Fixgen.rot3: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend as Fixgen
Lines 72-74 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend&start_line=72&end_line=74

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

# (z + s) + y == (y + z) + s
def rot3(+z: Nat, +s: Nat, +y: Nat) -> {Nat.add(Nat.add(z, s), y) == Nat.add(Nat.add(y, z), s) : Nat}:
  Equal.trans(Nat, Nat.add(Nat.add(z, s), y), Nat.add(y, Nat.add(z, s)), Nat.add(Nat.add(y, z), s), N.add_comm(Nat.add(z, s), y), Equal.sym(Nat, Nat.add(Nat.add(y, z), s), Nat.add(y, Nat.add(z, s)), N.add_assoc(y, z, s)))

Uses (6):
  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-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_comm