def p_slice_take

bend-osdev-bytes@0.1.1.0 · PROOF.bend:1228

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

1228def p_slice_take(+m: Nat, +i: Nat, +n: Nat, +o: B.Octets, +h: {Nat.is_le(Nat.add(i, n), m) == True{} : Bool}) -> {B.Octets.slice(i, n, B.Octets.take(m, o)) == B.Octets.slice(i, n, o) : B.Octets}:
1229  Equal.trans(B.Octets, B.Octets.take(n, B.Octets.drop(i, B.Octets.take(m, o))), B.Octets.take(n, B.Octets.take(Nat.sub(m, i), B.Octets.drop(i, o))), B.Octets.take(n, B.Octets.drop(i, o)),
1230    Equal.cong(B.Octets, B.Octets, x => B.Octets.take(n, x), B.Octets.drop(i, B.Octets.take(m, o)), B.Octets.take(Nat.sub(m, i), B.Octets.drop(i, o)), p_drop_take(i, m, o)),
1231    Equal.trans(B.Octets, B.Octets.take(n, B.Octets.take(Nat.sub(m, i), B.Octets.drop(i, o))), B.Octets.take(Nat.min(n, Nat.sub(m, i)), B.Octets.drop(i, o)), B.Octets.take(n, B.Octets.drop(i, o)),
1232      p_take_take(n, Nat.sub(m, i), B.Octets.drop(i, o)),
1233      Equal.cong(Nat, B.Octets, k => B.Octets.take(k, B.Octets.drop(i, o)), Nat.min(n, Nat.sub(m, i)), n, off.min_le(n, Nat.sub(m, i), off.le_sub(i, n, m, h)))))