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Proof step 40 from proof band-max (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 41:
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
Proof step 52:
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, j ≠ ~1 ∧ ¬ 0 ≤ j

Rule argument

fma: j ≠ ~1

Additional information

Used formulas: j ≠ ~1