SlicePROOF.sub_back: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend as SlicePROOF
Lines 121-129 of bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&start_line=121&end_line=129

import Base

# stop - low = 1 + rest gives stop = low + (1 + rest).
def sub_back(+stop: Nat, +low: Nat, +rest: Nat, e: {Nat.sub(stop, low) == 1n+rest : Nat}) -> {Nat.add(low, 1n+rest) == stop : Nat}:
  match stop low:
    case 0n _:
      Empty.absurd({Nat.add(low, 1n+rest) == 0n : Nat}, nat_clash(rest, Equal.sym(Nat, 0n, 1n+rest, e)))
    case 1n+ap 0n:
      Equal.sym(Nat, 1n+ap, 1n+rest, e)
    case 1n+ap 1n+lp:
      Equal.cong(Nat, Nat, x => 1n+x, Nat.add(lp, 1n+rest), ap, sub_back(ap, lp, rest, e))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&name=nat_clash