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(csequence_singleton
(singleton_is_nonempty_finite 0
(singleton_is_nonempty_finite-1 nil 3513602144
("" (skolem-typepred)
(("" (expand* "singleton_cseq?" "is_finite" "is_finite")
(("" (ground) nil nil)) nil))
nil)
((is_finite inductive-decl "bool" csequence_props nil)
(singleton_cseq? const-decl "bool" csequence_singleton nil)
(csequence type-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_singleton nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(singleton_cseq_length_TCC1 0
(singleton_cseq_length_TCC1-1 nil 3513602144
("" (skosimp)
(("" (use "singleton_is_nonempty_finite") (("" (flatten) nil nil))
nil))
nil)
((singleton_is_nonempty_finite judgement-tcc nil csequence_singleton
nil)
(T formal-type-decl nil csequence_singleton nil)
(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(singleton_cseq? const-decl "bool" csequence_singleton nil)
(cseq!1 skolem-const-decl "csequence[T]" csequence_singleton nil))
nil))
(singleton_cseq_length 0
(singleton_cseq_length-1 nil 3513602213 ("" (grind) nil nil)
((posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(T formal-type-decl nil csequence_singleton nil)
(singleton_cseq? const-decl "bool" csequence_singleton nil))
shostak))
(singleton_cseq_index 0
(singleton_cseq_index-1 nil 3513602225
("" (skolem-typepred)
(("" (expand* "singleton_cseq?" "index?" "index?")
(("" (ground) nil nil)) nil))
nil)
((index? def-decl "bool" csequence_nth nil)
(int_minus_int_is_int application-judgement "int" integers 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)
(singleton_cseq? const-decl "bool" csequence_singleton nil)
(csequence type-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_singleton nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
shostak))
(singleton_cseq_TCC1 0
(singleton_cseq_TCC1-1 nil 3513602144 ("" (subtype-tcc) nil nil)
((singleton_cseq? const-decl "bool" csequence_singleton nil)) nil))
(singleton_def_TCC1 0
(singleton_def_TCC1-1 nil 3513602144 ("" (subtype-tcc) nil nil)
((singleton_cseq? const-decl "bool" csequence_singleton nil)) nil))
(singleton_def 0
(singleton_def-1 nil 3513602256 ("" (grind-with-ext) nil nil)
((add adt-constructor-decl "[[T, csequence] -> (nonempty?)]"
csequence_codt nil)
(first adt-accessor-decl "[(nonempty?) -> T]" csequence_codt nil)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
nil)
(empty_cseq adt-constructor-decl "(empty?)" csequence_codt nil)
(csequence_add_extensionality formula-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_singleton nil)
(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(singleton_cseq? const-decl "bool" csequence_singleton nil)
(singleton_cseq const-decl "(singleton_cseq?)" csequence_singleton
nil))
shostak))
(singleton_cseq_first 0
(singleton_cseq_first-1 nil 3513602271 ("" (grind) nil nil)
((singleton_cseq const-decl "(singleton_cseq?)" csequence_singleton
nil))
shostak))
(singleton_cseq_rest 0
(singleton_cseq_rest-1 nil 3513602276 ("" (grind) nil nil)
((singleton_cseq const-decl "(singleton_cseq?)" csequence_singleton
nil))
shostak))
(singleton_cseq_last 0
(singleton_cseq_last-1 nil 3513602279 ("" (grind) nil nil)
((singleton_cseq const-decl "(singleton_cseq?)" csequence_singleton
nil)
(T formal-type-decl nil csequence_singleton nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(nth def-decl "T" csequence_nth nil)
(last const-decl "T" csequence_nth nil))
shostak))
(singleton_cseq_some 0
(singleton_cseq_some-1 nil 3513602283
("" (expand* "singleton_cseq" "some" "some") nil nil)
((some inductive-decl "boolean" csequence_codt nil)
(singleton_cseq const-decl "(singleton_cseq?)" csequence_singleton
nil))
shostak))
(singleton_cseq_every 0
(singleton_cseq_every-1 nil 3513602321
("" (expand* "singleton_cseq" "every" "every") nil nil)
((every coinductive-decl "boolean" csequence_codt nil)
(singleton_cseq const-decl "(singleton_cseq?)" csequence_singleton
nil))
shostak)))
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