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Proof step 89 from proof band-max (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ i;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ 0 ≤ i / 2 ↔ ~1 ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0);