PROOF.un.le_dbl: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 160-169 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=160&end_line=169

import Base

def un.le_dbl(x: Nat, y: Nat) -> {Nat.is_le(Nat.double(x), Nat.double(y)) == Nat.is_le(x, y) : Bool}:
  match x y:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      {==}
    case 1n+p 0n:
      {==}
    case 1n+p 1n+q:
      un.le_dbl(p, q)

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.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le