(composition_continuous
(composition_cont 0
(composition_cont-1 nil 3473169490
("" (skosimp*)
(("" (expand "continuous?")
(("" (skosimp*)
(("" (inst -2 "epsilon!1")
(("" (expand "o ")
(("" (skosimp*)
(("" (inst - "delta!1")
(("" (skolem!)
(("" (inst 1 "delta!2")
(("" (skosimp)
(("" (inst - "x!1")
(("" (assert)
(("" (inst - "f!1(x!1)")
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((real_minus_real_is_real application-judgement "real" reals nil)
(continuous? const-decl "bool" continuous_functions 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)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals 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)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(T2_pred const-decl "[real -> boolean]" composition_continuous nil)
(T2 formal-subtype-decl nil composition_continuous nil)
(T1_pred const-decl "[real -> boolean]" composition_continuous nil)
(T1 formal-subtype-decl nil composition_continuous nil)
(O const-decl "T3" function_props nil))
nil))
(composition_cont_set 0
(composition_cont_set-1 nil 3473169490
("" (skosimp*)
(("" (rewrite "continuous_on_def")
(("" (rewrite "continuous_on_def")
(("" (rewrite "continuous_on_def")
(("" (skosimp*)
(("" (grind :exclude ("convergence") :if-match nil)
(("" (inst?)
(("" (assert)
(("" (inst?)
(("1" (grind :exclude ("abs" "adh") :if-match nil)
(("1" (inst? -6)
(("1" (skolem!)
(("1" (inst -4 "delta!1")
(("1" (skolem!)
(("1"
(inst 1 "delta!2")
(("1"
(skosimp)
(("1"
(inst -4 "x!1")
(("1"
(inst -6 "f!1(x!1)")
(("1"
(assert)
(("1" (inst?) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2" (inst?)
(("2" (hide-all-but 1)
(("2" (typepred "y!1")
(("2" (expand "restrict")
(("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
nil nil))
(composition_cont_fun 0
(composition_cont_fun-1 nil 3473169490
("" (grind :defs nil :rewrites ("continuous_def2[T1]"))
(("" (rewrite "composition_cont_set")
(("1" (rewrite "continuity_subset2[T2]")
(("1" (delete -1 -2 2 3) (("1" (grind) nil)))))
("2" (rewrite "subset_reflexive") nil))))
nil)
((subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil)
(composition_cont_set formula-decl nil composition_continuous nil)
(bool nonempty-type-eq-decl nil booleans nil)
(setof type-eq-decl nil defined_types nil)
(set type-eq-decl nil sets nil)
(subset? const-decl "bool" sets nil)
(T2_pred const-decl "[real -> boolean]" composition_continuous nil)
(T2 formal-subtype-decl nil composition_continuous nil)
(continuity_subset2 formula-decl nil continuous_functions nil)
(restrict const-decl "R" restrict nil)
(Im const-decl "setof[real]" real_fun_props "reals/")
(subset_reflexive formula-decl nil sets_lemmas nil)
(continuous_def2 formula-decl nil continuous_functions 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)
(T1_pred const-decl "[real -> boolean]" composition_continuous nil)
(T1 formal-subtype-decl nil composition_continuous nil))
nil)))
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