def take_append_left

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/blake/blake3/lists.bend:54

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

54def take_append_left(-A: Data, +xs: List<&2,A>, +ys: List<&2,A>, +k: Nat, +h: {Nat.is_le(k,SC.length(A,xs)) == True{} : Bool}) -> {SC.take(A,SC.append(A,xs,ys),k) == SC.take(A,xs,k) : List<&2,A>}:
55  match xs k:
56    case Nil{} 0n: take_zero(A,ys)
57    case Nil{} 1n+j: Empty.absurd({SC.take(A,ys,1n+j) == Nil{} : List<&2,A>},L.false_true(h))
58    case Con{+a,+t} 0n: {==}
59    case Con{+a,+t} 1n+j: cons_cong(A,a,SC.take(A,SC.append(A,t,ys),j),SC.take(A,t,j),take_append_left(A,t,ys,j,h))