Quellcode-Bibliothek neg.prf
Sprache: Lisp
(neg
(cauchy_neg_TCC1 0
(cauchy_neg_TCC1-1 nil 3507981237
("" (skosimp*)
(("" (expand "cauchy_real?" )
(("" (typepred "cx!1" )
(("" (expand "cauchy_real?" )
(("" (skolem!)
(("" (inst 1 "-x!1" )
(("" (assert )
(("" (expand "cauchy_prop" )
(("" (skolem!)
(("" (inst - "p!1" )
(("" (assert ) (("" (grind) nil nil )) nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((cauchy_real? const-decl "bool" cauchy nil )
(minus_real_is_real application-judgement "real" reals nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(posint_exp application-judgement "posint" exponentiation nil )
(cauchy_prop const-decl "bool" cauchy 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 )
(int_plus_int_is_int application-judgement "int" integers nil )
(^ const-decl "real" exponentiation nil )
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil )
(int_minus_int_is_int application-judgement "int" integers nil )
(real_times_real_is_real application-judgement "real" reals nil )
(minus_int_is_int application-judgement "int" integers 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 )
(>= const-decl "bool" reals nil )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(cauchy_real nonempty-type-eq-decl nil cauchy nil ))
nil ))
(neg_lemma 0
(neg_lemma-1 nil 3507981237
("" (skosimp*)
(("" (expand "cauchy_prop" )
(("" (expand "cauchy_neg" )
(("" (split)
(("1" (skosimp*)
(("1" (inst - "p!1" ) (("1" (grind) nil nil )) nil )) nil )
("2" (skosimp*)
(("2" (inst - "p!1" ) (("2" (grind) nil nil )) nil )) nil ))
nil ))
nil ))
nil ))
nil )
((posint_exp application-judgement "posint" exponentiation nil )
(minus_real_is_real application-judgement "real" reals nil )
(cauchy_prop const-decl "bool" cauchy 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 "real" exponentiation nil )
(int_plus_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 )
(real_times_real_is_real application-judgement "real" reals nil )
(int_minus_int_is_int application-judgement "int" integers nil )
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil )
(cauchy_neg const-decl "cauchy_real" neg nil )
(minus_int_is_int application-judgement "int" integers nil ))
nil ))
(neg_cauchy_nzreal_is_cauchy_nzreal 0
(neg_cauchy_nzreal_is_cauchy_nzreal-1 nil 3507981237
("" (skosimp*)
(("" (typepred "nzcx!1" )
(("" (expand "cauchy_nzreal?" )
(("" (skolem!)
(("" (typepred "x!1" )
(("" (inst + "-x!1" )
(("" (lemma "neg_lemma" ("x" "x!1" "cx" "nzcx!1" ))
(("" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((cauchy_nzreal nonempty-type-eq-decl nil cauchy nil )
(cauchy_nzreal? const-decl "bool" cauchy nil )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(>= 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 )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(minus_nzreal_is_nzreal application-judgement "nzreal" real_types
nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(cauchy_real nonempty-type-eq-decl nil cauchy nil )
(cauchy_real? const-decl "bool" cauchy nil )
(neg_lemma formula-decl nil neg nil )
(nzreal nonempty-type-eq-decl nil reals nil )
(/= const-decl "boolean" notequal nil ))
nil ))
(neg_cauchy_posreal_is_cauchy_negreal 0
(neg_cauchy_posreal_is_cauchy_negreal-1 nil 3507981237
("" (skolem!)
(("" (typepred "pcx!1" )
(("" (expand "cauchy_negreal?" )
(("" (expand "cauchy_posreal?" )
(("" (skolem!)
(("" (typepred "x!1" )
(("" (inst + "-x!1" )
(("" (lemma "neg_lemma" ("x" "x!1" "cx" "pcx!1" ))
(("" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((cauchy_posreal nonempty-type-eq-decl nil cauchy nil )
(cauchy_posreal? const-decl "bool" cauchy nil )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(>= 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 )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(nonneg_real nonempty-type-eq-decl nil real_types nil )
(> const-decl "bool" reals nil )
(posreal nonempty-type-eq-decl nil real_types nil )
(neg_lemma formula-decl nil neg nil )
(cauchy_real? const-decl "bool" cauchy nil )
(cauchy_real nonempty-type-eq-decl nil cauchy 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 )
(neg_cauchy_nzreal_is_cauchy_nzreal application-judgement
"cauchy_nzreal" neg nil )
(<= const-decl "bool" reals nil )
(nonpos_real nonempty-type-eq-decl nil real_types nil )
(< const-decl "bool" reals nil )
(negreal nonempty-type-eq-decl nil real_types nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(minus_nzreal_is_nzreal application-judgement "nzreal" real_types
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 )
(cauchy_negreal? const-decl "bool" cauchy nil ))
nil ))
(neg_cauchy_negreal_is_cauchy_posreal 0
(neg_cauchy_negreal_is_cauchy_posreal-1 nil 3507981237
("" (skolem!)
(("" (typepred "ncx!1" )
(("" (expand "cauchy_negreal?" )
(("" (skolem!)
(("" (expand "cauchy_posreal?" )
(("" (inst + "-x!1" )
(("" (typepred "x!1" )
(("" (lemma "neg_lemma" ("x" "x!1" "cx" "ncx!1" ))
(("" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((cauchy_negreal nonempty-type-eq-decl nil cauchy nil )
(cauchy_negreal? const-decl "bool" cauchy nil )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(>= 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 )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans 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 )
(minus_nzreal_is_nzreal application-judgement "nzreal" real_types
nil )
(negreal nonempty-type-eq-decl nil real_types nil )
(< const-decl "bool" reals nil )
(nonpos_real nonempty-type-eq-decl nil real_types nil )
(<= const-decl "bool" reals nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(numfield nonempty-type-eq-decl nil number_fields 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 )
(neg_lemma formula-decl nil neg nil )
(cauchy_real? const-decl "bool" cauchy nil )
(cauchy_real nonempty-type-eq-decl nil cauchy 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 )
(neg_cauchy_nzreal_is_cauchy_nzreal application-judgement
"cauchy_nzreal" neg nil )
(cauchy_posreal? const-decl "bool" cauchy nil ))
nil )))
quality 94%
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2026-03-28