ProofPcg.plus1: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/proof_pcg.bend as ProofPcg
Lines 48-49 of bend-collections-laws-math@1.0.0.0/proofs/math/random/proof_pcg.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/proof_pcg.bend&start_line=48&end_line=49

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

def plus1(+x: Nat) -> {Nat.add(x, 1n) == 1n+x : Nat}:
  Equal.trans(Nat, Nat.add(x, 1n), 1n+Nat.add(x, 0n), 1n+x, NA.add_succ(x, 0n), Equal.cong(Nat, Nat, z => 1n+z, Nat.add(x, 0n), x, NA.add_zero(x)))

Uses (6):
  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.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/lemmas/proofs/nat_algebra.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_zero