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first_order_substitution.prf
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first_order_substitution.prf
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(|first_order_substitution|
(|subs_TCC1| 0
(|subs_TCC1-1| NIL 3922736114 ("" (TCC))
((|real_ge_is_total_order| NAME-JUDGEMENT "(total_order?[real])"
|real_props| NIL)
(<< ADT-DEF-DECL "(strict_well_founded?[first_order_term])"
|first_order_term_adt| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|int| NONEMPTY-TYPE-EQ-DECL NIL |integers| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL) (>= CONST-DECL "bool" |reals| 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)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| 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))
NIL
(|subs| TERMINATION
"first_order_substitution.subs(first_order_substitution.sigma_basic, first_order_substitution.t1)"
"NIL")))
(|subs_TCC2| 0
(|subs_TCC2-1| NIL 3922736114 ("" (TCC))
((|real_ge_is_total_order| NAME-JUDGEMENT "(total_order?[real])"
|real_props| NIL)
(<< ADT-DEF-DECL "(strict_well_founded?[first_order_term])"
|first_order_term_adt| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|int| NONEMPTY-TYPE-EQ-DECL NIL |integers| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL) (>= CONST-DECL "bool" |reals| 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)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| 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))
NIL
(|subs| TERMINATION
"first_order_substitution.subs(first_order_substitution.sigma_basic, first_order_substitution.t2)"
"NIL")))
(|subs_TCC3| 0
(|subs_TCC3-1| NIL 3922736114 ("" (TCC))
((|real_ge_is_total_order| NAME-JUDGEMENT "(total_order?[real])"
|real_props| NIL)
(<< ADT-DEF-DECL "(strict_well_founded?[first_order_term])"
|first_order_term_adt| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|int| NONEMPTY-TYPE-EQ-DECL NIL |integers| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL) (>= CONST-DECL "bool" |reals| 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)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| 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))
NIL
(|subs| TERMINATION
"first_order_substitution.subs(first_order_substitution.sigma_basic, first_order_substitution.arg)"
"NIL")))
(|subs_TCC4| 0
(|subs_TCC4-1| NIL 3922736114 ("" (TCC))
((<< ADT-DEF-DECL "(strict_well_founded?[list])" |list_adt| NIL)) NIL
(|subs| TERMINATION
"first_order_substitution.subs(first_order_substitution.tail)" "NIL")))
(|subs_TCC5| 0
(|subs_TCC5-1| NIL 3922736114 ("" (TCC))
((|int| NONEMPTY-TYPE-EQ-DECL NIL |integers| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|args| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL) (>= CONST-DECL "bool" |reals| 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)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(|list| TYPE-DECL NIL |list_adt| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| 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))
NIL
(|subs| SUBTYPE "first_order_substitution.args"
"(list_adt[first_order_term[constant, variable, f_symbol]].cons?)")))
(|subs_TCC6| 0
(|subs_TCC6-1| NIL 3922736114 ("" (TCC))
((|int| NONEMPTY-TYPE-EQ-DECL NIL |integers| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(<< ADT-DEF-DECL "(strict_well_founded?[list])" |list_adt| NIL)
(|args| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL) (>= CONST-DECL "bool" |reals| 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)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(|list| TYPE-DECL NIL |list_adt| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| 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))
NIL
(|subs| TERMINATION
"first_order_substitution.subs(first_order_substitution.sigma)(list_adt[first_order_term[constant, variable, f_symbol]].cdr(first_order_substitution.args))"
"NIL")))
(|subs_TCC7| 0
(|subs_TCC7-1| NIL 3922736114 ("" (TCC))
((|args| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL) (>= CONST-DECL "bool" |reals| 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)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(|list| TYPE-DECL NIL |list_adt| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| 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))
NIL
(|subs| SUBTYPE "first_order_substitution.args"
"(list_adt[first_order_term[constant, variable, f_symbol]].cons?)")))
(|subs_TCC8| 0
(|subs_TCC8-1| NIL 3922736114
("" (SKEEP)
(("" (LEMMA "finite_subset[first_order_term]")
(("" (INST?)
(("" (INST -1 "image(subs(sigma), fin_set_t)")
(("" (PROP)
(("" (EXPAND "subset?")
(("" (HIDE 2)
(("" (SKEEP)
(("" (EXPAND "member")
(("" (SKEEP) (("" (ASSERT) (("" (GRIND) NIL NIL)) NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL)
((|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|int| NONEMPTY-TYPE-EQ-DECL NIL |integers| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL) (>= CONST-DECL "bool" |reals| 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)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| NIL)
(|bool| NONEMPTY-TYPE-EQ-DECL NIL |booleans| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|boolean| NONEMPTY-TYPE-DECL NIL |booleans| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| NIL)
(|number| NONEMPTY-TYPE-DECL NIL |numbers| NIL)
(|finite_subset| FORMULA-DECL NIL |finite_sets| NIL)
(|finite_image| APPLICATION-JUDGEMENT "finite_set[R]" |function_image_aux|
NIL)
(|subset?| CONST-DECL "bool" |sets| NIL)
(|sub| TYPE-EQ-DECL NIL |first_order_substitution| NIL)
(|list| TYPE-DECL NIL |list_adt| NIL)
(|basic_sub| TYPE-EQ-DECL NIL |first_order_substitution| NIL)
(= CONST-DECL "[T, T -> boolean]" |equalities| NIL)
(|finite_set| TYPE-EQ-DECL NIL |finite_sets| NIL)
(|is_finite| CONST-DECL "bool" |finite_sets| NIL)
(|member| CONST-DECL "bool" |sets| NIL)
(|set| TYPE-EQ-DECL NIL |sets| NIL))
SHOSTAK
(|subs| SUBTYPE
"{t | EXISTS s: booleans.AND(sets[first_order_term[constant, variable, f_symbol]].member(first_order_substitution.s, first_order_substitution.fin_set_t), first_order_substitution.t = first_order_substitution.subs(first_order_substitution.sigma)(first_order_substitution.s))}"
"finite_set[first_order_term[constant, variable, f_symbol]]")))
(|supset_dom_TCC1| 0
(|supset_dom_TCC1-1| NIL 3922736114 ("" (TCC))
((|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)
(|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)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|real_ge_is_total_order| NAME-JUDGEMENT "(total_order?[real])"
|real_props| NIL))
NIL
(|supset_dom| SUBTYPE "first_order_substitution.sigma"
"(list_adt[basic_sub].cons?)")))
(|supset_dom_TCC2| 0
(|supset_dom_TCC2-1| NIL 3922736114 ("" (TCC))
((|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)
(|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)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|real_ge_is_total_order| NAME-JUDGEMENT "(total_order?[real])"
|real_props| NIL)
(<< ADT-DEF-DECL "(strict_well_founded?[list])" |list_adt| NIL))
NIL
(|supset_dom| TERMINATION
"first_order_substitution.supset_dom(list_adt[basic_sub].cdr(first_order_substitution.sigma))"
"NIL")))
(|supset_dom_TCC3| 0
(|supset_dom_TCC3-1| NIL 3922736114 ("" (TCC)) NIL NIL
(|supset_dom| SUBTYPE "first_order_substitution.sigma"
"(list_adt[basic_sub].cons?)")))
(|supset_dom_correct| 0
(|supset_dom_correct-1| NIL 3922736535
("" (INDUCT "sigma")
(("1" (GRIND) NIL NIL)
("2" (SKOLEM 1 ("hd" "tail"))
(("2" (PROP)
(("2" (SKEEP)
(("2" (EXPAND "subs" 1)
(("2" (EXPAND "subs" 1)
(("2" (INST -1 "X")
(("2" (ASSERT)
(("2" (PROP)
(("1" (HIDE 1)
(("1" (EXPAND "supset_dom" 1) (("1" (GRIND) NIL NIL))
NIL))
NIL)
("2" (EXPAND "subs" -1)
(("2" (REPLACE -1 1)
(("2" (HIDE -1)
(("2" (EXPAND "subs" 1)
(("2" (LIFT-IF)
(("2" (PROP)
(("2" (HIDE 1)
(("2" (EXPAND "supset_dom")
(("2" (EXPAND "member")
(("2" (EXPAND "add")
(("2" (ASSERT) NIL NIL)) NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL)
((|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| ADT-CONSTRUCTOR-DECL "[variable -> (var?)]"
|first_order_term_adt| NIL)
(|var?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL))
SHOSTAK))
(|dom_TCC1| 0
(|dom_TCC1-1| NIL 3922736114
("" (SKEEP)
((""
(NAME-REPLACE "dom"
"{X | subs(sigma)(X) /= variable[constant, variable, f_symbol](X)}")
(("" (CASE "subset?(dom, supset_dom(sigma))")
(("1" (LEMMA "finite_subset[variable]")
(("1" (INST?) (("1" (GRIND) NIL NIL)) NIL)) NIL)
("2" (EXPAND "subset?" 1)
(("2" (SKEEP)
(("2" (EXPAND "member")
(("2" (HIDE 2)
(("2" (EXPAND "dom")
(("2" (LEMMA "supset_dom_correct")
(("2" (INST?) (("2" (GRIND) NIL NIL)) NIL)) NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
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)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(= CONST-DECL "[T, T -> boolean]" |equalities| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(/= CONST-DECL "boolean" |notequal| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| NIL)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|basic_sub| TYPE-EQ-DECL NIL |first_order_substitution| NIL)
(|list| TYPE-DECL NIL |list_adt| NIL)
(|sub| TYPE-EQ-DECL NIL |first_order_substitution| NIL)
(|subs| CONST-DECL "first_order_term" |first_order_substitution| NIL)
(|var?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|variable| ADT-CONSTRUCTOR-DECL "[variable -> (var?)]"
|first_order_term_adt| NIL)
(|member| CONST-DECL "bool" |sets| NIL)
(|supset_dom_correct| FORMULA-DECL NIL |first_order_substitution| NIL)
(|finite_subset| FORMULA-DECL NIL |finite_sets| NIL)
(|set| TYPE-EQ-DECL NIL |sets| NIL)
(|subset?| CONST-DECL "bool" |sets| NIL)
(|is_finite| CONST-DECL "bool" |finite_sets| NIL)
(|finite_set| TYPE-EQ-DECL NIL |finite_sets| NIL)
(|supset_dom| DEF-DECL "finite_set[variable]" |first_order_substitution|
NIL))
SHOSTAK
(|dom| SUBTYPE
"{X | first_order_substitution.subs(first_order_substitution.sigma)(first_order_substitution.X) /= first_order_term_adt[constant, variable, f_symbol].variable(first_order_substitution.X)}"
"finite_set[variable]")))
(|supset_dom_correct2| 0
(|supset_dom_correct2-1| NIL 3922736535
("" (SKEEP)
(("" (EXPAND "subset?")
(("" (SKEEP)
(("" (EXPAND "dom")
(("" (EXPAND "member")
(("" (LEMMA "supset_dom_correct")
(("" (INST? -1) (("" (ASSERT) (("" (GRIND) NIL NIL)) NIL)) NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL)
((|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL))
SHOSTAK))
(|img_TCC1| 0
(|img_TCC1-1| NIL 3922736114
("" (SKEEP)
(("" (LEMMA "finite_subset[first_order_term]")
(("" (INST?)
(("" (INST -1 "image(subs(sigma), dom(sigma))")
(("" (PROP)
(("" (EXPAND "subset?")
(("" (HIDE 2)
(("" (SKEEP)
(("" (EXPAND "member")
(("" (SKEEP) (("" (GRIND) NIL NIL)) NIL)) NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL)
((|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|int| NONEMPTY-TYPE-EQ-DECL NIL |integers| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL) (>= CONST-DECL "bool" |reals| 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)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| NIL)
(|bool| NONEMPTY-TYPE-EQ-DECL NIL |booleans| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|boolean| NONEMPTY-TYPE-DECL NIL |booleans| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| NIL)
(|number| NONEMPTY-TYPE-DECL NIL |numbers| NIL)
(|finite_subset| FORMULA-DECL NIL |finite_sets| NIL)
(|finite_image| APPLICATION-JUDGEMENT "finite_set[R]" |function_image_aux|
NIL)
(|subset?| CONST-DECL "bool" |sets| NIL)
(|subs| CONST-DECL "first_order_term" |first_order_substitution| NIL)
(= CONST-DECL "[T, T -> boolean]" |equalities| NIL)
(|dom| CONST-DECL "finite_set[variable]" |first_order_substitution| NIL)
(|finite_set| TYPE-EQ-DECL NIL |finite_sets| NIL)
(|is_finite| CONST-DECL "bool" |finite_sets| NIL)
(|sub| TYPE-EQ-DECL NIL |first_order_substitution| NIL)
(|list| TYPE-DECL NIL |list_adt| NIL)
(|basic_sub| TYPE-EQ-DECL NIL |first_order_substitution| NIL)
(|member| CONST-DECL "bool" |sets| NIL)
(|set| TYPE-EQ-DECL NIL |sets| NIL))
SHOSTAK
(|img| SUBTYPE
"{t | EXISTS X: booleans.AND(sets[variable].member(first_order_substitution.X, first_order_substitution.dom(first_order_substitution.sigma)), first_order_substitution.subs(first_order_substitution.sigma)(first_order_substitution.X) = first_order_substitution.t)}"
"finite_set[first_order_term[constant, variable, f_symbol]]")))
(|nice_more_general_is_more_general| 0
(|nice_more_general_is_more_general-1| NIL 3941189896 ("" (GRIND) NIL NIL)
((|nice?| DEF-DECL "bool" |first_order_substitution| NIL)
(|sub| TYPE-EQ-DECL NIL |first_order_substitution| NIL)
(|list| TYPE-DECL NIL |list_adt| NIL)
(|basic_sub| TYPE-EQ-DECL NIL |first_order_substitution| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL) NIL
(PRED TYPE-EQ-DECL NIL |defined_types| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| 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)
(|subs| CONST-DECL "first_order_term" |first_order_substitution| NIL) NIL
NIL NIL)
SHOSTAK))
(|nice_more_general_is_more_general_set_vars| 0
(|nice_more_general_is_more_general_set_vars-1| NIL 3941190631
("" (GRIND) 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)
(>= CONST-DECL "bool" |reals| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|set| TYPE-EQ-DECL NIL |sets| NIL)
(|is_finite| CONST-DECL "bool" |finite_sets| NIL)
(|finite_set| TYPE-EQ-DECL NIL |finite_sets| NIL)
(|injective?| CONST-DECL "bool" |functions| NIL)
(|nice?| DEF-DECL "bool" |first_order_substitution| NIL)
(|sub| TYPE-EQ-DECL NIL |first_order_substitution| NIL)
(|list| TYPE-DECL NIL |list_adt| NIL)
(|basic_sub| TYPE-EQ-DECL NIL |first_order_substitution| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(TRUE CONST-DECL "bool" |booleans| NIL)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(|every| ADT-DEF-DECL "boolean" |first_order_term_adt| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|char| TYPE-EQ-DECL NIL |strings| NIL)
(|char?| ADT-RECOGNIZER-DECL "[character -> boolean]" |character_adt| NIL)
(|character| TYPE-DECL NIL |character_adt| NIL)
(|below| TYPE-EQ-DECL NIL |nat_types| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| NIL)
(|member| CONST-DECL "bool" |sets| NIL)
(|subs| CONST-DECL "first_order_term" |first_order_substitution| NIL)
(|equal?| CONST-DECL "bool" |first_order_substitution| NIL)
(|nice_more_general?| CONST-DECL "bool" |first_order_substitution| NIL)
(|more_general?| CONST-DECL "bool" |first_order_substitution| NIL))
SHOSTAK))
(|shift_TCC1| 0
(|shift_TCC1-1| NIL 3922736114 ("" (TCC))
((|int_minus_int_is_int| APPLICATION-JUDGEMENT "int" |integers| NIL)
(|real_ge_is_total_order| NAME-JUDGEMENT "(total_order?[real])"
|real_props| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| 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)
(|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))
NIL
(|shift| SUBTYPE "(number_fields.-)(first_order_substitution.n, 1)" "nat")))
(|shift_TCC2| 0
(|shift_TCC2-1| NIL 3922736114 ("" (TCC)) NIL NIL
(|shift| TERMINATION
"first_order_substitution.shift((number_fields.+)(first_order_substitution.start, 1), (number_fields.-)(first_order_substitution.n, 1), first_order_substitution.inc)"
"NIL")))
(|shift_TCC3| 0
(|shift_TCC3-1| NIL 3922736114 ("" (TCC))
((|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)
(|int_minus_int_is_int| APPLICATION-JUDGEMENT "int" |integers| NIL)
(|nat| NONEMPTY-TYPE-EQ-DECL NIL |naturalnumbers| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|int| NONEMPTY-TYPE-EQ-DECL NIL |integers| NIL)
(>= CONST-DECL "bool" |reals| 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)
(AND CONST-DECL "[bool, bool -> bool]" |booleans| NIL)
(|list| TYPE-DECL NIL |list_adt| NIL)
(PRED TYPE-EQ-DECL NIL |defined_types| 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))
NIL (|shift| SUBTYPE "first_order_substitution.inc" "nat")))
(|subs_const| 0
(|subs_const-1| NIL 3922736535
("" (INDUCT "sigma") (("1" (GRIND) NIL NIL) ("2" (GRIND) NIL NIL)) NIL)
((|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|const| ADT-CONSTRUCTOR-DECL "[constant -> (const?)]"
|first_order_term_adt| NIL)
(|const?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL))
SHOSTAK))
(|subs_unit| 0
(|subs_unit-1| NIL 3922736535
("" (INDUCT "sigma") (("1" (GRIND) NIL NIL) ("2" (GRIND) NIL NIL)) NIL)
((|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|unit| ADT-CONSTRUCTOR-DECL "(unit?)" |first_order_term_adt| NIL)
(|unit?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL))
SHOSTAK))
(|subs_pair| 0
(|subs_pair-1| NIL 3922736535
("" (INDUCT "sigma") (("1" (GRIND) NIL NIL) ("2" (GRIND) NIL NIL)) NIL)
((|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|pair| ADT-CONSTRUCTOR-DECL
"[[first_order_term, first_order_term] -> (pair?)]" |first_order_term_adt|
NIL)
(|pair?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL))
SHOSTAK))
(|subs_app| 0
(|subs_app-1| NIL 3922736536
("" (INDUCT "sigma")
(("1" (GRIND) NIL NIL)
("2" (SKOLEM 1 ("hd" "tail"))
(("2" (PROP)
(("2" (SKEEP)
(("2" (EXPAND "subs" 1)
(("2" (INST? -1)
(("2" (REPLACE -1 1)
(("2" (EXPAND "subs" 1 1) (("2" (PROPAX) NIL NIL)) NIL)) NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL)
((|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|app| ADT-CONSTRUCTOR-DECL "[[f_symbol, first_order_term] -> (app?)]"
|first_order_term_adt| NIL)
(|app?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL))
SHOSTAK))
(|subs_var| 0
(|subs_var-1| NIL 3922736536
("" (SKEEP)
(("" (CASE "const?(t)")
(("1" (LEMMA "first_order_term_const_eta")
(("1" (INST? -1)
(("1" (REPLACE -1 -3 :DIR RL)
(("1" (HIDE -1)
(("1" (REWRITE "subs_const") (("1" (GRIND) NIL NIL)) NIL)) NIL))
NIL))
NIL))
NIL)
("2" (CASE "unit?(t)")
(("1" (CASE "t=unit")
(("1" (REPLACE -1) (("1" (REWRITE "subs_unit") NIL NIL)) NIL)
("2" (GRIND) NIL NIL))
NIL)
("2" (CASE "pair?(t)")
(("1" (LEMMA "first_order_term_pair_eta")
(("1" (INST? -1)
(("1" (REPLACE -1 -3 :DIR RL)
(("1" (HIDE -1)
(("1" (REWRITE "subs_pair") (("1" (GRIND) NIL NIL)) NIL))
NIL))
NIL))
NIL))
NIL)
("2" (CASE "app?(t)")
(("1" (LEMMA "first_order_term_app_eta")
(("1" (INST -1 "t")
(("1" (REPLACE -1 -3 :DIR RL)
(("1" (REWRITE "subs_app") (("1" (GRIND) NIL NIL)) NIL))
NIL))
NIL))
NIL)
("2" (GRIND) NIL NIL))
NIL))
NIL))
NIL))
NIL))
NIL)
((|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|const?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|a| ADT-ACCESSOR-DECL "[(const?) -> constant]" |first_order_term_adt| NIL)
(|first_order_term_const_eta| FORMULA-DECL NIL |first_order_term_adt| NIL)
(|pair?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|term1| ADT-ACCESSOR-DECL "[(pair?) -> first_order_term]"
|first_order_term_adt| NIL)
(|term2| ADT-ACCESSOR-DECL "[(pair?) -> first_order_term]"
|first_order_term_adt| NIL)
(|first_order_term_pair_eta| FORMULA-DECL NIL |first_order_term_adt| NIL)
(|first_order_term_app_eta| FORMULA-DECL NIL |first_order_term_adt| NIL)
(|f_sym| ADT-ACCESSOR-DECL "[(app?) -> f_symbol]" |first_order_term_adt|
NIL)
(|arg| ADT-ACCESSOR-DECL "[(app?) -> first_order_term]"
|first_order_term_adt| NIL)
(|app?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|unit| ADT-CONSTRUCTOR-DECL "(unit?)" |first_order_term_adt| NIL)
(|unit?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL))
SHOSTAK))
(|subs_const2| 0
(|subs_const2-1| NIL 3922736536
("" (SKEEP)
(("" (LEMMA "first_order_term_opt")
(("" (INST -1 "t")
(("" (PROP)
(("1" (REPLACE -1) (("1" (REWRITE "subs_unit") NIL NIL)) NIL)
("2" (REPLACE -2)
(("2" (REWRITE "subs_pair") (("2" (ASSERT) NIL NIL)) NIL)) NIL)
("3" (REPLACE -2 -3)
(("3" (REWRITE "subs_app") (("3" (ASSERT) NIL NIL)) NIL)) NIL))
NIL))
NIL))
NIL))
NIL)
((|first_order_term_opt| FORMULA-DECL NIL |first_order_terms_properties|
NIL)
(|pair?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|term2| ADT-ACCESSOR-DECL "[(pair?) -> first_order_term]"
|first_order_term_adt| NIL)
(|term1| ADT-ACCESSOR-DECL "[(pair?) -> first_order_term]"
|first_order_term_adt| NIL)
(|app?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|arg| ADT-ACCESSOR-DECL "[(app?) -> first_order_term]"
|first_order_term_adt| NIL)
(|f_sym| ADT-ACCESSOR-DECL "[(app?) -> f_symbol]" |first_order_term_adt|
NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL))
SHOSTAK))
(|subs_pair2| 0
(|subs_pair2-1| NIL 3922736536
("" (INDUCT "sigma")
(("1" (GRIND) NIL NIL)
("2" (SKOLEM 1 ("hd" "tail"))
(("2" (PROP)
(("2" (SKEEP)
(("2" (EXPAND "subs" -2)
(("2" (INST -1 "t")
(("2" (GRIND)
(("2" (EXPAND "subs" -1 1)
(("2" (GRIND)
(("2" (LEMMA "subs_var")
(("2" (INST? -1) (("2" (ASSERT) NIL NIL)) NIL)) NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL)
((|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|var?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|pair?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL))
SHOSTAK))
(|subs_func| 0
(|subs_func-1| NIL 3922736536
("" (MEASURE-INDUCT "size(t)" "t")
(("" (SKOLEM 1 "t")
(("" (PROP)
(("" (SKEEP)
(("" (LEMMA "first_order_term_opt")
(("" (INST? -1)
(("" (PROP)
(("1" (REPLACE -2 -4)
(("1" (REWRITE "subs_const") (("1" (GRIND) NIL NIL)) NIL))
NIL)
("2" (REPLACE -1 -3)
(("2" (REWRITE "subs_unit") (("2" (GRIND) NIL NIL)) NIL))
NIL)
("3" (REPLACE -2 -4)
(("3" (REWRITE "subs_pair") (("3" (GRIND) NIL NIL)) NIL))
NIL)
("4" (REPLACE -2 -4)
(("4" (REWRITE "subs_app")
(("4" (HIDE -2)
(("4" (HIDE -2)
(("4" (LEMMA "first_order_term_app_eta")
(("4" (INST? -1)
(("4" (REPLACE -1 1 :DIR RL)
(("4" (REWRITE "subs_app")
(("4" (GRIND) NIL NIL)) NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL)
((|first_order_term_app_eta| FORMULA-DECL NIL |first_order_term_adt| NIL)
(|ord| CONST-DECL "upto(4)" |first_order_term_adt| NIL)
(|sym| CONST-DECL "string" |first_order_terms_properties| NIL)
(|arg| ADT-ACCESSOR-DECL "[(app?) -> first_order_term]"
|first_order_term_adt| NIL)
(|f_sym| ADT-ACCESSOR-DECL "[(app?) -> f_symbol]" |first_order_term_adt|
NIL)
(|pair?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|term2| ADT-ACCESSOR-DECL "[(pair?) -> first_order_term]"
|first_order_term_adt| NIL)
(|term1| ADT-ACCESSOR-DECL "[(pair?) -> first_order_term]"
|first_order_term_adt| NIL)
(|const?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|a| ADT-ACCESSOR-DECL "[(const?) -> constant]" |first_order_term_adt| NIL)
(|first_order_term_opt| FORMULA-DECL NIL |first_order_terms_properties|
NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|var?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|same_func?| CONST-DECL "bool" |first_order_terms_properties| NIL)
(|app?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL))
SHOSTAK))
(|subs_ord| 0
(|subs_ord-1| NIL 3922736536
("" (SKEEP)
(("" (LEMMA "first_order_term_opt")
(("" (INST?)
(("" (ASSERT)
(("" (SPLIT -1)
(("1" (FLATTEN)
(("1" (REPLACE -2 -3)
(("1" (REWRITE "subs_const") (("1" (GRIND) NIL NIL)) NIL))
NIL))
NIL)
("2" (FLATTEN) (("2" (GRIND) NIL NIL)) NIL)
("3" (REPLACE -1)
(("3" (REWRITE "subs_unit") (("3" (GRIND) NIL NIL)) NIL)) NIL)
("4" (FLATTEN)
(("4" (REPLACE -2 -3)
(("4" (REWRITE "subs_pair") (("4" (GRIND) NIL NIL)) NIL)) NIL))
NIL)
("5" (FLATTEN)
(("5" (REPLACE -2 -3)
(("5" (REWRITE "subs_app") (("5" (GRIND) NIL NIL)) NIL)) NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL)
((|first_order_term_opt| FORMULA-DECL NIL |first_order_terms_properties|
NIL)
(|app?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|arg| ADT-ACCESSOR-DECL "[(app?) -> first_order_term]"
|first_order_term_adt| NIL)
(|f_sym| ADT-ACCESSOR-DECL "[(app?) -> f_symbol]" |first_order_term_adt|
NIL)
(|pair?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|term2| ADT-ACCESSOR-DECL "[(pair?) -> first_order_term]"
|first_order_term_adt| NIL)
(|term1| ADT-ACCESSOR-DECL "[(pair?) -> first_order_term]"
|first_order_term_adt| NIL)
(|ord| CONST-DECL "upto(4)" |first_order_term_adt| NIL)
(|const?| ADT-RECOGNIZER-DECL "[first_order_term -> boolean]"
|first_order_term_adt| NIL)
(|a| ADT-ACCESSOR-DECL "[(const?) -> constant]" |first_order_term_adt| NIL)
(|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL))
SHOSTAK))
(|subs_mem| 0
(|subs_mem-1| NIL 3922736538
("" (INDUCT "args")
(("1" (GRIND) NIL NIL)
("2" (SKOLEM 1 ("hd" "tail"))
(("2" (PROP)
(("2" (SKEEP)
(("2" (EXPAND "subs" 1 1)
(("2" (EXPAND "member" 1 2)
(("2" (INST -1 "sigma" "t")
(("2" (EXPAND "member" 1 1)
(("2" (SPLIT 1)
(("1" (FLATTEN)
(("1" (SPLIT -1)
(("1" (INST 1 "hd") NIL NIL)
("2" (ASSERT)
(("2" (SKOLEM -2 "s") (("2" (GRIND) NIL NIL)) NIL))
NIL))
NIL))
NIL)
("2" (FLATTEN)
(("2" (SKOLEM -1 "s") (("2" (GRIND) NIL NIL)) NIL)) NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL))
NIL)
((|variable| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|constant| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|first_order_term| TYPE-DECL NIL |first_order_term_adt| NIL)
(|f_symbol| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL)
(|args| TYPE-EQ-DECL NIL |first_order_terms_properties| NIL))
SHOSTAK))
(|subs_len| 0
(|subs_len-1| NIL 3922736538
("" (INDUCT "args")
(("1" (GRIND) NIL NIL)