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Proof step 11 from proof bytes2int-size-01 (previous step)

b2i(by) < 0 → 2 ^ ((n→i(# bytes1) + 1) * 8 - 1) ≤ bytes2int(i2b(0) ' + by ' + bytes1), b2i(by) < 0, 256 * bytes2int(i2b(0) ' + by ' + bytes1) + band(255, b2i(by0)) < 2 ^ (8 * (2 + n→i(# bytes1)) - 1), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → b2i(by) < 0 → 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) ≤ bytes2int(i2b(0) ' + by ' + bytes0) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
b2i(by) < 0, 256 * bytes2int(i2b(0) ' + by ' + bytes1) + band(255, b2i(by0)) < 2 ^ (8 * (2 + n→i(# bytes1)) - 1), 2 ^ ((n→i(# bytes1) + 1) * 8 - 1) ≤ bytes2int(i2b(0) ' + by ' + bytes1), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → b2i(by) < 0 → 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) ≤ bytes2int(i2b(0) ' + by ' + bytes0) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;