def drop_append_le

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/argon2/memory.bend:365

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/logic.bend as L

365def drop_append_le(+xs: List<&2, U32>, +ys: List<&2, U32>, +n: Nat, +h: {Nat.is_le(n, SC.length(U32, xs)) == True{} : Bool}) -> {SC.drop(U32, SC.append(U32, xs, ys), n) == SC.append(U32, SC.drop(U32, xs, n), ys) : List<&2, U32>}:
366  match xs n:
367    case Nil{} 0n:
368      Equal.trans(List<&2, U32>, SC.drop(U32, ys, 0n), ys, SC.append(U32, SC.drop(U32, Nil{}, 0n), ys), drop_zero(ys), {==})
369    case Nil{} 1n+p:
370      Empty.absurd({SC.drop(U32, ys, 1n+p) == SC.append(U32, SC.drop(U32, Nil{}, 1n+p), ys) : List<&2, U32>}, L.false_true(h))
371    case Con{x, t} 0n:
372      {==}
373    case Con{x, +t} 1n+ +p:
374      drop_append_le(t, ys, p, h)