Step.rot: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/step.bend as Step
Lines 48-50 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/step.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/step.bend&start_line=48&end_line=50

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64mul.bend as WM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend as A

# a + (b + c) == (a + c) + b
def rot(+a: Nat, +b: Nat, +c: Nat) -> {Nat.add(a, Nat.add(b, c)) == Nat.add(Nat.add(a, c), b) : Nat}:
  A.tr(Nat.add(a, Nat.add(b, c)), Nat.add(a, Nat.add(c, b)), Nat.add(Nat.add(a, c), b), WM.cong_r(a, Nat.add(b, c), Nat.add(c, b), N.add_comm(b, c)), A.sy(Nat.add(Nat.add(a, c), b), Nat.add(a, Nat.add(c, b)), N.add_assoc(a, c, b)))

Uses (7):
  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-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend&name=sy
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend&name=tr
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64mul.bend&name=cong_r