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Proof step 194 from proof bytes2int-int2bytes-len-eq (previous step)

¬ b2i(by) < 0, band(b2i(by), 255) = i + 256, bytes1 = int2bytes(bytes2int(bytes1)), 0 < 256 * (bytes2int(bytes1) + 1) + i, i < 0, 255 < 256 * (bytes2int(bytes1) + 1) + i, 0 ≤ bytes2int(bytes1), ~129 < i, ~256 ≤ i, 0 < bytes2int(bytes1), ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = i2b(i), bytes1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 195:
b2i(by) = i + 256, bytes1 = int2bytes(bytes2int(bytes1)), 0 < bytes2int(bytes1), ~256 ≤ i, ~129 < i, 0 ≤ bytes2int(bytes1), 255 < 256 * (bytes2int(bytes1) + 1) + i, i < 0, 0 < 256 * (bytes2int(bytes1) + 1) + i, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 = [], by = i2b(i)

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ band(i, j) = band(j, i);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ b2i(by) % 256 = b2i(by);% ⊦ 0 ≤ i → band(i, 255) = i % 256;% ⊦ ¬ i < j ↔ j ≤ i;