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Proof step 64 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)) = 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 65:
int2bytes(bytes2int(i2b(0) ' + by ' + bytes1)) = i2b(0) ' + by ' + bytes1, int2bytes(band(b2i(by0), 255)).last = by0, band(b2i(by0), 255) < 256, 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), 0 ≤ bytes2int(i2b(0) ' + by ' + bytes1), 0 ≤ 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: ⊦ by ∈ by0 ' ↔ by = by0;% ⊦ by ∈ bytes + bytes0 ↔ ¬ ¬(by ∈ bytes ∨ by ∈ bytes0);% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ by ' + bytes = bytes0 → by ∈ bytes0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < j ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ i0 < j → (j * i + i0) % j = i0;