def sc_take_append_right

bend-collections-laws-crypto@1.0.0.0 · proofs/lib/list.bend:341

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

341def sc_take_append_right(-A: Data, +xs: List<&2, A>, +ys: List<&2, A>, +i: Nat, +h: {Nat.is_le(SC.length(A, xs), i) == True{} : Bool}) -> {SC.take(A, SC.append(A, xs, ys), i) == SC.append(A, xs, SC.take(A, ys, Nat.sub(i, SC.length(A, xs)))) : List<&2, A>}:
342  match xs i:
343    case Nil{} 0n:
344      {==}
345    case Nil{} 1n+j:
346      {==}
347    case Con{a, t} 0n:
348      Empty.absurd({SC.take(A, SC.append(A, Con{a, t}, ys), 0n) == SC.append(A, Con{a, t}, SC.take(A, ys, Nat.sub(0n, 1n+SC.length(A, t)))) : List<&2, A>}, L.false_true(h))
349    case Con{a, t} 1n+j:
350      cons_cong(A, a, SC.take(A, SC.append(A, t, ys), j), SC.append(A, t, SC.take(A, ys, Nat.sub(j, SC.length(A, t)))), sc_take_append_right(A, t, ys, j, h))