def double_inj

bend-collections-laws-crypto@1.0.0.0 · proofs/lib/nat.bend:340

import Base

340def double_inj(+a: Nat, +b: Nat, e: {Nat.double(a) == Nat.double(b) : Nat}) -> {a == b : Nat}:
341  match a b:
342    case 0n 0n:
343      {==}
344    case 0n 1n+q:
345      Empty.absurd({0n == 1n+q : Nat}, zero_succ(1n+Nat.double(q), e))
346    case 1n+p 0n:
347      Empty.absurd({1n+p == 0n : Nat}, succ_zero(1n+Nat.double(p), e))
348    case 1n+p 1n+q:
349      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))))