PROOF.un.lt_add_l: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 227-233 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=227&end_line=233

import Base

# A + X < A + Y exactly when X < Y, on either side
def un.lt_add_l(a: Nat, -x: Nat, -y: Nat) -> {Nat.is_lt(Nat.add(a, x), Nat.add(a, y)) == Nat.is_lt(x, y) : Bool}:
  match a:
    case 0n:
      {==}
    case 1n+p:
      un.lt_add_l(p, x, y)

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.is_lt