def length_take

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/blake/blake3/lists.bend:61

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

61def length_take(-A: Data, +xs: List<&2,A>, +k: Nat, +h: {Nat.is_le(k,SC.length(A,xs)) == True{} : Bool}) -> {SC.length(A,SC.take(A,xs,k)) == k : Nat}:
62  match xs k:
63    case Nil{} 0n: {==}
64    case Nil{} 1n+j: Empty.absurd({SC.length(A,SC.take(A,Nil{},1n+j)) == 1n+j : Nat},L.false_true(h))
65    case Con{+a,+t} 0n: {==}
66    case Con{+a,+t} 1n+j: N.succ_cong(SC.length(A,SC.take(A,t,j)),j,length_take(A,t,j,h))