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Proof step 9 from proof bytes2int-size-02 (previous step)

bytes = bytes1 + by0 ', 0 < b2i(by), 2 ^ ((n→i(# bytes) + 1) * 8 - 1) ≤ band(255, b2i(by0)) + 256 * bytes2int(by ' + bytes1), ∀ by, bytes0. # bytes0 < # bytes → true → 0 < b2i(by) → bytes2int(by ' + bytes0) < 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) ⊦ bytes = [], bytes = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
0 < b2i(by), 2 ^ (8 * (2 + n→i(# bytes1)) - 1) ≤ band(255, b2i(by0)) + 256 * bytes2int(by ' + bytes1), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → 0 < b2i(by) → bytes2int(by ' + bytes0) < 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ # by ' = 0 +1;% ⊦ #(bytes + bytes0) = # bytes + # bytes0;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ bytes + by ' ≠ [];