def p_slice_append_le

bend-osdev-bytes@0.1.1.0 · PROOF.bend:1217

import Base
import bend-osdev-bytes@0.1.1.0/bytes.bend as B

1217def p_slice_append_le(+i: Nat, +n: Nat, +a: B.Octets, +b: B.Octets, +h: {Nat.is_le(Nat.add(i, n), B.Octets.len(a)) == True{} : Bool}) -> {B.Octets.slice(i, n, B.Octets.append(a, b)) == B.Octets.slice(i, n, a) : B.Octets}:
1218  Equal.trans(B.Octets, B.Octets.take(n, B.Octets.drop(i, B.Octets.append(a, b))), B.Octets.take(n, B.Octets.append(B.Octets.drop(i, a), b)), B.Octets.take(n, B.Octets.drop(i, a)),
1219    Equal.cong(B.Octets, B.Octets, x => B.Octets.take(n, x), B.Octets.drop(i, B.Octets.append(a, b)), B.Octets.append(B.Octets.drop(i, a), b), p_drop_append_le(i, a, b, off.le_add_l(i, n, B.Octets.len(a), h))),
1220    p_take_append_le(n, B.Octets.drop(i, a), b,
1221      Equal.trans(Bool, Nat.is_le(n, B.Octets.len(B.Octets.drop(i, a))), Nat.is_le(n, Nat.sub(B.Octets.len(a), i)), True{},
1222        Equal.cong(Nat, Bool, k => Nat.is_le(n, k), B.Octets.len(B.Octets.drop(i, a)), Nat.sub(B.Octets.len(a), i), p_len_drop(i, a)),
1223        off.le_sub(i, n, B.Octets.len(a), h))))