(sub
(sub_lemma 0
(sub_lemma-1 nil 3251041975
("" (skosimp*)
(("" (expand "cauchy_sub" )
(("" (lemma "neg_lemma" ("x" "y!1" "cx" "cy!1" ))
((""
(lemma "add_lemma"
("x" "x!1" "y" "-y!1" "cx" "cx!1" "cy" "cauchy_neg(cy!1)" ))
(("" (assert ) nil nil )) nil ))
nil ))
nil ))
nil )
((cauchy_sub const-decl "cauchy_real" sub nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(cauchy_neg const-decl "cauchy_real" neg nil )
(add_lemma formula-decl nil add nil )
(minus_real_is_real application-judgement "real" reals nil )
(real_minus_real_is_real application-judgement "real" reals nil )
(neg_lemma formula-decl nil neg 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 )
(cauchy_real? const-decl "bool" cauchy nil )
(cauchy_real nonempty-type-eq-decl nil cauchy nil ))
shostak)))
quality 100%
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