ReduceFiberProof.add_comm: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend as ReduceFiberProof
Lines 21-24 of bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend&start_line=21&end_line=24

import Base
import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as Nats
import bendtorch-core@0.1.0.0/src/shape/broadcast_proofs.bend as Broadcast

def add_comm(+a: Nat, +b: Nat) -> {Nat.add(a, b) == Nat.add(b, a) : Nat}:
  %Broadcast.add_zero(b) : {Nat.add(a, _) == Nat.add(b, a) : Nat}
  %Broadcast.add_zero(a) : {Nat.add(a, Nat.add(b, 0n)) == Nat.add(b, _) : Nat}
  Nats.add_swap(a, b, 0n)

Uses (4):
  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=bendtorch-core@0.1.0.0/src/shape/broadcast_proofs.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend&name=add_swap