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Proof step 16 from proof bytes2int-size-06 (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 17:
j * i ≤ j * i0 + j0, 0 ≤ j0, j0 < j ⊦ i ≤ i0
Proof step 18:
0 < 255 * (2 ^ (8 * n→i(# bytes1)) + bytes2int(by ' + bytes1)) + band(255, b2i(by0)), 0 ≤ 256 * (bytes2int(by ' + bytes1) + 2 ^ (8 * n→i(# bytes1))) + band(255, b2i(by0)), b2i(by) < 0, bytes2int(by ' + bytes1) + 2 ^ (8 * n→i(# bytes1)) < 0, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → 0 ≤ bytes2int(by ' + bytes0) + 2 ^ (8 * n→i(# bytes0)) ∧ b2i(by) < 0 → b2i(by) = ~1 ⊦ 256 * 0 ≤ 256 * (bytes2int(by ' + bytes1) + 2 ^ (8 * n→i(# bytes1))) + band(255, b2i(by0)) ∧ 0 ≤ band(255, b2i(by0)) ∧ band(255, b2i(by0)) < 256, b2i(by) = ~1

Rule argument

seq: j * i ≤ j * i0 + j0, 0 ≤ j0, j0 < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [256, 0, bytes2int(by ' + bytes1) + 2 ^ (8 * n→i(# bytes1)), band(255, b2i(by0))] rotate: F spec: int-mult inst: name: modlep

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 256, 0, bytes2int(by ' + bytes1) + 2 ^ (8 * n→i(# bytes1)), band(255, b2i(by0))