| bytes = [], int2bytes(bytes2int(i2b(0) ' + by ' + bytes)) = i2b(0) ' + by ' + bytes, 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < # bytes → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦ |
int2bytes(bytes2int(i2b(0) ' + by ')) = i2b(0) ' + by ', 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < # [] → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦
Used simplifier rules: ⊦ by ∈ by0 ' ↔ by = by0;% ⊦ by ∈ bytes + bytes0 ↔ ¬ ¬(by ∈ bytes ∨ by ∈ bytes0);% ⊦ by ' + bytes = bytes0 → by ∈ bytes0; (forward)% ⊦ bytes + by ' = bytes0 → by ∈ bytes0; (forward)% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ bytes + [] = bytes;