def glue.fin.bnd.go

bend-kit-collections@0.1.4.1 · PROOF.bend:1117

import Base
import bend-mathlib@0.7.4.0/bool.bend as MBool
import bend-kit-collections@0.1.4.1/LAWS.bend as Laws
import bend-kit-collections@0.1.4.1/omap.bend as O

1117def glue.fin.bnd.go(
1118  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp),
1119  +mk: K, +mv: V, +t: O.OMap<K, V>, +lo: O.OMap<K, V>, +lb: Maybe<&2, K>,
1120  +ub: Maybe<&2, K>, +key: K,
1121  eka: {Laws.above(~K, ~cmp, lb, key) == True{} : Bool},
1122  el: {Laws.bounded(~K, ~V, ~cmp, lo, lb, Some{key}) == True{} : Bool},
1123  +pmr: {PM(~K, ~V, ~cmp, Some{key}, ub, {(mk, mv, t) : K & V & O.OMap<K, V>}) == True{} : Bool}
1124) -> {Laws.bounded(~K, ~V, ~cmp,
1125       O.OMap.glue.fin(K, V, lo, {(mk, mv, t) : K & V & O.OMap<K, V>}), lb, ub) == True{} : Bool}:
1126  +ab = Bool.and(Laws.above(~K, ~cmp, Some{key}, mk), Laws.below(~K, ~cmp, ub, mk))
1127  +c = Laws.bounded(~K, ~V, ~cmp, t, Some{mk}, ub)
1128  +eab = MBool.eq_true_of_and_left(ab, c, pmr)
1129  +km = MBool.eq_true_of_and_left(Laws.above(~K, ~cmp, Some{key}, mk), Laws.below(~K, ~cmp, ub, mk), eab)
1130  balance.bnd(~K, ~V, ~cmp, ~trans, lb, ub, mk, mv, lo, t,
1131    above_trans(~K, ~cmp, ~trans, lb, key, mk, eka, km),
1132    MBool.eq_true_of_and_right(Laws.above(~K, ~cmp, Some{key}, mk), Laws.below(~K, ~cmp, ub, mk), eab),
1133    weaken_hi(~K, ~V, ~cmp, ~trans, lo, lb, key, Some{mk}, el, km),
1134    MBool.eq_true_of_and_right(ab, c, pmr))