WordArithmetic.native_add: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/word_arithmetic.bend as WordArithmetic
Lines 129-135 of stelliferous@0.0.2.0/proofs/word_arithmetic.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/word_arithmetic.bend&start_line=129&end_line=135

import Base

def native_add(+a: Nat,+b: Nat) -> {U32.add(U32.from_nat(a),U32.from_nat(b)) == U32.from_nat(Nat.add(a,b)) : U32}:
  %Equal.sym(U32,U32.from_nat(Nat.add(a,b)),U32{encode(Nat.add(a,b),32n)},native_encoding(Nat.add(a,b))) : {U32.add(U32.from_nat(a),
      U32.from_nat(b)) == _ : U32}
  %Equal.sym(U32,U32.from_nat(a),U32{encode(a,32n)},native_encoding(a)) : {U32.add(_,U32.from_nat(b)) == U32{encode(Nat.add(a,b),32n)} : U32}
  %Equal.sym(U32,U32.from_nat(b),U32{encode(b,32n)},native_encoding(b)) : {U32.add(U32{encode(a,32n)},_) == U32{encode(Nat.add(a,b),32n)} : U32}
  %encode_add(a,b,32n) : {U32{Word.add(32n,encode(a,32n),encode(b,32n))} == U32{_} : U32}
  {==}

Uses (10):
  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=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=Word.add
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_arithmetic.bend&name=encode
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_arithmetic.bend&name=encode_add
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_arithmetic.bend&name=native_encoding