PROOF.off.le_add_l: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 785-793 of bend-osdev-bytes@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&start_line=785&end_line=793

import Base

# i + n <= m: i <= m
def off.le_add_l(+i: Nat, +n: Nat, +m: Nat) -> {Nat.is_le(Nat.add(i, n), m) == True{} : Bool} -> {Nat.is_le(i, m) == True{} : Bool}:
  match i m:
    case 0n _:
      h => off.le_zero(m)
    case 1n+p 0n:
      h => off.no({Nat.is_le(1n+p, 0n) == True{} : Bool}, h)
    case 1n+p 1n+q:
      h => off.le_add_l(p, n, q, h)

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=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_le
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=off.le_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=off.no