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Proof step 15 from proof bib-pos-low (previous step)

j ≤ 127, 64 ≤ i0 * 256 + j, lastn(8, int2bits(i0 * 256 + j)).first, 127 < i0 * 256 + j, 0 < i0, 0 ≤ j, 0 < i0 * 256 + j ⊦ 0 = i0 * 256 + j, b2i(i2b(bits2int(lastn(8, int2bits(i0 * 256 + j))))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ j0 ∧ j0 < 256 → int2bits(j * 256 + j0) = int2bits(j) + fillsgn(9, int2bits(j0)).rest subst: [j0, j] → [j, i0] rotate: F spec: int2bits inst: name: int2bits-mod256

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); Used terms: j, i0