|
(bernstein_minmax
(unit_box_lb_id 0
(unit_box_lb_id-1 nil 3507234900
(""
(case "FORALL (bsdegmono: DegreeMono, bspoly, bspolz: MultiBernstein,
cf: Coeff, intendpts: IntervalEndpoints,
nvars, terms: posnat,omm):
(FORALL (t: below(terms), v: below(nvars), i: upto(bsdegmono(v))):
bspoly(t)(v)(i) = bspolz(t)(v)(i))
IMPLIES
unit_box_lb?(bspoly, bsdegmono, nvars, terms, cf, intendpts)(omm) IMPLIES
unit_box_lb?(bspolz, bsdegmono, nvars, terms, cf, intendpts)(omm)")
(("1" (skeep)
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"nvars" "terms" "x!1")
(("1" (split -2)
(("1" (propax) nil nil) ("2" (propax) nil nil)
("3" (propax) nil nil))
nil))
nil))
nil)
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(inst -2 "bsdegmono" "bspolz" "bspoly" "cf" "intendpts"
"nvars" "terms" "x!1")
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(("1" (propax) nil nil) ("2" (propax) nil nil)
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nil))
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(("2" (ground)
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(("2" (replaces -2)
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(inst -1 "bspoly" "bspolz" "bsdegmono" "cf" "nvars"
"terms")
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(("1" (assert) nil nil) ("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((multibs_eval_id formula-decl nil multi_bernstein 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)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(DegreeMono type-eq-decl nil util nil)
(Polynomial type-eq-decl nil util nil)
(Polyproduct type-eq-decl nil util nil)
(MultiBernstein type-eq-decl nil util nil)
(Coeff type-eq-decl nil util nil)
(IntervalEndpoints type-eq-decl nil util nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(list type-decl nil list_adt nil)
(Outminmax type-eq-decl nil minmax nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(< const-decl "bool" reals nil)
(below type-eq-decl nil naturalnumbers nil)
(<= const-decl "bool" reals nil)
(upto nonempty-type-eq-decl nil naturalnumbers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(unit_box_lb? const-decl "bool" bernstein_minmax nil))
shostak))
(unit_box_ub_id 0
(unit_box_ub_id-1 nil 3507235724
(""
(case "FORALL (bsdegmono: DegreeMono, bspoly, bspolz: MultiBernstein,
cf: Coeff, intendpts: IntervalEndpoints,
nvars, terms: posnat,omm):
(FORALL (t: below(terms), v: below(nvars), i: upto(bsdegmono(v))):
bspoly(t)(v)(i) = bspolz(t)(v)(i))
IMPLIES
unit_box_ub?(bspoly, bsdegmono, nvars, terms, cf, intendpts)(omm) IMPLIES
unit_box_ub?(bspolz, bsdegmono, nvars, terms, cf, intendpts)(omm)")
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(("1" (iff)
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"nvars" "terms" "x!1")
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(("1" (propax) nil nil) ("2" (propax) nil nil)
("3" (propax) nil nil))
nil))
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(("2"
(inst -2 "bsdegmono" "bspolz" "bspoly" "cf" "intendpts"
"nvars" "terms" "x!1")
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(("1" (propax) nil nil) ("2" (propax) nil nil)
("3" (skeep)
(("3" (inst? -2) (("3" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(("2" (expand "unit_box_ub?")
(("2" (ground)
(("2" (replaces -2)
(("2" (replaces -2)
(("2" (lemma "multibs_eval_id")
(("2"
(inst -1 "bspoly" "bspolz" "bsdegmono" "cf" "nvars"
"terms")
(("2" (split -1)
(("1" (assert) nil nil) ("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((multibs_eval_id formula-decl nil multi_bernstein 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)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
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(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(DegreeMono type-eq-decl nil util nil)
(Polynomial type-eq-decl nil util nil)
(Polyproduct type-eq-decl nil util nil)
(MultiBernstein type-eq-decl nil util nil)
(Coeff type-eq-decl nil util nil)
(IntervalEndpoints type-eq-decl nil util nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(list type-decl nil list_adt nil)
(Outminmax type-eq-decl nil minmax nil)
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(< const-decl "bool" reals nil)
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(<= const-decl "bool" reals nil)
(upto nonempty-type-eq-decl nil naturalnumbers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(unit_box_ub? const-decl "bool" bernstein_minmax nil))
nil))
(sound_id 0
(sound_id-1 nil 3509143268
(""
(case "FORALL (bsdegmono: DegreeMono, bspoly, bspolz: MultiBernstein,
cf: Coeff, intendpts: IntervalEndpoints, nvars: posnat,
omm: Outminmax, terms: posnat):
(FORALL (t: below(terms), v: below(nvars), i: upto(bsdegmono(v))):
bspoly(t)(v)(i) = bspolz(t)(v)(i))
IMPLIES
sound?(bspoly, bsdegmono, nvars, terms, cf, intendpts)(omm) IMPLIES
sound?(bspolz, bsdegmono, nvars, terms, cf, intendpts)(omm)")
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nil))
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(inst -2 "bsdegmono" "bspolz" "bspoly" "cf" "intendpts"
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(inst -1 "bsdegmono" "bspoly" "bspolz" "cf"
"intendpts" "nvars" "terms")
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(("1" (assert) nil nil) ("2" (propax) nil nil))
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(inst -1 "bsdegmono" "bspoly" "bspolz" "cf"
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nil)
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(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(DegreeMono type-eq-decl nil util nil)
(Polynomial type-eq-decl nil util nil)
(Polyproduct type-eq-decl nil util nil)
(MultiBernstein type-eq-decl nil util nil)
(Coeff type-eq-decl nil util nil)
(IntervalEndpoints type-eq-decl nil util nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(list type-decl nil list_adt nil)
(Outminmax type-eq-decl nil minmax nil)
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(< const-decl "bool" reals nil)
(below type-eq-decl nil naturalnumbers nil)
(<= const-decl "bool" reals nil)
(upto nonempty-type-eq-decl nil naturalnumbers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(sound? const-decl "bool" bernstein_minmax nil))
shostak))
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(sound_lb_le_ub-1 nil 3509729500
("" (skeep)
(("" (expand "sound?")
(("" (flatten)
(("" (hide (-2 -3))
(("" (expand "forall_X_between")
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(("1" (flatten)
(("1" (expand "lb_le_ub?") (("1" (assert) nil nil))
nil))
nil)
("2" (hide-all-but 1)
(("2" (expand "unitbox?") (("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((sound? const-decl "bool" bernstein_minmax 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)
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(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Vars type-eq-decl nil util nil)
(unitbox? const-decl "bool" util nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(le_realorder name-judgement "RealOrder" util nil)
(lb_le_ub? const-decl "bool" minmax nil)
(forall_X_between const-decl "bool" multi_bernstein nil))
shostak))
(combine_sound 0
(combine_sound-1 nil 3508072307
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(("1" (hide (-3 -4 -5 -6 -7 -8))
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(grind :exclude ("multibs_eval" "unitbox?"))
nil nil))
nil))
nil)
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(("2"
(grind :exclude
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nil nil))
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nil)
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("12" (lift-if) (("12" (ground) nil nil)) nil)
("13" (lift-if) (("13" (ground) nil nil)) nil)
("14" (lift-if) (("14" (ground) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(lt_realorder name-judgement "RealOrder" util nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(gt_realorder name-judgement "RealOrder" util nil)
(nonneg_rat_max application-judgement
"{s: nonneg_rat | s >= q AND s >= r}" real_defs nil)
(nat_max application-judgement "{k: nat | i <= k AND j <= k}"
real_defs nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(le_realorder name-judgement "RealOrder" util nil)
(min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
(max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
(combine const-decl "Outminmax" minmax 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)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
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(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Vars type-eq-decl nil util nil)
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(nvars skolem-const-decl "posnat" bernstein_minmax nil)
(X!1 skolem-const-decl "Vars" bernstein_minmax nil)
(forall_X_between const-decl "bool" multi_bernstein nil)
(unit_box_lb? const-decl "bool" bernstein_minmax nil)
(unit_box_ub? const-decl "bool" bernstein_minmax nil)
(ge_realorder name-judgement "RealOrder" util nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(length_eq? const-decl "bool" minmax nil)
(sound? const-decl "bool" bernstein_minmax nil))
shostak))
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(Bern_coeffs_minmax_rec_TCC1-1 nil 3505487851
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nil)
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("2"
(replace -9 +)
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(replace -7 +)
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(replace -9 +)
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