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Proof step 66 from proof band-max (previous step)

¬(true ∧ ¬ bitsand(int2bits(i / 2), int2bits(i1 / 2)).first ∧ bitsand(int2bits(i / 2), int2bits(i1 / 2)) ≠ []), i % 2 = 1, ~1 = (i1 + 1) % 2, i1 < 0, 0 < i, 1 < i, 0 ≤ i, i < bits2int(bitsand(int2bits(i / 2), int2bits(i1 / 2)) + true '), i1 + 1 < bits2int(bitsand(int2bits(i / 2), int2bits(i1 / 2)) + true '), i1 < ~1, 1 < bits2int(bitsand(int2bits(i / 2), int2bits(i1 / 2)) + true '), 0 < bits2int(bitsand(int2bits(i / 2), int2bits(i1 / 2)) + true '), ∀ i0, j. i→n(i0) < i→n(i) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ ~2 = i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
i % 2 = 1, ~1 = (i1 + 1) % 2, i1 < 0, 0 < i, 1 < i, 0 ≤ i, i < bits2int(bitsand(int2bits(i / 2), int2bits(i1 / 2)) + true '), i1 + 1 < bits2int(bitsand(int2bits(i / 2), int2bits(i1 / 2)) + true '), i1 < ~1, 1 < bits2int(bitsand(int2bits(i / 2), int2bits(i1 / 2)) + true '), 0 < bits2int(bitsand(int2bits(i / 2), int2bits(i1 / 2)) + true '), bitsand(int2bits(i / 2), int2bits(i1 / 2)).first, ∀ 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: and-notempty-09: ⊦ bitsand(int2bits(i), int2bits(i0)) ≠ [];