|
(derivative_props
(deriv_domain 0
(deriv_domain-1 nil 3472398507
("" (lemma "connected_deriv_domain[T]")
(("" (lemma connected_domain)
(("" (lemma not_one_element) (("" (assert) nil nil)) nil)) nil))
nil)
((connected_domain formula-decl nil derivative_props nil)
(not_one_element formula-decl nil derivative_props nil)
(connected_deriv_domain formula-decl nil deriv_domain_def 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)
(T_pred const-decl "[real -> boolean]" derivative_props nil)
(T formal-subtype-decl nil derivative_props nil))
shostak))
(deriv_maximum_TCC1 0
(deriv_maximum_TCC1-1 nil 3601996896
("" (skeep)
(("" (lemma "deriv_domain") (("" (propax) nil nil)) nil)) nil)
((deriv_domain formula-decl nil derivative_props nil)) nil))
(deriv_maximum_TCC2 0
(deriv_maximum_TCC2-1 nil 3601996896
("" (lemma "not_one_element") (("" (skosimp*) nil nil)) nil)
((not_one_element formula-decl nil derivative_props nil)) nil))
(deriv_maximum 0
(deriv_maximum-1 nil 3297598424
("" (skosimp*)
(("" (auto-rewrite "deriv_TCC[T]")
(("" (expand "deriv")
(("" (expand "derivable?")
(("" (assert)
(("" (rewrite "lim_fun_def[(A[T](c!1))]")
(("" (expand "convergent?")
(("" (skolem!)
(("" (case "l!1 <= 0 AND 0 <= l!1")
(("1" (ground) nil nil)
("2" (delete 2)
(("2" (expand "convergence")
(("2" (split)
(("1"
(name "E"
"{ x : real| 0 < x AND x < b!1 - c!1}")
(("1" (case "adh[(A[T](c!1))](E)(0)")
(("1"
(assert)
(("1"
(use
"convergence_upper_bound[(A[T](c!1))]"
("f" "NQ(f!1, c!1)" "E" "E"))
(("1"
(ground)
(("1"
(use
"subset_convergence2[(A[T](c!1))]"
("E1" "E" "E2" "fullset[real]"))
(("1"
(assert)
(("1"
(rewrite "subset_fullset")
nil
nil))
nil))
nil)
("2"
(replace -2 + rl)
(("2"
(delete -1 -2 -3 -4 -5 2)
(("2"
(grind :if-match nil)
(("2"
(inst? -4)
(("2"
(assert)
(("2"
(rewrite
"div_mult_pos_le1")
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(replace -1 + rl)
(("2"
(delete -1 -2 -4 -5 2)
(("2"
(grind
:exclude
"abs"
:if-match
nil)
(("2"
(inst
1
"min(e!1/2, (b!1-c!1)/2)")
(("1" (grind) nil nil)
("2"
(grind)
(("1"
(lemma "connected_domain")
(("1"
(expand "connected?")
(("1"
(inst - "c!1" "b!1" "_")
(("1"
(inst?)
(("1"
(assert)
nil
nil))
nil))
nil))
nil))
nil)
("2"
(lemma "connected_domain")
(("2"
(expand "connected?")
(("2"
(inst - "c!1" "b!1" "_")
(("2"
(inst?)
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(name "E"
"{ x : real | a!1 - c!1 < x AND x < 0}")
(("2" (case "adh[(A[T](c!1))](E)(0)")
(("1"
(assert)
(("1"
(use
"convergence_lower_bound[(A[T](c!1))]"
("f" "NQ(f!1, c!1)" "E" "E"))
(("1"
(ground)
(("1"
(use
"subset_convergence2[(A[T](c!1))]"
("E1" "E" "E2" "fullset[real]"))
(("1"
(assert)
(("1"
(rewrite "subset_fullset")
nil
nil))
nil))
nil)
("2"
(replace -2 + rl)
(("2"
(delete -1 -2 -3 -4 -5 2)
(("2"
(grind :if-match nil)
(("2"
(inst? -4)
(("2"
(assert)
(("2"
(rewrite
"div_mult_neg_le2")
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(replace -1 + rl)
(("2"
(delete -1 -3 -4 -5 2)
(("2"
(grind
:exclude
"abs"
:if-match
nil)
(("2"
(inst
1
"max(-e!1/2, (a!1 - c!1)/2)")
(("1" (grind) nil nil)
("2"
(grind)
(("1"
(lemma "connected_domain")
(("1"
(expand "connected?")
(("1"
(inst - "a!1" "c!1" "_")
(("1"
(inst?)
(("1"
(assert)
nil
nil))
nil))
nil))
nil))
nil)
("2"
(lemma "connected_domain")
(("2"
(expand "connected?")
(("2"
(inst - "a!1" "c!1" "_")
(("2"
(inst?)
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((derivable? const-decl "bool" derivatives_def nil)
(connected? const-decl "bool" deriv_domain_def nil)
(deriv const-decl "real" derivatives_def nil))
nil))
(deriv_minimum 0
(deriv_minimum-1 nil 3297598424
("" (skosimp)
(("" (use "deriv_maximum" ("f" "-f!1"))
(("" (auto-rewrite "neg_derivable[T]" "deriv_neg[T]")
(("" (assert)
(("" (delete -1 -2 -3 2)
(("" (grind :if-match nil)
(("" (inst?) (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil)
((deriv_maximum formula-decl nil derivative_props 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)
(T_pred const-decl "[real -> boolean]" derivative_props nil)
(T formal-subtype-decl nil derivative_props nil)
(- const-decl "[T -> real]" real_fun_ops "reals/")
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(neg_derivable formula-decl nil derivatives_def nil)
(deriv_neg formula-decl nil derivatives_def nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(minus_real_is_real application-judgement "real" reals nil))
nil))
(mean_value_aux_TCC1 0
(mean_value_aux_TCC1-1 nil 3297598424
("" (lemma "deriv_domain") (("" (propax) nil nil)) nil)
((deriv_domain formula-decl nil derivative_props nil)) nil))
(mean_value_aux_TCC2 0
(mean_value_aux_TCC2-1 nil 3601996896
("" (lemma "not_one_element") (("" (propax) nil nil)) nil)
((not_one_element formula-decl nil derivative_props nil)) nil))
(mean_value_aux_TCC3 0
(mean_value_aux_TCC3-1 nil 3601996896
("" (skosimp*)
(("" (expand "derivable?") (("" (inst?) nil nil)) nil)) nil)
((derivable? const-decl "bool" derivatives 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)
(T_pred const-decl "[real -> boolean]" derivative_props nil)
(T formal-subtype-decl nil derivative_props nil))
nil))
(mean_value_aux 0
(mean_value_aux-1 nil 3297598424
("" (skosimp)
((""
(case "FORALL (x : T) : a!1 <= x AND x <= b!1 IMPLIES f!1(x) = f!1(a!1)")
(("1" (case "T_pred((a!1 + b!1)/2)")
(("1" (inst 1 "(a!1 + b!1)/2")
(("1" (assert)
(("1"
(use "deriv_constant2"
("a" "a!1" "b" "b!1" "c" "(a!1 + b!1)/2"))
(("1" (ground)
(("1" (skosimp)
(("1" (inst-cp -4 "(a!1+b!1)/2")
(("1" (inst -4 "x!1") (("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil)
("2" (lemma "connected_domain")
(("2" (expand "connected?")
(("2" (inst - "a!1" "b!1" "_")
(("2" (inst?) (("2" (assert) nil nil)) nil)) nil))
nil))
nil))
nil)
("2" (skosimp)
(("2" (forward-chain "derivable_cont_fun[T]")
(("2" (case "f!1(x!1) < f!1(a!1)")
(("1" (use "min_in_interval[T]" ("a" "a!1" "b" "b!1"))
(("1" (assert)
(("1" (skosimp)
(("1" (expand "derivable?")
(("1" (inst -8 "c!1")
(("1"
(use "deriv_minimum"
("a" "a!1" "b" "b!1" "c" "c!1"))
(("1" (inst-cp -4 "x!1")
(("1" (assert)
(("1" (inst 2 "c!1")
(("1"
(ground)
(("1"
(skosimp)
(("1"
(inst?)
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "connected_domain")
(("2" (expand "connected?") (("2" (propax) nil nil))
nil))
nil))
nil)
("2" (use "max_in_interval[T]" ("a" "a!1" "b" "b!1"))
(("1" (assert)
(("1" (skosimp)
(("1" (inst-cp -3 "x!1")
(("1" (assert)
(("1" (expand "derivable?")
(("1" (inst -8 "c!1")
(("1"
(use "deriv_maximum"
("a" "a!1" "b" "b!1" "c" "c!1"))
(("1" (inst 3 "c!1")
(("1"
(ground)
(("1"
(skosimp)
(("1"
(inst?)
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "connected_domain")
(("2" (expand "connected?") (("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((connected? const-decl "bool" deriv_domain_def nil)
(derivable_cont_fun formula-decl nil derivatives nil)
(max_in_interval formula-decl nil continuous_functions_props nil)
(min_in_interval formula-decl nil continuous_functions_props nil)
(derivable? const-decl "bool" derivatives nil))
nil))
(mean_value_TCC1 0
(mean_value_TCC1-1 nil 3297598424
("" (skosimp*)
(("" (expand "derivable?" -) (("" (inst?) nil nil)) nil)) nil)
((derivable? const-decl "bool" derivatives 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)
(T_pred const-decl "[real -> boolean]" derivative_props nil)
(T formal-subtype-decl nil derivative_props nil))
nil))
(mean_value 0
(mean_value-2 nil 3445340249
("" (skosimp)
(("" (name-replace "C" "b!1 - a!1" :hide? nil)
(("" (name-replace "B" "f!1(b!1) - f!1(a!1)" :hide? nil)
(("" (assert)
((""
(auto-rewrite-theory "derivatives[T]" :exclude
("derivable?" "deriv") :always? t)
((""
(auto-rewrite-theory "derivatives_def[T]" :exclude
("derivable?" "deriv") :always? t)
((""
(use "mean_value_aux"
("f"
"f!1 - (B/C) * (I[T] - const_fun(a!1::real))"))
(("" (ground)
(("1" (skosimp)
(("1" (inst?)
(("1" (expand "derivable?")
(("1" (inst -6 "c!1")
(("1" (assert)
(("1" (rewrite "deriv_diff[T]")
(("1"
(case-replace "deriv(f!1, c!1)= B/C")
(("1" (rewrite "div_cancel2") nil nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (delete -3 2)
(("2" (grind)
(("2" (case "(B/C) * (b!1 - a!1) = B")
(("1" (assert) nil nil)
("2" (replace -2 1)
(("2" (rewrite "div_cancel2") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((real_minus_real_is_real application-judgement "real" reals nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" 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)
(T_pred const-decl "[real -> boolean]" derivative_props nil)
(T formal-subtype-decl nil derivative_props nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(diff_derivable_fun formula-decl nil derivatives nil)
(scal_derivable formula-decl nil derivatives_def nil)
(diff_derivable formula-decl nil derivatives_def nil)
(const_derivable formula-decl nil derivatives_def nil)
(identity_derivable formula-decl nil derivatives_def nil)
(deriv_diff formula-decl nil derivatives_def nil)
(real_times_real_is_real application-judgement "real" reals nil)
(deriv_identity formula-decl nil derivatives_def nil)
(deriv_const formula-decl nil derivatives_def nil)
(deriv_scal formula-decl nil derivatives_def nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(div_cancel2 formula-decl nil real_props nil)
(derivable? const-decl "bool" derivatives_def nil)
(deriv const-decl "real" derivatives_def nil)
(derivable? const-decl "bool" derivatives nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(derivable_id name-judgement "deriv_fun" derivatives nil)
(id_fun_continuous name-judgement "continuous_fun"
continuous_functions nil)
(derivable_const application-judgement "deriv_fun" derivatives nil)
(const_fun_continuous application-judgement "continuous_fun"
continuous_functions nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(derivable_diff application-judgement "deriv_fun" derivatives nil)
(diff_fun_continuous application-judgement "continuous_fun"
continuous_functions nil)
(derivable_scal application-judgement "deriv_fun" derivatives nil)
(scal_fun_continuous application-judgement "continuous_fun"
continuous_functions nil)
(mean_value_aux formula-decl nil derivative_props nil)
(- const-decl "[T -> real]" real_fun_ops "reals/")
(* const-decl "[T -> real]" real_fun_ops "reals/")
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(bool nonempty-type-eq-decl nil booleans nil)
(bijective? const-decl "bool" functions nil)
(I const-decl "(bijective?[T, T])" identity nil)
(const_fun const-decl "[T -> real]" real_fun_ops "reals/"))
nil)
(mean_value-1 nil 3297598424
("" (skosimp)
(("" (name-replace "C" "b!1 - a!1" :hide? nil)
(("" (name-replace "B" "f!1(b!1) - f!1(a!1)" :hide? nil)
(("" (assert)
((""
(auto-rewrite-theory "derivatives[T]" :exclude
("derivable" "deriv") :always? t)
((""
(auto-rewrite-theory "derivatives_def[T]" :exclude
("derivable" "deriv") :always? t)
((""
(use "mean_value_aux"
("f"
"f!1 - (B/C) * (I[T] - const_fun(a!1::real))"))
(("" (ground)
(("1" (skosimp)
(("1" (inst?)
(("1" (expand "derivable?")
(("1" (inst -6 "c!1")
(("1" (assert)
(("1" (rewrite "deriv_diff[T]")
(("1"
(case-replace "deriv(f!1, c!1)= B/C")
(("1" (rewrite "div_cancel2") nil nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (delete -3 2)
(("2" (grind)
(("2" (case "(B/C) * (b!1 - a!1) = B")
(("1" (assert) nil nil)
("2" (replace -2 1)
(("2" (rewrite "div_cancel2") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((diff_derivable_fun formula-decl nil derivatives nil)
(scal_derivable formula-decl nil derivatives_def nil)
(diff_derivable formula-decl nil derivatives_def nil)
(const_derivable formula-decl nil derivatives_def nil)
(identity_derivable formula-decl nil derivatives_def nil)
(deriv_diff formula-decl nil derivatives_def nil)
(deriv_identity formula-decl nil derivatives_def nil)
(deriv_const formula-decl nil derivatives_def nil)
(deriv_scal formula-decl nil derivatives_def nil)
(deriv const-decl "real" derivatives_def nil)
(derivable_id name-judgement "deriv_fun" derivatives nil)
(id_fun_continuous name-judgement "continuous_fun"
continuous_functions nil)
(derivable_const application-judgement "deriv_fun" derivatives nil)
(const_fun_continuous application-judgement "continuous_fun"
continuous_functions nil)
(derivable_diff application-judgement "deriv_fun" derivatives nil)
(diff_fun_continuous application-judgement "continuous_fun"
continuous_functions nil)
(derivable_scal application-judgement "deriv_fun" derivatives nil)
(scal_fun_continuous application-judgement "continuous_fun"
continuous_functions nil)
(const_fun const-decl "[T -> real]" real_fun_ops "reals/"))
nil))
(mean_value_abs_TCC1 0
(mean_value_abs_TCC1-1 nil 3299345045
("" (skosimp*)
(("" (expand "derivable?" -1) (("" (inst?) nil nil)) nil)) nil)
((derivable? const-decl "bool" derivatives 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)
(T_pred const-decl "[real -> boolean]" derivative_props nil)
(T formal-subtype-decl nil derivative_props nil))
shostak))
(mean_value_abs 0
(mean_value_abs-1 nil 3299344268
("" (skosimp*)
(("" (lemma "mean_value")
(("" (case "a!1 < b!1")
(("1" (inst?)
(("1" (assert)
(("1" (skosimp*)
(("1" (inst + "c!1")
(("1" (expand "min")
(("1" (expand "max")
(("1" (assert)
(("1" (factor -4)
(("1" (case "(b!1 - a!1) = abs(b!1 - a!1)")
(("1" (replace -1 -)
(("1" (assert)
(("1"
(replace -5 + rl)
(("1"
(assert)
(("1"
(rewrite "abs_mult")
(("1" (rewrite "abs_abs") nil nil)
("2"
(expand "derivable?" -6)
(("2" (inst?) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide-all-but 1)
(("2" (grind) nil nil)) nil))
nil)
("2" (expand "derivable?")
(("2" (inst?)
(("2" (expand "derivable?")
(("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (inst - "b!1" "a!1" "f!1")
(("2" (assert)
(("2" (skosimp*)
(("2" (inst + "c!1")
(("2" (expand "min")
(("2" (expand "max")
(("2" (factor -3)
(("1" (case "(a!1 - b!1) = abs(a!1 - b!1)")
(("1" (replace -1 -)
(("1" (lemma "abs_neg")
(("1" (inst - "(f!1(b!1) - f!1(a!1))")
(("1"
(replace -1 + rl)
(("1"
(replace -5 + rl)
(("1"
(rewrite "abs_mult")
(("1"
(rewrite "abs_abs")
(("1"
(assert)
(("1"
(lemma "abs_neg")
(("1"
(inst - "(b!1-a!1)")
(("1" (assert) nil nil))
nil))
nil))
nil))
nil)
("2"
(expand "derivable?" -6)
(("2" (inst?) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide-all-but 1) (("2" (grind) nil nil))
nil))
nil)
("2" (expand "derivable?" -4)
(("2" (inst?) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((derivable? const-decl "bool" derivatives_def nil)
(deriv const-decl "real" derivatives_def nil))
shostak))
(nonneg_derivative_TCC1 0
(nonneg_derivative_TCC1-1 nil 3297598424
("" (skolem-typepred)
(("" (expand "derivable?" -) (("" (inst?) nil nil)) nil)) nil)
((deriv_fun type-eq-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil)
(T formal-subtype-decl nil derivative_props nil)
(T_pred const-decl "[real -> boolean]" derivative_props 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))
nil))
(nonneg_derivative 0
(nonneg_derivative-1 nil 3297598424
("" (skolem-typepred)
(("" (expand "derivable?")
(("" (expand "increasing?")
(("" (prop)
(("1" (skosimp*)
(("1" (expand "deriv")
(("1" (use "lim_ge1[(A[T](x!1))]")
(("1" (ground)
(("1" (expand "derivable?")
(("1" (inst? -2) nil nil)) nil)
("2" (delete -2 2)
(("2" (grind :if-match nil)
(("2" (rewrite "pos_div_ge")
(("2" (ground)
(("1" (inst -2 "x!1 + x!2" "x!1")
(("1" (assert) nil nil)) nil)
("2" (inst -2 "x!1" "x!1+x!2")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp)
(("2" (use "mean_value" ("a" "x!1" "b" "y!1"))
(("2" (ground)
(("2" (skosimp)
(("2" (inst?)
(("2"
(lemma "pos_times_ge"
("x" "deriv(g!1, c!1)" "y" "y!1 - x!1"))
(("1" (assert) nil nil) ("2" (inst?) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((deriv const-decl "real" derivatives_def nil)
(derivable? const-decl "bool" derivatives_def nil)
(increasing? const-decl "bool" real_fun_preds "reals/")
(deriv_fun type-eq-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil))
nil))
(nonpos_derivative 0
(nonpos_derivative-1 nil 3297598424
("" (skolem-typepred)
(("" (expand "derivable?")
(("" (expand "decreasing?")
(("" (prop)
(("1" (skosimp*)
(("1" (expand "deriv")
(("1" (use "lim_le1[(A[T](x!1))]")
(("1" (ground)
(("1" (expand "derivable?")
(("1" (inst? -2) nil nil)) nil)
("2" (delete -2 2)
(("2" (grind :if-match nil)
(("2" (rewrite "neg_div_le")
(("2" (ground)
(("1" (inst -2 "x!1 + x!2" "x!1")
(("1" (assert) nil nil)) nil)
("2" (inst -2 "x!1" "x!1+x!2")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp)
(("2" (use "mean_value" ("a" "x!1" "b" "y!1"))
(("2" (ground)
(("2" (skosimp)
(("2" (inst?)
(("2"
(lemma "neg_times_le"
("x" "deriv(g!1, c!1)" "y" "y!1 - x!1"))
(("1" (assert) nil nil) ("2" (inst?) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((deriv const-decl "real" derivatives_def nil)
(derivable? const-decl "bool" derivatives_def nil)
(decreasing? const-decl "bool" real_fun_preds "reals/")
(deriv_fun type-eq-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil))
nil))
(positive_derivative 0
(positive_derivative-1 nil 3297598424
("" (expand "strict_increasing?")
(("" (skosimp* :preds? t)
(("" (use "mean_value" ("b" "y!1"))
(("" (assert)
(("" (skosimp)
(("" (inst?)
((""
(lemma "pos_times_gt"
("x" "deriv(g!1, c!1)" "y" "y!1 - x!1"))
(("1" (assert) nil nil)
("2" (expand "derivable?" -) (("2" (inst?) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((deriv_fun type-eq-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil)
(T formal-subtype-decl nil derivative_props nil)
(T_pred const-decl "[real -> boolean]" derivative_props 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)
(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)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(deriv const-decl "real" derivatives_def nil)
(derivable? const-decl "bool" derivatives_def nil)
(pos_times_gt formula-decl nil real_props nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(mean_value formula-decl nil derivative_props nil)
(strict_increasing? const-decl "bool" real_fun_preds "reals/"))
nil))
(negative_derivative 0
(negative_derivative-1 nil 3297598424
("" (expand "strict_decreasing?")
(("" (skosimp* :preds? t)
(("" (use "mean_value" ("a" "x!1"))
(("" (assert)
(("" (skosimp)
(("" (inst?)
((""
(lemma "neg_times_lt"
("x" "deriv(g!1, c!1)" "y" "y!1 - x!1"))
(("1" (assert) nil nil)
("2" (expand "derivable?" -) (("2" (inst?) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((deriv_fun type-eq-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil)
(T formal-subtype-decl nil derivative_props nil)
(T_pred const-decl "[real -> boolean]" derivative_props 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)
(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)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(deriv const-decl "real" derivatives_def nil)
(derivable? const-decl "bool" derivatives_def nil)
(neg_times_lt formula-decl nil real_props nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(mean_value formula-decl nil derivative_props nil)
(strict_decreasing? const-decl "bool" real_fun_preds "reals/"))
nil))
(null_derivative 0
(null_derivative-1 nil 3297598424
("" (skolem!)
(("" (prop)
(("1" (skolem!)
(("1" (auto-rewrite "const_derivable_fun[T]" "deriv_const[T]")
(("1" (case-replace "g!1 = const_fun(g!1(x!1))")
(("1" (assert) nil nil)
("2" (delete 2)
(("2" (apply-extensionality :hide? t)
(("2" (grind) nil nil)) nil))
nil))
nil))
nil))
nil)
("2" (case "FORALL (x, y : T) : x < y IMPLIES g!1(x) = g!1(y)")
(("1" (delete -2)
(("1" (expand "constant?")
(("1" (skosimp)
(("1" (inst-cp - "x!1" "y!1")
(("1" (inst - "y!1" "x!1") (("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp)
(("2" (use "mean_value" ("b" "y!1"))
(("2" (assert)
(("2" (skosimp)
(("2" (inst?) (("2" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
((constant? const-decl "bool" real_fun_preds "reals/")
(deriv_const formula-decl nil derivatives_def nil)
(const_fun const-decl "[T -> real]" real_fun_ops "reals/")
(deriv_fun type-eq-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil)
(bool nonempty-type-eq-decl nil booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(T formal-subtype-decl nil derivative_props nil)
(T_pred const-decl "[real -> boolean]" derivative_props 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)
(const_fun_continuous application-judgement "continuous_fun"
continuous_functions nil)
(derivable_const application-judgement "deriv_fun" derivatives nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(mean_value formula-decl nil derivative_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(< const-decl "bool" reals nil))
nil))
(minimum_derivative 0
(minimum_derivative-2 nil 3306078765
("" (skosimp*)
(("" (typepred "g!1")
(("" (lemma "mean_value")
(("" (lemma "trich_lt" ("x" "x!1" "y" "y1!1"))
(("" (split -1)
(("1" (inst -2 "x!1" "y1!1" "g!1")
(("1" (assert)
(("1" (skosimp* -2)
(("1" (expand "deriv" -8)
(("1" (inst - "c!1")
(("1" (assert)
(("1"
(lemma "both_sides_times_pos_gt1"
("pz" "c!1-x!1" "x" "deriv(g!1,c!1)" "y"
"0"))
(("1" (replace -1 -9)
(("1"
(lemma "posreal_times_posreal_is_posreal"
("px" "deriv(g!1,c!1)" "py" "y1!1-x!1"))
(("1" (assert) nil nil)
("2" (assert) nil nil))
nil))
nil)
("2" (expand "derivable?" -6)
(("2" (inst - "c!1") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (propax) nil nil)
("3" (inst -2 "y1!1" "x!1" "g!1")
(("3" (assert)
(("3" (skosimp*)
(("3" (expand "deriv" -7)
(("3" (inst - "c!1")
(("3" (assert)
(("3"
(lemma "both_sides_times_neg_gt1"
("nz" "c!1-x!1" "x" "deriv(g!1,c!1)" "y"
"0"))
(("1"
(lemma "negreal_times_negreal_is_posreal"
("nx" "deriv(g!1,c!1)" "ny" "y1!1-x!1"))
(("1" (assert) nil nil)
("2" (assert)
(("2"
(expand "deriv" 1)
(("2"
(expand "deriv" -1)
(("2"
(expand ">" -1)
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (expand "derivable?" -5)
(("2" (inst - "c!1") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((deriv_fun type-eq-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil)
(T formal-subtype-decl nil derivative_props nil)
(T_pred const-decl "[real -> boolean]" derivative_props 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)
(trich_lt formula-decl nil real_props 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)
(both_sides_times_neg_gt1 formula-decl nil real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(negreal_times_negreal_is_posreal judgement-tcc nil real_types nil)
(deriv const-decl "real" derivatives_def nil)
(derivable? const-decl "bool" derivatives_def nil)
(- 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)
(both_sides_times_pos_gt1 formula-decl nil real_props 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)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(posreal_times_posreal_is_posreal judgement-tcc nil real_types nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(deriv const-decl "[T -> real]" derivatives 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)
(mean_value formula-decl nil derivative_props nil))
nil)
(minimum_derivative-1 nil 3297611200
("" (skosimp*)
(("" (typepred "g!1")
(("" (lemma "mean_value[T]")
(("" (lemma "trich_lt" ("x" "x!1" "y" "y1!1"))
(("" (split -1)
(("1" (inst -2 "x!1" "y1!1" "g!1")
(("1" (assert)
(("1" (skosimp* -2)
(("1" (expand "deriv" -8)
(("1" (inst - "c!1")
(("1" (assert)
(("1"
(lemma "both_sides_times_pos_gt1"
("pz" "c!1-x!1" "x" "deriv(g!1,c!1)" "y"
"0"))
(("1" (replace -1 -9)
(("1"
(lemma "posreal_times_posreal_is_posreal"
("px" "deriv(g!1,c!1)" "py" "y1!1-x!1"))
(("1" (assert) nil nil)
("2" (assert) nil nil))
nil))
nil)
("2" (expand "derivable?" -6)
(("2" (inst - "c!1") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (propax) nil nil)
("3" (inst -2 "y1!1" "x!1" "g!1")
(("3" (assert)
(("3" (skosimp*)
(("3" (expand "deriv" -7)
(("3" (inst - "c!1")
(("3" (assert)
(("3"
(lemma "both_sides_times_neg_gt1"
("nz" "c!1-x!1" "x" "deriv(g!1,c!1)" "y"
"0"))
(("1"
(lemma "negreal_times_negreal_is_posreal"
("nx" "deriv(g!1,c!1)" "ny" "y1!1-x!1"))
(("1" (assert) nil nil)
("2" (assert)
(("2"
(expand "deriv" 1)
(("2"
(expand "deriv" -1)
(("2"
(expand ">" -1)
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (expand "derivable?" -5)
(("2" (inst - "c!1") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((deriv_fun type-eq-decl nil derivatives nil)
(deriv const-decl "[T -> real]" derivatives nil)
(deriv const-decl "[T -> real]" derivatives nil))
nil))
(maximum_derivative 0
(maximum_derivative-2 nil 3303059356
("" (skosimp*)
(("" (lemma "neg_derivable_fun" ("f" "g!1"))
(("" (typepred "g!1")
(("" (lemma "deriv_neg_fun" ("ff" "g!1"))
((""
(lemma "minimum_derivative"
("x" "x!1" "y1" "y1!1" "g" "-g!1"))
(("" (replace -2 -1)
(("" (split -1)
(("1" (expand "-" -1) (("1" (assert) nil nil)) nil)
("2" (expand "-" 1) (("2" (assert) nil nil)) nil)
("3" (assert) nil nil)
("4" (skosimp*)
(("4" (assert)
(("4" (expand "-" 2)
(("4" (assert)
(("4" (inst?) (("4" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((T formal-subtype-decl nil derivative_props nil)
(T_pred const-decl "[real -> boolean]" derivative_props 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)
(deriv_fun type-eq-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil)
(bool nonempty-type-eq-decl nil booleans nil)
(neg_derivable_fun formula-decl nil derivatives nil)
(deriv_neg_fun formula-decl nil derivatives nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(minus_real_is_real application-judgement "real" reals nil)
(- const-decl "[T -> real]" real_fun_ops "reals/")
(minimum_derivative formula-decl nil derivative_props nil)
(neg_fun_continuous application-judgement "continuous_fun"
continuous_functions nil)
(derivable_neg application-judgement "deriv_fun" derivatives nil)
(NOT const-decl "[bool -> bool]" booleans nil))
nil)
(maximum_derivative-1 nil 3297611227
("" (skosimp*)
(("" (lemma "neg_derivable_fun" ("f" "g!1"))
(("" (typepred "g!1")
(("" (lemma "deriv_neg_fun" ("ff" "g!1"))
((""
(lemma "minimum_derivative"
("x" "x!1" "y" "y!1" "g" "-g!1"))
(("" (replace -2 -1)
(("" (split -1)
(("1" (expand "-" -1) (("1" (assert) nil nil)) nil)
("2" (expand "-" 1) (("2" (assert) nil nil)) nil)
("3" (assert) nil nil)
("4" (skosimp*)
(("4" (inst -5 "y!2")
(("4" (assert)
(("4" (expand "-" 2) (("4" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((deriv_fun type-eq-decl nil derivatives nil)
(neg_derivable_fun formula-decl nil derivatives nil)
(deriv_neg_fun formula-decl nil derivatives nil))
nil))
(strict_minimum_derivative 0
(strict_minimum_derivative-2 nil 3297611289
("" (skosimp*)
(("" (lemma "minimum_derivative" ("x" "x!1" "g" "g!1" "y1" "y!1"))
(("" (split -1)
(("1" (propax) nil nil) ("2" (propax) nil nil)
("3" (assert) nil nil)
("4" (skosimp*)
(("4" (lemma "trich_lt" ("x" "y!2" "y" "x!1"))
(("4" (split -1)
(("1" (expand "strict_increasing?")
(("1" (inst - "y!2" "x!1")
(("1" (assert)
(("1"
(lemma "negreal_times_negreal_is_posreal"
("nx" "deriv(g!1)(y!2)" "ny" "y!2-x!1"))
(("1" (assert) nil nil)) nil))
nil))
nil))
nil)
("2" (propax) nil nil)
("3" (expand "strict_increasing?")
(("3" (inst - "x!1" "y!2")
(("3" (assert)
(("3"
(lemma "posreal_times_posreal_is_posreal"
("px" "deriv(g!1)(y!2)" "py" "y!2-x!1"))
(("3" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((deriv_fun type-eq-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil)
(bool nonempty-type-eq-decl nil booleans nil)
(T formal-subtype-decl nil derivative_props nil)
(T_pred const-decl "[real -> boolean]" derivative_props 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)
(minimum_derivative formula-decl nil derivative_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(deriv const-decl "[T -> real]" derivatives 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)
(negreal_times_negreal_is_posreal judgement-tcc nil real_types nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(strict_increasing? const-decl "bool" real_fun_preds "reals/")
(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)
(posreal_times_posreal_is_posreal judgement-tcc nil real_types nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(trich_lt formula-decl nil real_props nil))
nil)
(strict_minimum_derivative-1 nil 3297611254
("" (skosimp*)
(("" (lemma "neg_derivable_fun" ("f" "g!1"))
(("" (typepred "g!1")
(("" (lemma "deriv_neg_fun" ("ff" "g!1"))
((""
(lemma "minimum_derivative"
("x" "x!1" "y" "y!1" "g" "-g!1"))
(("" (replace -2 -1)
(("" (split -1)
(("1" (expand "-" -1) (("1" (assert) nil)))
("2" (expand "-" 1) (("2" (assert) nil)))
("3" (assert) nil)
("4" (skosimp*)
(("4" (inst -5 "y!2")
(("4" (assert)
(("4" (expand "-" 2)
(("4" (assert) nil))))))))))))))))))))))
nil)
nil nil))
(strict_maximum_derivative 0
(strict_maximum_derivative-1 nil 3297611310
("" (skosimp*)
(("" (lemma "maximum_derivative" ("x" "x!1" "y1" "y!1" "g" "g!1"))
(("" (expand "strict_decreasing?")
(("" (assert)
(("" (skosimp*)
(("" (lemma "trich_lt" ("x" "y!2" "y" "x!1"))
(("" (split -1)
(("1" (inst - "y!2" "x!1")
(("1" (assert)
(("1" (replace -3)
(("1"
(lemma "posreal_times_posreal_is_posreal"
("px" "deriv(g!1)(y!2)" "py" "x!1-y!2"))
(("1" (assert) nil nil)) nil))
nil))
nil))
nil)
("2" (propax) nil nil)
("3" (inst - "x!1" "y!2")
(("3" (assert)
(("3"
(lemma "negreal_times_negreal_is_posreal"
("nx" "deriv(g!1)(y!2)" "ny" "x!1-y!2"))
(("3" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((deriv_fun type-eq-decl nil derivatives nil)
(derivable? const-decl "bool" derivatives nil)
(bool nonempty-type-eq-decl nil booleans nil)
(T formal-subtype-decl nil derivative_props nil)
(T_pred const-decl "[real -> boolean]" derivative_props 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)
(maximum_derivative formula-decl nil derivative_props 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)
(trich_lt formula-decl nil real_props 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)
(negreal_times_negreal_is_posreal judgement-tcc nil real_types nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(AND const-decl "[bool, bool -> bool]" booleans 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)
(posreal_times_posreal_is_posreal judgement-tcc nil real_types 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 const-decl "[T -> real]" derivatives nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(strict_decreasing? const-decl "bool" real_fun_preds "reals/"))
nil))
(monotonic_antideriv 0
(monotonic_antideriv-1 nil 3603196696
("" (skolem 1 ("a" "b" "ff" "gg"))
(("" (flatten)
(("" (case "a=b")
(("1" (replace -1) (("1" (assert) nil nil)) nil)
("2" (lemma "nonneg_derivative[T]")
(("2" (name "fg" "LAMBDA(c:T):ff(c)-gg(c)")
(("2" (case "derivable?(fg)")
(("1" (inst -3 "fg")
(("1" (flatten)
(("1" (hide -3)
(("1" (split -3)
(("1" (hide -4)
(("1" (replace -3 :dir rl :hide? t)
(("1" (expand "increasing?")
(("1" (inst -1 "a" "b")
(("1" (assert) nil nil)) nil))
nil))
nil))
nil)
("2" (replace -2 :dir rl :hide? t)
(("2" (skolem 1 "x")
(("2" (inst -2 "x")
(("2" (lemma "deriv_diff[T]")
(("2"
(inst -1 "ff" "gg" "x")
(("2"
(split -1)
(("1"
(expand "-")
(("1"
(replace -1)
(("1"
(expand "deriv" -3)
(("1" (assert) nil nil))
nil))
nil))
nil)
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.80 Sekunden
(vorverarbeitet)
¤
|
Haftungshinweis
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
|
