PROOF.app2: def of bendtorch@1.3.0.0
Import: import bendtorch@1.3.0.0/PROOF.bend as PROOF
Lines 279-281 of bendtorch@1.3.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch@1.3.0.0/PROOF.bend&start_line=279&end_line=281

import Base

# a ++ b == a2 ++ b2 from a == a2 and b == b2
def app2(-A: Type, -a: List<&1, A>, -a2: List<&1, A>, -b: List<&1, A>, -b2: List<&1, A>, ea: {a == a2 : List<&1, A>}, eb: {b == b2 : List<&1, A>}) -> {List.append(&1, A, a, b) == List.append(&1, A, a2, b2) : List<&1, A>}:
  Equal.trans(List<&1, A>, List.append(&1, A, a, b), List.append(&1, A, a2, b), List.append(&1, A, a2, b2), Equal.cong(List<&1, A>, List<&1, A>, z => List.append(&1, A, z, b), a, a2, ea), Equal.cong(List<&1, A>, List<&1, A>, z => List.append(&1, A, a2, z), b, b2, eb))

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append