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Proof step 58 from proof no-leading-zero (previous step)

255 < bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255), int2bytes((bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) / 256) + int2bytes((bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) % 256).last ' = i2b(0) ' + by ' + bytes1 + by0 ', 0 ≤ b2i(by), ∀ 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 59:
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 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ by ∈ by0 ' ↔ by = by0;% ⊦ by ∈ bytes + bytes0 ↔ ¬ ¬(by ∈ bytes ∨ by ∈ bytes0);%i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ by ' + bytes = bytes0 → by ∈ bytes0; (forward)% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ bytes + by ' = bytes0 + by0 ' ↔ bytes = bytes0 ∧ by = by0;