def pm.bnd

bend-kit-collections@0.1.4.1 · PROOF.bend:1100

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

1100def pm.bnd(
1101  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp),
1102  lo: O.OMap<K, V>, +lb: Maybe<&2, K>, +ub: Maybe<&2, K>, +k: K, +v: V,
1103  +hi: O.OMap<K, V>,
1104  +e: {Laws.bounded(~K, ~V, ~cmp, O.OBin{0, k, v, lo, hi}, lb, ub) == True{} : Bool}
1105) -> {PM(~K, ~V, ~cmp, lb, ub, O.OMap.pop_min(K, V, lo, k, v, hi)) == True{} : Bool}:
1106  match lo:
1107    case O.OTip{}:
1108      MBool.and_eq_true(Bool.and(Laws.above(~K, ~cmp, lb, k), Laws.below(~K, ~cmp, ub, k)), Laws.bounded(~K, ~V, ~cmp, hi, Some{k}, ub), MBool.and_eq_true(Laws.above(~K, ~cmp, lb, k), Laws.below(~K, ~cmp, ub, k), bn.a(~K, ~V, ~cmp, lb, ub, k, v, O.OTip{}, hi, e), bn.b(~K, ~V, ~cmp, lb, ub, k, v, O.OTip{}, hi, e)), bn.h(~K, ~V, ~cmp, lb, ub, k, v, O.OTip{}, hi, e))
1109    case O.OBin{s, +lk, +lv, +ll, +lh}:
1110      +lo = {O.OBin{0, lk, lv, ll, lh} : O.OMap<K, V>}
1111      pm.fin.bnd(~K, ~V, ~cmp, ~trans, O.OMap.pop_min(K, V, ll, lk, lv, lh), lb, ub, k, v, hi,
1112        pm.bnd(~K, ~V, ~cmp, ~trans, ll, lb, Some{k}, lk, lv, lh,
1113          bn.l(~K, ~V, ~cmp, lb, ub, k, v, lo, hi, e)),
1114        bn.b(~K, ~V, ~cmp, lb, ub, k, v, lo, hi, e),
1115        bn.h(~K, ~V, ~cmp, lb, ub, k, v, lo, hi, e))