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Proof step 11 from proof bytes2int-size-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ i * (j + j0) = i * j + i * j0
Proof step 13:
0 < b2i(by), band(255, b2i(by0)) + 256 * bytes2int(by ' + bytes1) < 2 ^ (8 * n→i(# bytes1) + 8 * 1), 2 ^ (n→i(# bytes1) * 8) ≤ bytes2int(by ' + bytes1), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → bytes2int(by ' + bytes0) < 2 ^ (n→i(# bytes0) * 8) ∧ 0 < b2i(by) → false ⊦

Rule argument

seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [1, n→i(# bytes1), 8] rotate: F spec: int-mult inst: name: dist-rsplit

Additional information

Used terms: 1, n→i(# bytes1), 8