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Proof step 57 from proof band-max (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
0 < i, 1 < i, 0 ≤ i, i < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(i1 / 2) + (~1 = (i1 + 1) % 2)')), i1 + 1 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(i1 / 2) + (~1 = (i1 + 1) % 2)')), i1 < ~1, 1 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(i1 / 2) + (~1 = (i1 + 1) % 2)')), 0 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(i1 / 2) + (~1 = (i1 + 1) % 2)')), i1 < 0, ∀ i0, j. i→n(i0) < i→n(i) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ ~2 = i1

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < 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;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ i + 1 = ~1 ↔ i + 1 + 1 = 0;