NatAlgebra.double_self: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NatAlgebra
Lines 83-88 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&start_line=83&end_line=88

import Base

def double_self(n: Nat) -> {Nat.double(n) == Nat.add(n, n) : Nat}:
  match n:
    case 0n: {==}
    case 1n++p:
      %Equal.sym(Nat, Nat.double(p), Nat.add(p, p), double_self(p)) : {2n+_ == 1n+Nat.add(p, 1n+p) : Nat}
      succ_equal(1n+Nat.add(p, p), Nat.add(p, 1n+p), Equal.sym(Nat, Nat.add(p, 1n+p), 1n+Nat.add(p, p), add_succ(p, p)))

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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=succ_equal