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(* const-decl "Vector" vectors "vectors/")
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(- const-decl "real" vectors "vectors/")
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(- const-decl "[numfield -> numfield]" number_fields nil)
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real_props nil)
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nil)
(cv_scal-2 nil 3459517322
(";;; Proof cv_scal-1 for formula limit_vect2_real.cv_scal"
(skosimp)
((";;; Proof cv_scal-1 for formula limit_vect2_real.cv_scal"
(rewrite "scal_function")
((";;; Proof cv_scal-1 for formula limit_vect2_real.cv_scal"
(rewrite "cv_prod")
((";;; Proof cv_scal-1 for formula limit_vect2_real.cv_scal"
(hide 2)
((";;; Proof cv_scal-1 for formula limit_vect2_real.cv_scal"
(rewrite "cv_const") nil))))))))
";;; developed with shostak decision procedures")
nil nil)
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(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))
nil))
(lim_scal_fun 0
(lim_scal_fun-1 nil 3459529190
("" (skosimp*)
(("" (lemma "scal_fun_convergent")
(("" (inst - "a!1" "f!1" "k!1")
(("" (prop)
(("" (lemma "lim_fun_def")
((""
(inst - "(LAMBDA (v): k!1 * f!1(v))" "k!1 * lim(f!1,a!1)"
"a!1")
(("" (replace -1)
(("" (lemma "lim_fun_def")
(("" (inst - "f!1" "lim(f!1,a!1)" "a!1")
(("" (prop)
(("" (lemma "cv_scal")
(("" (inst - "a!1" "f!1" "k!1" "lim(f!1,a!1)")
(("" (prop) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((scal_fun_convergent formula-decl nil limit_vect nil)
(* const-decl "Vector" vectors "vectors/")
(convergent? const-decl "bool" limit_vect nil)
(lim const-decl "Vector[m]" limit_vect nil)
(cv_scal formula-decl nil limit_vect nil)
(lim_fun_def formula-decl nil limit_vect nil)
(m formal-const-decl "posnat" limit_vect nil)
(Vector type-eq-decl nil vectors "vectors/")
(Index type-eq-decl nil vectors "vectors/")
(n formal-const-decl "posnat" limit_vect nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(< const-decl "bool" reals 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))
shostak)))
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