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Proof step 21 from proof bytes2int-size (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ ¬ j < 0 → abs(j) = j

Rule argument

seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [band(255, b2i(by0))] rotate: F spec: int-abs inst: name: Abs-pos

Additional information

Used simplifier rules: ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ ¬ 256 ≤ band(i, 255);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i); Used terms: band(255, b2i(by0))