NatOrder.commutative: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 272-279 of stelliferous@0.0.2.0/proofs/nat_order.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&start_line=272&end_line=279

import Base
import stelliferous@0.0.2.0/proofs/natural_addition.bend as Addition

def commutative(+a: Nat,+b: Nat) -> {Nat.add(a,b) == Nat.add(b,a) : Nat}:
  match a:
    case 0n:
      Equal.sym(Nat,Nat.add(b,0n),b,Addition.zero_right(b))
    case 1n+ +p:
      %Equal.sym(Nat,Nat.add(b,1n+p),1n+Nat.add(b,p),Addition.successor_right(b,p)) : {1n+Nat.add(p,b) == _ : Nat}
      %commutative(p,b) : {1n+Nat.add(p,b) == 1n+_ : Nat}
      {==}

Uses (5):
  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=stelliferous@0.0.2.0/proofs/natural_addition.bend&name=successor_right
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/natural_addition.bend&name=zero_right