BoundedU32Arithmetic.add_commutative: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend as BoundedU32Arithmetic
Lines 36-43 of stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend&start_line=36&end_line=43

import Base
import stelliferous@0.0.2.0/proofs/nat_order.bend as Order

def add_commutative(+left: U32,+right: U32) -> {(left + right : U32) == (right + left : U32) : U32}:
  %Equal.sym(U32,(left + right : U32),U32.from_nat(Nat.add(U32.to_nat(left),U32.to_nat(right))),native_add(left,right)) :
    {_ == (right + left : U32) : U32}
  %Equal.sym(U32,(right + left : U32),U32.from_nat(Nat.add(U32.to_nat(right),U32.to_nat(left))),native_add(right,left)) :
    {U32.from_nat(Nat.add(U32.to_nat(left),U32.to_nat(right))) == _ : U32}
  %Order.commutative(U32.to_nat(left),U32.to_nat(right)) :
    {U32.from_nat(Nat.add(U32.to_nat(left),U32.to_nat(right))) == U32.from_nat(_) : U32}
  {==}

Uses (8):
  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.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.to_nat
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend&name=native_add
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=commutative