))
 (Fopp_mult_right 0
 (Fopp_mult_right-1 nil 3545043574 ("" (grind) nil nil)
 ((Fopp const-decl "float" float nil)
 (- const-decl "float" float nil)
 (Fmult const-decl "float" float nil)
 (* const-decl "float" float nil)
 (mult_divides2 application-judgement "(divides(m))" divides
 nil)
 (mult_divides1 application-judgement "(divides(n))" divides
 nil)
 (minus_int_is_int application-judgement "int" integers nil))
 shostak))
 (FabsCorrect 0
 (FabsCorrect-1 nil 3319889181
 ("" (skeep)
 (("" (expand* "Fabs" "FtoR")
 (("" (rewrite "abs_mult")
 (("" (expand "abs" 1 3) (("" (propax) nil nil)) nil))
 nil))
 nil))
 nil)
 ((FtoR const-decl "real" float nil)
 (rat_times_rat_is_rat application-judgement "rat" rationals
 nil)
 (posrat_exp application-judgement "posrat" exponentiation
 nil)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
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 shostak))
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 (("" (split)
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 nil)
 (mult_divides2 application-judgement "(divides(m))" divides
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 (FulpOpp_TCC1 0
 (FulpOpp_TCC1-1 nil 3319817879
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 shostak))
 (FulpAbs_TCC1 0
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 (case-replace
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 (case-replace
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 nil))
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 (("" (expand "Fulp")
 (("" (rewrite "Exp_increq_1")
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 shostak))
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 Fcanonic?(b)(p) =>
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 "b"
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 "Fnormalize(b)(p)"))
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 (inst 1
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 number_fields nil)
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 (Fnormalize def-decl
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 float nil)
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 (real_lt_is_strict_total_order name-judgement
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 nil)
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 (mult_divides2 application-judgement "(divides(m))" divides
 nil)
 (posint_times_posint_is_posint application-judgement "posint"
 integers nil)
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 nil)
 (* const-decl "[numfield, numfield -> numfield]"
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 (nznum nonempty-type-eq-decl nil number_fields nil)
 (/= const-decl "boolean" notequal nil)
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 nil)
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 (- const-decl "[numfield, numfield -> numfield]"
 number_fields nil)
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 nil)
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 (posnat nonempty-type-eq-decl nil integers nil)
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 shostak))
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 (rewrite -1)
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 (expand "Fopp")
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 (hide 2)
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 (rewrite
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 ("b" "b"))
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 (case
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 (rewrite -1)
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 (rewrite "FoppCorrect")
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 (rewrite "FoppCorrect")
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 nil)
 ("2"
 (lemma "FcanonicOpp")
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 (inst
 -1
 "b"
 "Fnormalize(b)(p)")
 (("2" (assert) nil nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
 nil))
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 nil))
 nil)
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 number_fields nil)
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 nil)
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 shostak))
 (FpredFoppFsucc 0
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 (("" (expand* "Fpred" "Fopp" "Fsucc")
 (("" (grind-reals) nil nil)) nil))
 nil)
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 nil)
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 nil)
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 nil)
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 (div_cancel4 formula-decl nil real_props nil)
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 (minus_nzrat_is_nzrat application-judgement "nzrat" rationals
 nil)
 (posrat_div_posrat_is_posrat application-judgement "posrat"
 rationals nil)
 (int_plus_int_is_int application-judgement "int" integers
 nil))
 shostak))
 (FsuccFoppFpred 0
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--> --------------------

--> maximum size reached

--> --------------------

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