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Proof step 11 from proof bytes2int-rec-first-zero (previous step)

i2b(0) ' + bytes1 ≠ [], ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → bytes0 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes0) = band(b2i(by), 255) * 256 ^ n→i(# bytes0) + bytes2int(i2b(0) ' + bytes0) ⊦ band(255, b2i(by0)) + 256 * bytes2int((i2b(0) ' + by ') + bytes1) = (bytes2int(i2b(0) ' + bytes1) * 256 + band(b2i(by0), 255)) + 256 ^ (n→i(# bytes1) + 1) * band(b2i(by), 255)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → bytes0 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes0) = band(b2i(by), 255) * 256 ^ n→i(# bytes0) + bytes2int(i2b(0) ' + bytes0) ⊦ 256 * bytes2int((i2b(0) ' + by ') + bytes1) = bytes2int(i2b(0) ' + bytes1) * 256 + 256 ^ (n→i(# bytes1) + 1) * band(b2i(by), 255)

Rule argument

Additional information

Used simplifier rules: ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ by ' + bytes ≠ [];% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ band(i, j) = band(j, i);