PROOFDiv.ud.lt_add: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF_div.bend as PROOFDiv
Lines 97-103 of bend-osdev-u32@0.1.0.0/PROOF_div.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF_div.bend&start_line=97&end_line=103

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

def ud.lt_add(+m: Nat, +r: Nat) -> {Nat.is_lt(r, 1n+Nat.add(m, r)) == True{} : Bool}:
  match r:
    case 0n:
      {==}
    case 1n+p:
      %Equal.sym(Nat, Nat.add(m, 1n+p), 1n+Nat.add(m, p), UL.nat_add_succ(m, p)) : {Nat.is_lt(1n+p, 1n+_) == True{} : Bool}
      ud.lt_add(m, p)

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=Equal.sym
  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/LAWS.bend&name=nat_add_succ