ProofValue.wn.add_swap: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_value.bend as ProofValue
Lines 70-72 of bend-osdev-word64@0.1.1.0/proof_value.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&start_line=70&end_line=72

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

# (a + b) + c = (a + c) + b
def wn.add_swap(+a: Nat, +b: Nat, +c: Nat) -> {Nat.add(Nat.add(a, b), c) == Nat.add(Nat.add(a, c), b) : Nat}:
  Equal.trans(Nat, Nat.add(Nat.add(a, b), c), Nat.add(a, Nat.add(b, c)), Nat.add(Nat.add(a, c), b), UL.nat_add_assoc(a, b, c), Equal.trans(Nat, Nat.add(a, Nat.add(b, c)), Nat.add(a, Nat.add(c, b)), Nat.add(Nat.add(a, c), b), Equal.cong(Nat, Nat, v => Nat.add(a, v), Nat.add(b, c), Nat.add(c, b), UL.nat_add_comm(b, c)), Equal.sym(Nat, Nat.add(Nat.add(a, c), b), Nat.add(a, Nat.add(c, b)), UL.nat_add_assoc(a, c, b))))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_comm