(critical_pairs
(IMP_critical_pairs_aux_TCC1 0
(IMP_critical_pairs_aux_TCC1-1 nil 3420229945
("" (lemma "var_countable" ) (("" (propax) nil nil )) nil )
((var_countable formula-decl nil critical_pairs nil )) nil ))
(CP?_TCC1 0
(CP?_TCC1-1 nil 3395743409
("" (skosimp*)
(("" (lemma "ext_preserv_pos" )
(("" (inst?) (("" (assert ) nil nil )) nil )) nil ))
nil )
((arity formal-const-decl "[symbol -> nat]" critical_pairs 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 )
(symbol formal-nonempty-type-decl nil critical_pairs nil )
(variable formal-nonempty-type-decl nil critical_pairs nil )
(ext_preserv_pos formula-decl nil substitution nil )
(Sub type-eq-decl nil substitution nil )
(Sub? const-decl "bool" substitution nil )
(V const-decl "set[term]" variables_term nil )
(positions? type-eq-decl nil positions nil )
(member const-decl "bool" sets nil ) (set type-eq-decl nil sets nil )
(lhs const-decl "term" rewrite_rules nil )
(rewrite_rule type-eq-decl nil rewrite_rules nil )
(rewrite_rule? const-decl "bool" rewrite_rules nil )
(positionsOF def-decl "positions" positions nil )
(positions type-eq-decl nil positions nil )
(term type-decl nil term_adt nil )
(position type-eq-decl nil positions nil )
(posnat nonempty-type-eq-decl nil integers nil )
(> const-decl "bool" reals nil )
(nonneg_int nonempty-type-eq-decl nil integers nil )
(below type-eq-decl nil nat_types nil ))
nil ))
(CP_lemma_aux1a_TCC1 0
(CP_lemma_aux1a_TCC1-1 nil 3406618276
("" (skosimp*)
(("" (hide-all-but 2)
(("" (typepred "alpha!1" "rho!1" )
(("" (hide -3) (("" (rewrite "subs_o" ) nil nil )) nil )) nil ))
nil ))
nil )
((subs_o formula-decl nil substitution nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(variable formal-nonempty-type-decl nil critical_pairs nil )
(symbol formal-nonempty-type-decl nil critical_pairs 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 )
(arity formal-const-decl "[symbol -> nat]" critical_pairs nil )
(term type-decl nil term_adt nil ) (set type-eq-decl nil sets nil )
(V const-decl "set[term]" variables_term nil )
(Sub? const-decl "bool" substitution nil )
(Sub type-eq-decl nil substitution nil )
(Ren? const-decl "bool" substitution nil )
(Ren type-eq-decl nil substitution nil ))
nil ))
(CP_lemma_aux1a 0
(CP_lemma_aux1a-1 nil 3406746822
("" (skosimp*)
(("" (lemma "exists_renaming" )
(("" (inst -1 "Vars(lhs(e2!1))" "Vars(lhs(e1!1))" )
(("1" (skosimp*)
(("1" (lemma "inverse_renaming" )
(("1" (inst?)
(("1" (skosimp*)
(("1" (lemma "inverse_rename_identity" )
(("1" (inst -1 "rho!1" "rho1!1" "lhs(e2!1)" )
(("1" (prop)
(("1" (inst 2 "comp(sg2!1, rho1!1)" "rho!1" )
(("1" (split)
(("1" (lemma "vars_term_rename" )
(("1" (inst?)
(("1"
(assert )
(("1"
(lemma
"IUnion_extra[(V)].disjoint_subset" )
(("1"
(inst
-1
"Vars(lhs(e1!1))"
"Vars(lhs(e1!1))"
"Vars(ext(rho!1)(lhs(e2!1)))"
"restrict[term[variable, symbol, arity], ((V)), boolean](Ran(rho!1))" )
(("1"
(assert )
(("1"
(hide-all-but 1)
(("1"
(expand * "subset?" "member" )
(("1" (skeep) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide (-4 2))
(("2" (rewrite "o_ass" )
(("2"
(rewrite "ext_o" )
(("2"
(expand "o" )
(("2" (replaces -1) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (rewrite "subs_o" ) nil nil ))
nil )
("2" (hide-all-but (-2 1))
(("2" (expand * "subset?" "member" )
(("2" (skosimp*)
(("2" (decompose-equality -2)
(("2"
(inst -1 "x!1" )
(("2"
(iff)
(("2" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide-all-but 1)
(("2" (rewrite "vars_of_term_finite" ) nil nil )) nil )
("3" (hide-all-but 1)
(("3" (rewrite "vars_of_term_finite" ) nil nil )) nil ))
nil ))
nil ))
nil )
((arity formal-const-decl "[symbol -> nat]" critical_pairs 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 )
(symbol formal-nonempty-type-decl nil critical_pairs nil )
(variable formal-nonempty-type-decl nil critical_pairs nil )
(exists_renaming formula-decl nil substitution nil )
(vars_of_term_finite formula-decl nil subterm nil )
(Ren type-eq-decl nil substitution nil )
(Ren? const-decl "bool" substitution nil )
(Sub type-eq-decl nil substitution nil )
(Sub? const-decl "bool" substitution nil )
(inverse_rename_identity formula-decl nil substitution nil )
(subs_o formula-decl nil substitution nil )
(disjoint_subset formula-decl nil IUnion_extra nil )
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil )
(subset? const-decl "bool" sets nil )
(ext def-decl "term" substitution nil )
(restrict const-decl "R" restrict nil )
(Ran const-decl "set[term]" substitution nil )
(vars_term_rename formula-decl nil substitution nil )
(o_ass formula-decl nil substitution nil )
(O const-decl "T3" function_props nil )
(ext_o formula-decl nil substitution nil )
(rho1!1 skolem-const-decl "Ren[variable, symbol, arity]"
critical_pairs nil )
(sg2!1 skolem-const-decl "Sub[variable, symbol, arity]"
critical_pairs nil )
(comp const-decl "term" substitution nil )
(Dom const-decl "set[(V)]" substitution nil )
(= const-decl "[T, T -> boolean]" equalities nil )
(inverse_renaming formula-decl nil substitution nil )
(finite_set type-eq-decl nil finite_sets nil )
(e1!1 skolem-const-decl "{e1 | member(e1, E!1)}" critical_pairs
nil )
(term type-decl nil term_adt nil ) (set type-eq-decl nil sets nil )
(V const-decl "set[term]" variables_term nil )
(is_finite const-decl "bool" finite_sets nil )
(Vars const-decl "set[(V)]" subterm nil )
(rewrite_rule? const-decl "bool" rewrite_rules nil )
(rewrite_rule type-eq-decl nil rewrite_rules nil )
(lhs const-decl "term" rewrite_rules nil )
(member const-decl "bool" sets nil )
(E!1 skolem-const-decl "set[rewrite_rule]" critical_pairs nil )
(e2!1 skolem-const-decl "{e2 | member(e2, E!1)}" critical_pairs
nil ))
shostak))
(CP_lemma_aux1_TCC1 0
(CP_lemma_aux1_TCC1-1 nil 3402063728
("" (skosimp*)
(("" (hide-all-but (-1 2))
(("" (rewrite "ext_preserv_pos" ) nil nil )) nil ))
nil )
((arity formal-const-decl "[symbol -> nat]" critical_pairs 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 )
(symbol formal-nonempty-type-decl nil critical_pairs nil )
(variable formal-nonempty-type-decl nil critical_pairs nil )
(Sub type-eq-decl nil substitution nil )
(Sub? const-decl "bool" substitution nil )
(V const-decl "set[term]" variables_term nil )
(member const-decl "bool" sets nil ) (set type-eq-decl nil sets nil )
(lhs const-decl "term" rewrite_rules nil )
(rewrite_rule type-eq-decl nil rewrite_rules nil )
(rewrite_rule? const-decl "bool" rewrite_rules nil )
(term type-decl nil term_adt nil )
(position type-eq-decl nil positions nil )
(posnat nonempty-type-eq-decl nil integers nil )
(> const-decl "bool" reals nil )
(nonneg_int nonempty-type-eq-decl nil integers nil )
(below type-eq-decl nil nat_types nil )
(ext_preserv_pos formula-decl nil substitution nil ))
nil ))
(CP_lemma_aux1 0
(CP_lemma_aux1-1 nil 3402063736
("" (skosimp*)
(("" (lemma "CP_lemma_aux1a" )
(("" (inst?)
(("" (assert )
(("" (skosimp*)
((""
(case "ext(union_subs((restriction(sg1!1)(Vars(lhs(e1!1))), restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))))(subtermOF(lhs(e1!1), p!1)) = ext(union_subs((restriction(sg1!1)(Vars(lhs(e1!1))), restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))))(ext(rho!1)(lhs(e2!1)))" )
(("1" (lemma "unification" )
(("1"
(inst -1 "subtermOF(lhs(e1!1), p!1)"
"ext(rho!1)(lhs(e2!1))" )
(("1" (prop)
(("1" (skosimp*)
(("1" (copy -1)
(("1" (expand "mgu" -1)
(("1" (flatten)
(("1" (hide -1)
(("1"
(inst
-1
"union_subs(restriction(sg1!1)(Vars(lhs(e1!1))), restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))" )
(("1"
(expand "member" -1)
(("1"
(expand "U" -1)
(("1"
(expand "unifier" -1)
(("1"
(assert )
(("1"
(expand "<=" )
(("1"
(skosimp*)
(("1"
(inst
2
"ext(theta!1)(rhs(e1!1))"
"replaceTerm(ext(theta!1)(lhs(e1!1)), ext(theta!1)(ext(rho!1)(rhs(e2!1))),p!1)"
"tau!1" )
(("1"
(lemma "ext_o" )
(("1"
(inst
-1
"tau!1"
"theta!1" )
(("1"
(decompose-equality
-1)
(("1"
(split)
(("1"
(hide -1)
(("1"
(expand
"CP?" )
(("1"
(inst
1
"theta!1"
"rho!1"
"e1!1"
"e2!1"
"p!1" )
(("1"
(assert )
nil
nil ))
nil ))
nil ))
nil )
("2"
(inst
-1
"rhs(e1!1)" )
(("2"
(expand "o" )
(("2"
(replace
-1
1
rl)
(("2"
(hide -1)
(("2"
(replace
-1
1
rl)
(("2"
(hide
-1)
(("2"
(lemma
"restriction_union" )
(("2"
(inst
-1
"restriction(sg1!1)(Vars(lhs(e1!1)))"
"restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
"rhs(e1!1)" )
(("1"
(lemma
"dom_restriction" )
(("1"
(copy
-1)
(("1"
(inst
-1
"Vars(lhs(e1!1))"
"sg1!1" )
(("1"
(inst
-2
"Vars(ext(rho!1)(lhs(e2!1)))"
"alpha!1" )
(("1"
(lemma
"IUnion_extra[(V)].disjoint_subset" )
(("1"
(inst
-1
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Vars(lhs(e1!1))"
"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
(("1"
(assert )
(("1"
(prop)
(("1"
(replace
-1
1)
(("1"
(lemma
"restriction_term" )
(("1"
(inst?)
(("1"
(prop)
(("1"
(assert )
nil
nil )
("2"
(hide-all-but
1)
(("2"
(typepred
"e1!1" )
(("2"
(expand
"rewrite_rule?" )
(("2"
(expand *
"lhs"
"rhs" )
(("2"
(prop)
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide-all-but
(-2
-3
-6
1))
(("2"
(lemma
"IUnion_extra[(V)].disjoint_subset" )
(("2"
(inst
-1
"Vars(rhs(e1!1))"
"Vars(rhs(e1!1))"
"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
(("2"
(prop)
(("1"
(hide-all-but
1)
(("1"
(expand *
"subset?"
"member" )
(("1"
(skeep)
nil
nil ))
nil ))
nil )
("2"
(hide-all-but
(-3
1))
(("2"
(lemma
"IUnion_extra[(V)].disjoint_subset" )
(("2"
(inst
-1
"Vars(rhs(e1!1))"
"Vars(lhs(e1!1))"
"Vars(ext(rho!1)(lhs(e2!1)))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
(("2"
(prop)
(("1"
(hide
(-1
2))
(("1"
(typepred
"e1!1" )
(("1"
(expand *
"rewrite_rule?"
"lhs"
"rhs" )
(("1"
(assert )
nil
nil ))
nil ))
nil ))
nil )
("2"
(hide
(-1
2))
(("2"
(expand *
"subset?"
"member" )
(("2"
(skeep)
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(rewrite
"restriction_Subs" )
nil
nil )
("3"
(rewrite
"restriction_Subs" )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("3"
(lemma
"ext_replace_ext" )
(("3"
(inst?)
(("3"
(prop)
(("1"
(replaces
-1)
(("1"
(copy
-1)
(("1"
(inst
-1
"ext(rho!1)(rhs(e2!1))" )
(("1"
(inst
-2
"lhs(e1!1)" )
(("1"
(expand
"o" )
(("1"
(replace
-1
1
rl)
(("1"
(replace
-2
1
rl)
(("1"
(replace
-3
1
rl)
(("1"
(hide
(-1
-2
-3))
(("1"
(lemma
"restriction_union" )
(("1"
(copy
-1)
(("1"
(inst
-1
"restriction(sg1!1)(Vars(lhs(e1!1)))"
"restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
"lhs(e1!1)" )
(("1"
(inst
-2
"restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
"restriction(sg1!1)(Vars(lhs(e1!1)))"
"ext(rho!1)(rhs(e2!1))" )
(("1"
(lemma
"dom_restriction" )
(("1"
(copy
-1)
(("1"
(inst
-1
"Vars(lhs(e1!1))"
"sg1!1" )
(("1"
(inst
-2
"Vars(ext(rho!1)(lhs(e2!1)))"
"alpha!1" )
(("1"
(lemma
"IUnion_extra[(V)].disjoint_subset" )
(("1"
(inst
-1
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Vars(lhs(e1!1))"
"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
(("1"
(assert )
(("1"
(lemma
"IUnion_extra[(V)].disjoint_commute" )
(("1"
(inst
-1
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))" )
(("1"
(assert )
(("1"
(prop)
(("1"
(rewrite
"union_commute" )
(("1"
(replaces
-1)
(("1"
(replaces
-1)
(("1"
(lemma
"restriction_term" )
(("1"
(copy
-1)
(("1"
(inst
-1
"Vars(ext(rho!1)(lhs(e2!1)))"
"alpha!1"
"ext(rho!1)(rhs(e2!1))" )
(("1"
(inst
-2
"Vars(lhs(e1!1))"
"sg1!1"
"lhs(e1!1)" )
(("1"
(prop)
(("1"
(replace
-1
1
rl)
(("1"
(replace
-2
1
rl)
(("1"
(rewrite
"ext_o" )
(("1"
(expand
"o" )
(("1"
(case-replace
"ext(alpha!1)(ext(rho!1)(rhs(e2!1))) = ext(sg2!1)(rhs(e2!1))" )
(("1"
(hide-all-but
(-10
-12
1))
(("1"
(replaces
-1)
(("1"
(lemma
"ext_o" )
(("1"
(inst
-1
"alpha!1"
"rho!1" )
(("1"
(copy
-1)
(("1"
(decompose-equality
-1)
(("1"
(decompose-equality
-2)
(("1"
(inst
-1
"lhs(e2!1)" )
(("1"
(inst
-2
"rhs(e2!1)" )
(("1"
(expand
"o" )
(("1"
(replace
-1
*
rl)
(("1"
(replace
-2
*
rl)
(("1"
(hide
(-1
-2))
(("1"
(lemma
"same_substitution" )
(("1"
(inst
-1
"comp(alpha!1, rho!1)"
"sg2!1"
"lhs(e2!1)" )
(("1"
(assert )
(("1"
(lemma
"same_term" )
(("1"
(inst
-1
"comp(alpha!1, rho!1)"
"sg2!1"
"rhs(e2!1)" )
(("1"
(prop)
(("1"
(skosimp*)
(("1"
(hide
(-3
2))
(("1"
(inst
-2
"x!1" )
(("1"
(assert )
(("1"
(hide
1)
(("1"
(typepred
"e2!1" )
(("1"
(hide
-2)
(("1"
(expand
"rewrite_rule?" )
(("1"
(flatten)
(("1"
(expand *
"subset?"
"rhs"
"lhs" )
(("1"
(inst?)
(("1"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide-all-but
1)
(("2"
(expand *
"subset?"
"member" )
(("2"
(skeep)
nil
nil ))
nil ))
nil )
("3"
(hide-all-but
1)
(("3"
(typepred
"e2!1" )
(("3"
(expand
"rewrite_rule?" )
(("3"
(flatten)
(("3"
(lemma
"rename_preserv_inclusion" )
(("3"
(expand *
"rhs"
"lhs" )
(("3"
(inst?)
(("3"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("4"
(hide-all-but
1)
(("4"
(expand *
"subset?"
"member" )
(("4"
(skeep)
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide-all-but
(-4
-8
1))
(("2"
(lemma
"IUnion_extra[(V)].disjoint_subset" )
(("2"
(case
"disjoint?(Vars(lhs(e1!1)), Vars(ext(rho!1)(rhs(e2!1))))" )
(("1"
(inst
-2
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Vars(lhs(e1!1))"
"Vars(ext(rho!1)(rhs(e2!1)))"
"Vars(ext(rho!1)(rhs(e2!1)))" )
(("1"
(prop)
(("1"
(lemma
"IUnion_extra[(V)].disjoint_commute" )
(("1"
(inst
-1
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Vars(ext(rho!1)(rhs(e2!1)))" )
(("1"
(assert )
nil
nil ))
nil ))
nil )
("2"
(hide-all-but
1)
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(expand *
"subset?"
"member" )
(("2"
(skeep)
nil
nil ))
nil ))
nil ))
nil ))
nil )
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(hide-all-but
(-1
-3
1))
(("2"
(typepred
"e2!1" )
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(expand
"rewrite_rule?" )
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(flatten)
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(expand *
"lhs"
"rhs" )
(("2"
(lemma
"rename_preserv_inclusion" )
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(inst
-1
"rho!1"
"e2!1`1"
"e2!1`2" )
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(inst
-4
"Vars(e1!1`1)"
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"Vars(ext(rho!1)(e2!1`1))" )
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(hide-all-but
1)
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"subset?"
"member" )
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(skeep)
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("3"
(hide-all-but
(-5
-8
1))
(("3"
(lemma
"IUnion_extra[(V)].disjoint_subset" )
(("3"
(inst
-1
"Vars(lhs(e1!1))"
"Vars(lhs(e1!1))"
"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
(("3"
(prop)
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(hide-all-but
1)
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(expand *
"subset?"
"member" )
(("3"
(skeep)
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("4"
(hide-all-but
(-3
-7
1))
(("4"
(lemma
"IUnion_extra[(V)].disjoint_subset" )
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(case
"disjoint?(Vars(ext(rho!1)(rhs(e2!1))), Vars(lhs(e1!1)))" )
(("1"
(inst
-2
"Vars(ext(rho!1)(rhs(e2!1)))"
"Vars(ext(rho!1)(rhs(e2!1)))"
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Vars(lhs(e1!1))" )
(("1"
(prop)
(("1"
(hide-all-but
1)
(("1"
(expand *
"subset?"
"member" )
(("1"
(skeep)
nil
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide
(-2
2))
(("2"
(typepred
"e2!1" )
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(expand
"rewrite_rule?" )
(("2"
(flatten)
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(lemma
"rename_preserv_inclusion" )
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(inst
-1
"rho!1"
"e2!1`1"
"e2!1`2" )
(("2"
(assert )
(("2"
(inst
-4
"Vars(e1!1`1)"
"Vars(e1!1`1)"
"Vars(ext(rho!1)(e2!1`2))"
"Vars(ext(rho!1)(e2!1`1))" )
(("2"
(prop)
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(expand *
"rhs"
"lhs" )
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(hide-all-but
(-1
2))
(("1"
(lemma
"IUnion_extra[(V)].disjoint_commute" )
(("1"
(inst
-1
"Vars(e1!1`1)"
"Vars(ext(rho!1)(e2!1`2))" )
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(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil )
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(hide-all-but
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"member" )
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(skeep)
nil
nil ))
nil ))
nil )
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"rhs"
"lhs" )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide-all-but
1)
(("2"
(rewrite
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nil
nil ))
nil )
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(hide-all-but
1)
(("3"
(rewrite
"restriction_Subs" )
nil
nil ))
nil ))
nil )
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(hide-all-but
1)
(("2"
(rewrite
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nil
nil ))
nil )
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(hide-all-but
1)
(("3"
(rewrite
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nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide-all-but
(-7 1))
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nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide-all-but (-6 1))
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nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide-all-but 1)
(("2"
(rewrite "restriction_Subs" )
nil
nil ))
nil )
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(hide-all-but 1)
(("3"
(rewrite "restriction_Subs" )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
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(inst 1
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(("1" (propax) nil nil )) nil )
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(("2" (rewrite "restriction_Subs" ) nil
nil ))
nil )
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(("3" (rewrite "restriction_Subs" ) nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide 3)
(("2" (lemma "restriction_union" )
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(inst -1 "restriction(sg1!1)(Vars(lhs(e1!1)))"
"restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
"subtermOF(lhs(e1!1), p!1)" )
(("1" (lemma "dom_restriction" )
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(lemma "IUnion_extra[(V)].disjoint_subset" )
(("1"
(inst -1
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Vars(lhs(e1!1))"
"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
(("1" (lemma "dom_restriction" )
(("1"
(inst
-1
"Vars(ext(rho!1)(lhs(e2!1)))"
"alpha!1" )
(("1"
(assert )
(("1"
(lemma
"IUnion_extra[(V)].disjoint_subset" )
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(inst
-1
"Vars(lhs(e1!1))"
"Vars(lhs(e1!1))"
"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
(("1"
(prop)
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(replaces -1)
(("1"
(lemma "restriction_union" )
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(inst
-1
"restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
"restriction(sg1!1)(Vars(lhs(e1!1)))"
"ext(rho!1)(lhs(e2!1))" )
(("1"
(lemma
"IUnion_extra[(V)].disjoint_commute" )
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(inst
-1
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))" )
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(lemma
"IUnion_extra[(V)].disjoint_subset" )
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-1
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Vars(lhs(e1!1))"
"Vars(ext(rho!1)(lhs(e2!1)))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
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"restriction_term" )
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(inst?)
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-1
1
rl)
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(lemma
"restriction_term" )
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-1
"Vars(ext(rho!1)(lhs(e2!1)))"
"alpha!1"
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(prop)
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-1
1
rl)
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"o" )
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(propax)
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nil ))
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(hide-all-but
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nil
nil ))
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nil ))
nil ))
nil ))
nil )
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(hide-all-but
(-1 1))
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(rewrite
"IUnion_extra[(V)].disjoint_commute" )
nil
nil ))
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(hide-all-but
1)
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(skeep)
nil
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(-5
-6
1))
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(lemma
"IUnion_extra[(V)].disjoint_subset" )
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(inst
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"Vars(lhs(e1!1))"
"Vars(ext(rho!1)(lhs(e2!1)))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
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(hide
(-2
-3))
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-1
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
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(assert )
nil
nil ))
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-2
2))
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nil ))
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nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide-all-but 1)
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(rewrite
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nil
nil ))
nil ))
nil ))
nil ))
nil )
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(hide-all-but (-1 1))
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"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))" )
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(prop)
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nil ))
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nil ))
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nil )
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(hide-all-but (-1 -4 1))
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(lemma
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(inst
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"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
"Vars(ext(rho!1)(lhs(e2!1)))"
"Vars(lhs(e1!1))"
"Vars(lhs(e1!1))" )
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(lemma
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(inst?)
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(assert )
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(hide
(-2 -3 -4))
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(-1
2))
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(lemma
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(inst?)
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nil
nil ))
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nil ))
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nil ))
nil ))
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nil ))
nil ))
nil ))
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nil )
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nil ))
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(("2" (rewrite "restriction_Subs" ) nil nil )) nil ))
nil ))
nil )
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(("4" (inst -1 "Vars(lhs(e1!1))" "sg1!1" )
(("4"
(inst -2 "Vars(ext(rho!1)(lhs(e2!1)))"
"alpha!1" )
(("4"
(lemma "IUnion_extra[(V)].disjoint_subset" )
(("4"
(inst -1
"Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
"Vars(lhs(e1!1))"
"Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
"Vars(ext(rho!1)(lhs(e2!1)))" )
(("4" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("5" (hide-all-but 1)
(("5" (rewrite "restriction_Subs" ) nil nil )) nil )
("6" (hide-all-but 1)
(("6" (rewrite "restriction_Subs" ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((CP_lemma_aux1a formula-decl nil critical_pairs nil )
(subtermOF def-decl "term" subterm nil )
(positions? type-eq-decl nil positions nil )
(positionsOF def-decl "positions" positions nil )
(positions type-eq-decl nil positions nil )
(Ren type-eq-decl nil substitution nil )
(Ren? const-decl "bool" substitution nil )
(lhs const-decl "term" rewrite_rules nil )
(Vars const-decl "set[(V)]" subterm nil )
(restriction const-decl "term" substitution nil )
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(unifier const-decl "bool" unification nil )
(<= const-decl "bool" unification nil )
(theta!1 skolem-const-decl "Sub[variable, symbol, arity]"
critical_pairs nil )
(p!1 skolem-const-decl "position[variable, symbol, arity]"
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sets_lemmas nil )
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(O const-decl "T3" function_props nil )
(ext_o formula-decl nil substitution nil )
(U const-decl "set[Sub]" unification nil )
(e2!1 skolem-const-decl "{e2 | member(e2, E!1)}" critical_pairs
nil )
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critical_pairs nil )
(alpha!1 skolem-const-decl "Sub[variable, symbol, arity]"
critical_pairs nil )
(e1!1 skolem-const-decl "{e1 | member(e1, E!1)}" critical_pairs
nil )
(E!1 skolem-const-decl "set[rewrite_rule]" critical_pairs nil )
(sg1!1 skolem-const-decl "Sub[variable, symbol, arity]"
critical_pairs nil )
(unification formula-decl nil unification nil )
(vars_subterm formula-decl nil subterm nil )
(union_is_sub formula-decl nil substitution nil )
(member const-decl "bool" sets nil )
(position type-eq-decl nil positions nil )
(posnat nonempty-type-eq-decl nil integers nil )
(> const-decl "bool" reals nil )
(nonneg_int nonempty-type-eq-decl nil integers nil )
(below type-eq-decl nil nat_types nil )
(rewrite_rule type-eq-decl nil rewrite_rules nil )
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(integer_pred const-decl "[rational -> boolean]" integers nil )
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nil )
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(variable formal-nonempty-type-decl nil critical_pairs nil ))
shostak))
(CP_lemma_aux2_TCC1 0
(CP_lemma_aux2_TCC1-1 nil 3412313494
("" (skosimp*)
(("" (lemma "Pos_var_is_finite" )
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nil )
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nil )
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nil ))
(CP_lemma_aux2_TCC2 0
(CP_lemma_aux2_TCC2-1 nil 3420229945
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nil )
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critical_pairs nil )
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shostak))
(CP_Theorem 0
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(inst?)
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(hide
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-3
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(lemma
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(inst?)
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(-5
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--> --------------------
--> maximum size reached
--> --------------------
Messung V0.5 in Prozent C=100 H=100 G=100
¤ Dauer der Verarbeitung: 0.464 Sekunden
(vorverarbeitet am 2026-04-25)
¤
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