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Proof step 131 from proof bytes2int-int2bytes-len-eq (previous step)

0 ≤ b2i(by0), 256 * b2i(by0) + band(b2i(by), 255) < 0, ~256 < 256 * b2i(by0) + band(b2i(by), 255), 256 * b2i(by0) + band(b2i(by), 255) < ~128, ∀ bytes0. # bytes0 < #((by0 + []) + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ i2b(~1) = by0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 132:
¬ i < 0, ¬ j < 0 ⊦ ¬ i + j < 0

Rule argument

seq: ¬ i < 0, ¬ j < 0 ⊦ ¬ i + j < 0 subst: [j, i] → [band(b2i(by), 255), 256 * b2i(by0)] rotate: F spec: int-basic2 inst: name: pls-01

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ band(i, j) = band(j, i);% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i + j = j + i; Used terms: band(b2i(by), 255), 256 * b2i(by0)