Nat.double_inj: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 340-349 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&start_line=340&end_line=349

import Base

def double_inj(+a: Nat, +b: Nat, e: {Nat.double(a) == Nat.double(b) : Nat}) -> {a == b : Nat}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      Empty.absurd({0n == 1n+q : Nat}, zero_succ(1n+Nat.double(q), e))
    case 1n+p 0n:
      Empty.absurd({1n+p == 0n : Nat}, succ_zero(1n+Nat.double(p), e))
    case 1n+p 1n+q:
      succ_cong(p, q, double_inj(p, q, succ_inj(Nat.double(p), Nat.double(q), succ_inj(1n+Nat.double(p), 1n+Nat.double(q), e))))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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/nat.bend&name=succ_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=succ_inj
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=succ_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=zero_succ