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Proof step 18 from proof bib-pos-low (previous step)

j ≤ 127, 64 ≤ i0 * 256 + j, lastn(8, int2bits(i0) + fillsgn(9, int2bits(j)).rest).first, 127 < i0 * 256 + j, 0 < i0, 0 ≤ j, 0 < i0 * 256 + j ⊦ 0 = i0 * 256 + j, b2i(i2b(bits2int(lastn(8, int2bits(i0) + fillsgn(9, int2bits(j)).rest)))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ m + 1 = n ∧ # bits0 < n → lastn(m, bits + fillsgn(n, bits0).rest) = fillsgn(n -1, bits0) subst: [bits0, n, bits, m] → [int2bits(j), 9, int2bits(i0), 8] rotate: F spec: bitopsaux inst: name: fill-lastN

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ fillsgn(n, int2bits(j)).first ↔ int2bits(j).first;% ⊦ int2bits(j).first ↔ j < 0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: int2bits(j), 9, int2bits(i0), 8