ProofTab.gt.add_nat: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/proof_tab.bend as ProofTab
Lines 113-120 of bend-osdev-gf@0.1.1.0/proof_tab.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&start_line=113&end_line=120

import Base

# the sum of two counts, as U32, is the U32 of their sum
def gt.add_nat(+p: Nat, +q: Nat) -> {U32.add(U32.from_nat(p), U32.from_nat(q)) == U32.from_nat(Nat.add(q, p)) : U32}:
  match q:
    case 0n:
      gt.add_zero(U32.from_nat(p))
    case 1n+r:
      %gt.add_nat(p, r) : {U32.add(U32.from_nat(p), U32.inc(U32.from_nat(r))) == U32.inc(_) : U32}
      gt.add_inc(U32.from_nat(p), U32.from_nat(r))

Uses (8):
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.inc
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.add_inc
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.add_zero