def balance.if.get

bend-kit-collections@0.1.4.1 · PROOF.bend:869

import Base
import bend-kit-collections@0.1.4.1/LAWS.bend as Laws
import bend-kit-collections@0.1.4.1/omap.bend as O

869def balance.if.get(
870  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~refl: Refl(~K, ~cmp), ~eq: Eq(~K, ~cmp),
871  ~flip: Flip(~K, ~cmp), ~trans: Trans(~K, ~cmp),
872  heavy_hi: Bool, heavy_lo: Bool, +lb: Maybe<&2, K>, +ub: Maybe<&2, K>, +x: K,
873  +k: K, +v: V, +lo: O.OMap<K, V>, +hi: O.OMap<K, V>,
874  el: {Laws.bounded(~K, ~V, ~cmp, lo, lb, Some{k}) == True{} : Bool},
875  eh: {Laws.bounded(~K, ~V, ~cmp, hi, Some{k}, ub) == True{} : Bool}
876) -> {g(~K, ~V, ~cmp, O.OMap.balance.if(K, V, heavy_hi, heavy_lo, k, v, lo, hi), x)
877      == g(~K, ~V, ~cmp, O.OBin{0, k, v, lo, hi}, x) : Maybe<&2, V>}:
878  match heavy_hi heavy_lo:
879    case True{} _:
880      rot_lo.get(~K, ~V, ~cmp, ~refl, ~eq, ~flip, ~trans, hi, ub, x, k, v, lo, eh)
881    case False{} True{}:
882      rot_hi.get(~K, ~V, ~cmp, ~refl, ~eq, ~flip, ~trans, lo, lb, x, k, v, hi, el)
883    case False{} False{}:
884      {==}