|
(poly_minmax
(sound_poly_lb_le_ub 0
(sound_poly_lb_le_ub-1 nil 3509729606
("" (skeep)
(("" (expand "sound_poly?")
(("" (label "altb" -2)
(("" (assert)
(("" (hide (-2 -3))
(("" (split -)
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(("1" (expand "sound_poly_fin?")
(("1" (flatten)
(("1" (hide (-3 -4))
(("1" (expand "forall_X_poly_between")
(("1"
(case "EXISTS (ABv:Vars): boxbetween?(nvars)(Avars, Bvars, intendpts, boundedpts)(ABv)")
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(assert)
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(expand "lb_le_ub?")
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nil))
nil))
nil))
nil)
("2"
(name "ABvv"
"LAMBDA (i:nat): (Avars(i) + Bvars(i))/2")
(("2"
(case "FORALL (ij:nat): ij)
(("1"
(inst + "ABvv")
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(hide -4)
(("1"
(expand "boxbetween?")
(("1"
(expand "interval_between?")
(("1"
(skosimp*)
(("1"
(inst - "j!1")
(("1"
(expand
"bounded_points_true?")
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(inst - "j!1")
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nil))
nil))
nil))
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nil))
nil))
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(hide 2)
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(hide -3)
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(skosimp*)
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(reveal "altb")
(("2"
(expand "lt_below?")
(("2"
(inst - "ij!1")
(("2"
(expand "ABvv" +)
(("2" (ground) nil nil))
nil))
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nil))
nil))
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nil))
nil))
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nil))
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((sound_poly? const-decl "bool" poly_minmax nil)
(sound_poly_fin? const-decl "bool" poly_minmax nil)
(boxbetween? const-decl "bool" util nil)
(IntervalEndpoints type-eq-decl nil util nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(Vars type-eq-decl nil util nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(lb_le_ub? const-decl "bool" minmax nil)
(ge_realorder name-judgement "RealOrder" util nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(le_realorder name-judgement "RealOrder" util nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(< const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(lt_realorder name-judgement "RealOrder" util nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(interval_between? const-decl "bool" util nil)
(below type-eq-decl nil naturalnumbers nil)
(bounded_points_true? const-decl "bool" util nil)
(ij!1 skolem-const-decl "nat" poly_minmax nil)
(nvars skolem-const-decl "posnat" poly_minmax nil)
(ABvv skolem-const-decl "[nat -> real]" poly_minmax nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(lt_below? const-decl "bool" util nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(forall_X_poly_between const-decl "bool" multi_polynomial nil)
(sound_poly_inf? const-decl "bool" poly_minmax nil)
(RealOrder type-eq-decl nil util nil)
(realorder? const-decl "bool" util nil)
(gt_realorder name-judgement "RealOrder" util nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
shostak))
(multipolynomial_minmax_TCC1 0
(multipolynomial_minmax_TCC1-7 nil 3600444242
("" (skosimp*)
((""
(case "FORALL (AXYZ:Vars): boxbetween?(nvars!1)(zeroes, ones, infintendpts!1, boundedpts_true)(AXYZ) IMPLIES EXISTS (cr: posreal):
cr *
multipoly_eval(multipoly_translate(mpoly!1,
polydegmono!1,
nvars!1,
boundedpts!1)
(Avars!1, Bvars!1),
polydegmono!1, cf!1, nvars!1, terms!1)
(AXYZ)
=
multibs_eval(bspoly!1, polydegmono!1, cf!1, nvars!1, terms!1)(AXYZ)")
(("1" (label "AXYZlem" -1)
(("1" (hide "AXYZlem")
(("1"
(case "FORALL (ll:list[real]): length(ll)=nvars!1 AND (FORALL (ii:below(nvars!1)): (NOT (boundedpts!1(ii)`1 AND boundedpts!1(ii)`2)) IMPLIES nth(ll,ii)>0) IMPLIES (EXISTS (ccrr:posreal): (bounded_points_true?(nvars!1)(boundedpts!1) IMPLIES ccrr=1) AND
( ccrr*multipoly_eval(multipoly_translate(mpoly!1,
polydegmono!1,
nvars!1,
boundedpts!1)
(Avars!1, Bvars!1),
polydegmono!1, cf!1, nvars!1, terms!1)
(list2array(0)(ll))
=
multipoly_eval(mpoly!1, polydegmono!1, cf!1, nvars!1, terms!1)
(list2array(0)
(denormalize_listreal(ll)
(Avars!1,
Bvars!1,
boundedpts!1)))))")
(("1" (label "mlem" -1)
(("1" (hide "mlem")
(("1" (label "mpolytrname" -1)
(("1" (hide -1)
(("1" (label "bspolyname" -1)
(("1" (hide -1)
(("1" (label "infintendptsname" -1)
(("1" (hide -1)
(("1" (label "bsminmaxname" -1)
(("1"
(hide -1)
(("1"
(typepred "bs_minmax!1")
(("1"
(expand "sound_poly?")
(("1"
(flatten)
(("1"
(expand "sound?")
(("1"
(flatten)
(("1"
(case
"bounded_points_true?(nvars!1)(boundedpts!1)")
(("1"
(case
"NOT FORALL (iijj:below(nvars!1)): infintendpts!1(iijj) = intendpts!1(iijj)")
(("1"
(hide-all-but (1 -))
(("1"
(skosimp*)
(("1"
(expand
"bounded_points_true?")
(("1"
(inst - "iijj!1")
(("1"
(flatten)
(("1"
(reveal
"infintendptsname")
(("1"
(replace
"infintendptsname"
+)
(("1"
(hide
"infintendptsname")
(("1"
(expand
"interval_endpoints_inf_trans")
(("1"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(label "infdef" -1)
(("2"
(hide "infdef")
(("2"
(assert)
(("2"
(hide 2)
(("2"
(expand
"sound_poly_fin?")
(("2"
(split +)
(("1"
(hide
(-3 -4))
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(expand
"forall_X_poly_between")
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(reveal
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-
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"cf!1"
"mpolytr!1"
"nvars!1"
"polydegmono!1"
"terms!1")
(("1"
(split
-)
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(expand
"forall_X_between")
(("1"
(replace
-1
:dir
rl)
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(hide
-1)
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(reveal
"mpolytrname")
(("1"
(replace
"mpolytrname")
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(hide
"mpolytrname")
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(lemma
"multipoly_translate_bounded_def")
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(inst?)
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(inst
-
"X!1"
"intendpts!1")
(("1"
(assert)
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-
"normalize_lambda(nvars!1, X!1, boundedpts!1)
(Avars!1, Bvars!1)")
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-1)
(("1"
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-4)
(("1"
(ground)
nil
nil)
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(hide
2)
(("2"
(case
"normalize_lambda(nvars!1, X!1, boundedpts!1)
(Avars!1, Bvars!1) = (LAMBDA (i: nat):
IF i < nvars!1 THEN
(X!1(i) - Avars!1(i)) /
(Bvars!1(i) - Avars!1(i))
ELSE 0
ENDIF)")
(("1"
(replace
-1)
(("1"
(hide
-1)
(("1"
(hide
-1)
(("1"
(expand
"boxbetween?")
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(expand
"interval_between?")
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(expand
"unitbox?")
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"Avars!1(j!1) <= X!1(j!1) AND X!1(j!1) <= Bvars!1(j!1)")
(("1"
(flatten)
(("1"
(split
+)
(("1"
(cross-mult
1)
(("1"
(assert)
nil
nil))
nil)
("2"
(cross-mult
1)
(("2"
(assert)
nil
nil))
nil))
nil))
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("2"
(ground)
nil
nil))
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("2"
(hide
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-1)
(("2"
(decompose-equality)
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(expand
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"x!1")
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(expand
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(-1
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"i!1")
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("2"
(hide
(-2 -4))
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(expand
"unit_box_lb?")
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= nvars!1")
(("1"
(hide
2)
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(assert)
nil
nil))
nil)
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(typepred
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.47 Sekunden
(vorverarbeitet)
¤
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