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Proof step 15 from proof bytes2int-size-05 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [8 * (1 + n→i(# bytes1)), 8, 2] rotate: F spec: int-pot inst: name: pot-dist-pos

Additional information

Used simplifier rules: ⊦ i * j + i = i * (j + 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i < 0 ⊦ (* i) ≤ n→i(n); Used terms: 8 * (1 + n→i(# bytes1)), 8, 2