PROOF.un.lt_add_r: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 235-238 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=235&end_line=238

import Base

def un.lt_add_r(+x: Nat, +y: Nat, +a: Nat) -> {Nat.is_lt(Nat.add(x, a), Nat.add(y, a)) == Nat.is_lt(x, y) : Bool}:
  %un.add_comm(a, x) : {Nat.is_lt(_, Nat.add(y, a)) == Nat.is_lt(x, y) : Bool}
  %un.add_comm(a, y) : {Nat.is_lt(Nat.add(a, x), _) == Nat.is_lt(x, y) : Bool}
  un.lt_add_l(a, x, y)

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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.lt_add_l