def take_all

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/argon2/memory.bend:56

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N

56def take_all(+xs: List<&2, U32>, +n: Nat, +h: {SC.length(U32, xs) == n : Nat}) -> {SC.take(U32, xs, n) == xs : List<&2, U32>}:
57  match xs n:
58    case Nil{} _:
59      {==}
60    case Con{h1, t} 0n:
61      Empty.absurd({SC.take(U32, Con{h1, t}, 0n) == Con{h1, t} : List<&2, U32>}, N.succ_zero(SC.length(U32, t), h))
62    case Con{+h1, +t} 1n+ +p:
63      Equal.cong(List<&2, U32>, List<&2, U32>, z => Con{h1, z}, SC.take(U32, t, p), t, take_all(t, p, N.succ_inj(SC.length(U32, t), p, h)))