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Proof step 55 from proof band-max (previous step)

j < 0 ∧ j ≠ ~1, 0 < i, 1 < i, 0 ≤ i, i < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits((j - 1) / 2) + (~1 = j % 2)')), 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)')), j ≤ 1, j < i, j < 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 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
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

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;