def p_take_append_add

bend-osdev-bytes@0.1.1.0 · PROOF.bend:1185

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

1185def p_take_append_add(+a: B.Octets, +n: Nat, +b: B.Octets) -> {B.Octets.take(Nat.add(B.Octets.len(a), n), B.Octets.append(a, b)) == B.Octets.append(a, B.Octets.take(n, b)) : B.Octets}:
1186  match a b:
1187    case B.Octets{+xs} B.Octets{+ys}:
1188      %F_app(xs, ys) : {B.Octets{B.w8s.take.fast(Nat.add(B.w8s.len.fast(xs), n), _)} == B.Octets{B.w8s.append.fast(xs, B.w8s.take.fast(n, ys))} : B.Octets}
1189      %F_len(xs) : {B.Octets{B.w8s.take.fast(Nat.add(_, n), List.append(&2, B.OctByte, xs, ys))} == B.Octets{B.w8s.append.fast(xs, B.w8s.take.fast(n, ys))} : B.Octets}
1190      %F_take(Nat.add(List.length(&2, B.OctByte, xs), n), List.append(&2, B.OctByte, xs, ys)) : {B.Octets{_} == B.Octets{B.w8s.append.fast(xs, B.w8s.take.fast(n, ys))} : B.Octets}
1191      %F_take(n, ys) : {B.Octets{B.w8s.take(Nat.add(List.length(&2, B.OctByte, xs), n), List.append(&2, B.OctByte, xs, ys))} == B.Octets{B.w8s.append.fast(xs, _)} : B.Octets}
1192      %F_app(xs, B.w8s.take(n, ys)) : {B.Octets{B.w8s.take(Nat.add(List.length(&2, B.OctByte, xs), n), List.append(&2, B.OctByte, xs, ys))} == B.Octets{_} : B.Octets}
1193      Equal.cong(List<&2, B.OctByte>, B.Octets, l => B.Octets{l}, B.w8s.take(Nat.add(List.length(&2, B.OctByte, xs), n), List.append(&2, B.OctByte, xs, ys)), List.append(&2, B.OctByte, xs, B.w8s.take(n, ys)), off.take_app_add(xs, n, ys))