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Proof step 35 from proof getShort-isi (previous step)

~128 ≤ b2i(byi), b2i(byi) ≤ 127, b2i(byi) < 256, b2i(byi) * 256 + band(b2i(byj), 255) < ~32768, band(b2i(byj), 255) < 256, 0 ≤ band(b2i(byj), 255), b2i(byi) < 0, b2i(byi) < band(b2i(byj), 255), b2i(byi) < 255, ~128 < band(b2i(byj), 255) ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [256, b2i(byi), band(b2i(byj), 255), ~128] rotate: F spec: int-mult inst: name: modlsp-02

Additional information

Used simplifier rules: byte-and-le-256: ⊦ ¬ 256 ≤ band(b2i(by), 255);%byte-and-lsz: ⊦ ¬ band(b2i(by), 255) < 0;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ band(i, j) = band(j, i);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ 0 ≤ i → abs(i) = i;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j); Used terms: 256, b2i(byi), band(b2i(byj), 255), ~128