def slice_one

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/argon2/memory.bend:224

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

224def slice_one(+ws: List<&2, U32>, +base: Nat, +h: {Nat.is_lt(base, SC.length(U32, ws)) == True{} : Bool}) -> {slice(ws, base, 1n) == Con{nthv(ws, base), Nil{}} : List<&2, U32>}:
225  match ws base:
226    case Nil{} _:
227      Empty.absurd({slice(Nil{}, base, 1n) == Con{nthv(Nil{}, base), Nil{}} : List<&2, U32>}, N.lt_zero_absurd(base, h))
228    case Con{+x, +t} 0n:
229      Equal.cong(List<&2, U32>, List<&2, U32>, z => Con{x, z}, SC.take(U32, t, 0n), Nil{}, LL.sc_take_zero(U32, t))
230    case Con{x, +t} 1n+ +b:
231      slice_one(t, b, h)