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Proof step 61 from proof no-leading-zero (previous step)

¬(0 < 256 ∧ 0 ≤ bytes2int(i2b(0) ' + by ' + bytes1) ∧ 0 ≤ band(b2i(by0), 255) ∧ band(b2i(by0), 255) < 256), int2bytes((bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) / 256) = i2b(0) ' + by ' + bytes1, int2bytes((bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) % 256).last = by0, 255 < bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255), 0 ≤ b2i(by), 0 < bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
int2bytes((bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) % 256).last = by0, int2bytes((bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) / 256) = i2b(0) ' + by ' + bytes1, bytes2int(i2b(0) ' + by ' + bytes1) < 0, 0 < bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255), 0 ≤ b2i(by), 255 < bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

Rule argument

Additional information

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