|
(deriv_domains
(IMP_derivatives_def_TCC1 0
(IMP_derivatives_def_TCC1-1 nil 3471264254 3477816156
("" (expand "deriv_domain?")
(("" (skosimp*) (("" (inst + e!1/2) (("" (grind) nil nil)) nil))
nil))
nil)
proved
((abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
real_defs nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(>= const-decl "bool" reals nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(TRUE const-decl "bool" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(/= const-decl "boolean" notequal 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)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(deriv_domain? const-decl "bool" deriv_domain_def nil))
33333 60 t nil))
(IMP_derivatives_def_TCC2 0
(IMP_derivatives_def_TCC2-1 nil 3471264254 3477816177
("" (expand "not_one_element?")
(("" (skosimp*) (("" (inst + "x!1+1") (("" (assert) nil nil)) nil))
nil))
nil)
proved
((+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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)
(real_plus_real_is_real application-judgement "real" reals nil)
(not_one_element? const-decl "bool" deriv_domain_def nil))
17936 30 t nil))
(IMP_derivatives_def_TCC3 0
(IMP_derivatives_def_TCC3-1 nil 3471264323 3477816197
("" (expand "deriv_domain?")
(("" (skosimp*)
(("" (typepred "x!1")
(("" (inst + "min(abs(x!1/2),e!1/2)")
(("1" (grind) nil nil) ("2" (grind) nil nil)) nil))
nil))
nil))
nil)
proved
((real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
real_defs nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posreal_min application-judgement
"{z: posreal | z <= x AND z <= y}" real_defs nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(e!1 skolem-const-decl "posreal" deriv_domains nil)
(x!1 skolem-const-decl "posreal" deriv_domains nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
(<= const-decl "bool" reals nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers 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)
(>= 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)
(deriv_domain? const-decl "bool" deriv_domain_def nil)
(real_plus_real_is_real application-judgement "real" reals nil))
15573 190 t nil))
(IMP_derivatives_def_TCC4 0
(IMP_derivatives_def_TCC4-1 nil 3471264323 3477816210
("" (expand "not_one_element?")
(("" (skosimp*) (("" (inst + "x!1+1") (("" (assert) nil nil)) nil))
nil))
nil)
proved
((+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(not_one_element? const-decl "bool" deriv_domain_def nil))
9534 40 t nil))
(IMP_derivatives_def_TCC5 0
(IMP_derivatives_def_TCC5-1 nil 3471264606 3477816225
("" (expand "deriv_domain?")
(("" (skosimp*)
(("" (typepred "x!1")
(("" (inst + -e!1/2) (("" (grind) nil nil)) nil)) nil))
nil))
nil)
proved
((real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(minus_nzreal_is_nzreal application-judgement "nzreal" real_types
nil)
(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil)
(/= const-decl "boolean" notequal nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields 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)
(nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
real_defs nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers 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)
(<= const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(deriv_domain? const-decl "bool" deriv_domain_def nil)
(real_plus_real_is_real application-judgement "real" reals nil))
7893 100 t nil))
(IMP_derivatives_def_TCC6 0
(IMP_derivatives_def_TCC6-1 nil 3471264606 3477816240
("" (expand "not_one_element?")
(("" (skosimp*) (("" (inst + "x!1-1") (("" (assert) nil nil)) nil))
nil))
nil)
proved
((- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(real_minus_real_is_real application-judgement "real" reals nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(not_one_element? const-decl "bool" deriv_domain_def nil))
10837 30 t nil))
(IMP_derivatives_def_TCC7 0
(IMP_derivatives_def_TCC7-1 nil 3471611038 3477816253
("" (expand "deriv_domain?")
(("" (skosimp*)
(("" (typepred "x!1")
(("" (flatten)
(("" (case "x!1 > 0")
(("1" (inst-cp + e!1/2)
(("1" (grind) nil nil)
("2" (flatten) (("2" (assert) nil nil)) nil))
nil)
("2" (inst-cp + -e!1/2)
(("1" (grind) nil nil)
("2" (flatten) (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
proved
((minus_nzreal_is_nzreal application-judgement "nzreal" real_types
nil)
(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(x!1 skolem-const-decl "nzreal" deriv_domains nil)
(e!1 skolem-const-decl "posreal" deriv_domains nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(>= const-decl "bool" reals nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
real_defs nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(> const-decl "bool" reals nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers nil)
(/= const-decl "boolean" notequal 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)
(nzreal nonempty-type-eq-decl nil reals nil)
(deriv_domain? const-decl "bool" deriv_domain_def nil)
(real_plus_real_is_real application-judgement "real" reals nil))
8762 130 t nil))
(IMP_derivatives_def_TCC8 0
(IMP_derivatives_def_TCC8-1 nil 3471611038 3477816266
("" (expand "not_one_element?")
(("" (skosimp*)
(("" (typepred "x!1")
(("" (flatten)
(("" (inst + "x!1/2") (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil)
proved
((numfield nonempty-type-eq-decl nil number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers nil)
(/= const-decl "boolean" notequal 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)
(nzreal nonempty-type-eq-decl nil reals nil)
(not_one_element? const-decl "bool" deriv_domain_def nil))
9520 40 t nil)))
¤ Dauer der Verarbeitung: 0.19 Sekunden
(vorverarbeitet)
¤
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