|
(min (cauchy_min_TCC1 0
(cauchy_min_TCC1-1 nil 3251054266
("" (skosimp*)
(("" (typepred "cx!1")
(("" (typepred "cy!1")
(("" (expand "cauchy_real?")
(("" (skosimp*)
(("" (inst + "min(x!1,x!2)")
(("" (expand "cauchy_prop")
(("" (skosimp*)
(("" (inst - "p!1")
(("" (inst - "p!1")
(("" (lemma "expt_pos" ("px" "2" "i" "p!1"))
(("" (case "cx!1(p!1) < cy!1(p!1)")
(("1"
(lemma
"both_sides_times_pos_lt1"
("x" "x!1" "y" "x!2" "pz" "2^p!1"))
(("1" (grind) nil nil))
nil)
("2"
(lemma
"both_sides_times_pos_lt1"
("x" "x!2" "y" "x!1" "pz" "2^p!1"))
(("2" (grind) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
(<= const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(< const-decl "bool" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_times_real_is_real application-judgement "real" reals
nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(real_minus_real_is_real application-judgement "real" reals
nil)
(^ const-decl "real" exponentiation nil)
(/= const-decl "boolean" notequal nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(both_sides_times_pos_lt1 formula-decl nil real_props nil)
(real_plus_real_is_real application-judgement "real" reals 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)
(expt_pos formula-decl nil exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(int_min application-judgement "{k: int | k <= i AND k <= j}"
real_defs nil)
(posint_exp application-judgement "posint" exponentiation nil))
shostak))
(min_lemma 0
(min_lemma-1 nil 3251053661
("" (expand "cauchy_min")
(("" (expand "cauchy_prop")
(("" (skosimp*)
(("" (case "cx!1(p!1))
(("1" (replace -1)
(("1" (inst - "p!1")
(("1" (inst - "p!1")
(("1" (lemma "expt_pos" ("px" "2" "i" "p!1"))
(("1"
(lemma "both_sides_times_pos_lt1"
("x" "y!1" "y" "x!1" "pz" "2^p!1"))
(("1" (grind) nil nil)) nil))
nil))
nil))
nil))
nil)
("2" (replace 1)
(("2" (lemma "expt_pos" ("px" "2" "i" "p!1"))
(("2" (inst - "p!1")
(("2" (inst - "p!1")
(("2"
(lemma "both_sides_times_pos_lt1"
("x" "x!1" "y" "y!1" "pz" "2^p!1"))
(("2" (grind) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((posint_exp application-judgement "posint" exponentiation nil)
(int_min application-judgement "{k: int | k <= i AND k <= j}"
real_defs nil)
(cauchy_prop const-decl "bool" cauchy nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(< 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)
(both_sides_times_pos_lt1 formula-decl nil real_props nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(/= const-decl "boolean" notequal nil)
(^ const-decl "real" exponentiation nil)
(min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(real_times_real_is_real application-judgement "real" reals
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)
(expt_pos formula-decl nil exponentiation nil)
(real_minus_real_is_real application-judgement "real" reals
nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(cauchy_min const-decl "cauchy_real" min nil))
shostak)))
¤ Dauer der Verarbeitung: 0.4 Sekunden
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