def take_snoc

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/argon2/memory.bend:198

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/list.bend as LL
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N

198def take_snoc(+ys: List<&2, U32>, +k: Nat, +h: {Nat.is_lt(k, SC.length(U32, ys)) == True{} : Bool}) -> {SC.take(U32, ys, 1n+k) == SC.append(U32, SC.take(U32, ys, k), Con{nthv(ys, k), Nil{}}) : List<&2, U32>}:
199  match ys k:
200    case Nil{} _:
201      Empty.absurd({SC.take(U32, Nil{}, 1n+k) == SC.append(U32, SC.take(U32, Nil{}, k), Con{nthv(Nil{}, k), Nil{}}) : List<&2, U32>}, N.lt_zero_absurd(k, h))
202    case Con{+x, +t} 0n:
203      Equal.cong(List<&2, U32>, List<&2, U32>, z => Con{x, z}, SC.take(U32, t, 0n), Nil{}, LL.sc_take_zero(U32, t))
204    case Con{+x, +t} 1n+ +p:
205      Equal.cong(List<&2, U32>, List<&2, U32>, z => Con{x, z}, SC.take(U32, t, 1n+p), SC.append(U32, SC.take(U32, t, p), Con{nthv(t, p), Nil{}}), take_snoc(t, p, h))