def sc_length_take

bend-collections-laws-math@1.0.0.0 · proofs/lib/list.bend:288

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

288def sc_length_take(-A: Data, +xs: List<&2, A>, +n: Nat, +h: {Nat.is_le(n, SC.length(A, xs)) == True{} : Bool}) -> {SC.length(A, SC.take(A, xs, n)) == n : Nat}:
289  match xs n:
290    case Nil{} 0n:
291      {==}
292    case Nil{} 1n+m:
293      Empty.absurd({SC.length(A, SC.take(A, Nil{}, 1n+m)) == 1n+m : Nat}, L.false_true(h))
294    case Con{a, t} 0n:
295      {==}
296    case Con{a, t} 1n+m:
297      N.succ_cong(SC.length(A, SC.take(A, t, m)), m, sc_length_take(A, t, m, h))