def below_trans

bend-kit-collections@0.1.4.1 · PROOF.bend:251

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

251def below_trans(
252  ~K: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp), ub: Maybe<&2, K>,
253  +k: K, +hk: K, e: {Cmp.is_lt(cmp(k, hk)) == True{} : Bool},
254  eb: {Laws.below(~K, ~cmp, ub, hk) == True{} : Bool}
255) -> {Laws.below(~K, ~cmp, ub, k) == True{} : Bool}:
256  match ub:
257    case None{}:
258      {==}
259    case Some{+u}:
260      lt_trans(~K, ~cmp, ~trans, k, hk, u, e, eb)