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Proof step 56 from proof band-max (previous step)

0 < i, 1 < i, 0 ≤ i, i < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits((j - 1) / 2) + (~1 = j % 2)')), j < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits((j - 1) / 2) + (~1 = j % 2)')), j < 0, 1 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits((j - 1) / 2) + (~1 = j % 2)')), 0 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits((j - 1) / 2) + (~1 = j % 2)')), ∀ i0, j. i→n(i0) < i→n(i) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ j = ~1

Heuristic var elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 57:
j = i1 + 1, 0 < i, 1 < i, 0 ≤ i, i < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(i1 / 2) + (~1 = j % 2)')), j < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(i1 / 2) + (~1 = j % 2)')), j < 0, 1 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(i1 / 2) + (~1 = j % 2)')), 0 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(i1 / 2) + (~1 = j % 2)')), ∀ i0, j. i→n(i0) < i→n(i) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ j = ~1

Rule argument

seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [j, 1, i1] rotate: T spec: int-abs inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: j, 1, i1