def update_append_left

bend-collections-laws-crypto@1.0.0.0 · proofs/lib/list.bend:81

import Base
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

81def update_append_left(-A: Data, +xs: List<&2, A>, +ys: List<&2, A>, +i: Nat, +v: A, +h: {Nat.is_lt(i, SC.length(A, xs)) == True{} : Bool}) -> {SC.update(A, SC.append(A, xs, ys), i, v) == SC.append(A, SC.update(A, xs, i, v), ys) : List<&2, A>}:
82  match xs i:
83    case Nil{} _:
84      Empty.absurd({SC.update(A, ys, i, v) == SC.append(A, Nil{}, ys) : List<&2, A>}, N.lt_zero_absurd(i, h))
85    case Con{h1, t} 0n:
86      {==}
87    case Con{+h1, t} 1n+p:
88      cons_cong(A, h1, SC.update(A, SC.append(A, t, ys), p, v), SC.append(A, SC.update(A, t, p, v), ys), update_append_left(A, t, ys, p, v, h))