PROOF.lt_trans: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 233-238 of bend-kit-collections@0.1.4.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&start_line=233&end_line=238

import Base

def lt_trans(
  ~K: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp), +x: K, +y: K, +z: K,
  e1: {Cmp.is_lt(cmp(x, y)) == True{} : Bool},
  e2: {Cmp.is_lt(cmp(y, z)) == True{} : Bool}
) -> {Cmp.is_lt(cmp(x, z)) == True{} : Bool}:
  lt_true(cmp(x, z), trans(x, y, z, lt_of(cmp(x, y), e1), lt_of(cmp(y, z), e2)))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=Trans
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=lt_of
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=lt_true