PROOF.nat_lt_add: def of bend-osdev-aead@0.1.0.0
Import: import bend-osdev-aead@0.1.0.0/PROOF.bend as PROOF
Lines 114-121 of bend-osdev-aead@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-aead@0.1.0.0/PROOF.bend&start_line=114&end_line=121

import Base

def nat_lt_add(+x: Nat, t: Nat) -> {False{} == Nat.is_lt(Nat.add(x, t), t) : Bool}:
  match t:
    case 0n:
      %nat_add_zero(x) : {False{} == Nat.is_lt(_, 0n) : Bool}
      nat_lt_zero(x)
    case 1n+(+u):
      %nat_add_succ(x, u) : {False{} == Nat.is_lt(_, 1n+u) : Bool}
      nat_lt_add(x, u)

Uses (7):
  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-aead@0.1.0.0/PROOF.bend&name=nat_add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-aead@0.1.0.0/PROOF.bend&name=nat_add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-aead@0.1.0.0/PROOF.bend&name=nat_lt_zero