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real_types nil)
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"(strict_total_order?[real])" real_props nil)
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shostak))
(sqrt_derivable_fun_TCC2 0
(sqrt_derivable_fun_TCC2-1 nil 3262649447
("" (expand "not_one_element?")
(("" (skolem!) (("" (inst + "x!1+1") (("" (assert) nil nil)) nil))
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(not_one_element? const-decl "bool" deriv_domain_def nil))
shostak))
(sqrt_derivable_fun 0
(sqrt_derivable_fun-1 nil 3262648257
(""
(lemma "inverse_derivable_fun"
("F" "LAMBDA (x:posreal):sq(x)" "G" "LAMBDA (x:posreal):sqrt(x)"
"f" "LAMBDA (x:posreal): 2*x"))
(("1" (split -1)
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nil))
nil))
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nil))
nil))
nil))
nil)
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(("4"
(lemma "deriv_prod_fun"
("ff1" "LAMBDA (x: posreal): x" "ff2"
"LAMBDA (x: posreal): x"))
(("1" (expand "*")
(("1" (expand "+")
(("1" (replace -2 -1)
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nil))
nil))
nil)
("2" (lemma "identity_derivable_fun[posreal]")
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nil))
nil))
nil))
nil)
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(("5" (expand "inverse?")
(("5" (skosimp*) (("5" (rewrite "sq_sqrt") nil nil)) nil))
nil))
nil))
nil)
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(("2" (skosimp*)
(("2" (inst + "x!1+1") (("2" (assert) nil nil)) nil)) nil))
nil)
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(("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil))
nil)
((real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
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(restrict const-decl "R" restrict nil)
(I const-decl "(bijective?[T, T])" identity nil)
(* const-decl "[T -> real]" real_fun_ops "reals/")
(prod_derivable_fun formula-decl nil derivatives nil)
(identity_derivable_fun formula-decl nil derivatives nil)
(bijective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(sq_sqrt formula-decl nil sqrt "reals/")
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(injective? const-decl "bool" functions nil)
(sq_eq formula-decl nil sq "reals/")
(deriv_prod_fun formula-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil)
(deriv_fun type-eq-decl nil derivatives nil)
(+ const-decl "[T -> real]" real_fun_ops "reals/")
(deriv_id_fun formula-decl nil derivatives nil)
(inverse? const-decl "bool" function_inverse_def nil)
(not_one_element? const-decl "bool" deriv_domain_def nil)
(connected? const-decl "bool" deriv_domain_def nil)
(sq_nz_pos application-judgement "posreal" sq "reals/")
(sqrt_pos application-judgement "posreal" sqrt "reals/")
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(inverse_derivable_fun formula-decl nil derivative_inverse nil)
(sq const-decl "nonneg_real" sq "reals/")
(nnreal type-eq-decl nil real_types nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt "reals/")
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(nzreal nonempty-type-eq-decl nil reals 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)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
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(nonneg_real nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil))
shostak))
(deriv_sqrt_fun_TCC1 0
(deriv_sqrt_fun_TCC1-1 nil 3262649471
("" (lemma "sqrt_derivable_fun") (("" (propax) nil nil)) nil)
((sqrt_derivable_fun formula-decl nil sqrt_derivative nil))
shostak))
(deriv_sqrt_fun 0
(deriv_sqrt_fun-1 nil 3262649090
("" (lemma "sqrt_derivable_fun")
((""
(lemma "deriv_inverse_fun[posreal,posreal]"
("F" "LAMBDA (x:posreal): sq(x)" "G"
"LAMBDA (x:posreal): sqrt(x)" "f" "LAMBDA (x:posreal):2*x"))
(("1" (split -1)
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(lemma "prod_derivable_fun"
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(lemma "deriv_prod_fun"
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(("1" (lemma "deriv_id_fun[posreal]")
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(("1" (replace -1)
(("1" (expand "*")
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(("1" (propax) nil nil)) nil))
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(("4" (expand "injective?")
(("4" (expand "surjective?")
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(("2" (inst + "sqrt(y!1)")
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nil))
nil))
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nil))
nil))
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("5" (hide-all-but 1)
(("5" (expand "inverse?")
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real_props nil)
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(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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shostak))
(deriv_sqrt 0
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("" (lemma "sqrt_derivable_fun")
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real_types nil)
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shostak))
(sqrt_continuous 0
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("" (rewrite "derivable_cont_fun[posreal]")
(("" (hide 2) (("" (rewrite "sqrt_derivable_fun") nil nil)) nil))
nil)
((sqrt_derivable_fun formula-decl nil sqrt_derivative nil)
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(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(= const-decl "[T, T -> boolean]" equalities nil)
(nnreal type-eq-decl nil real_types nil)
(restrict const-decl "R" restrict nil)
(derivable_cont_fun formula-decl nil derivatives nil))
shostak)))
¤ Dauer der Verarbeitung: 0.26 Sekunden
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