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Proof step 41 from proof band-max (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
0 < i, 1 < i, 0 ≤ i, i < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(j))), 1 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(j))), 0 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(j))), j ≤ 1, j < i, j < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(j))), 0 ≤ j, ∀ 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: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)