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Proof step 34 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))), ∀ i0, j. i→n(i0) < i→n(i) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ 1 < i → int2bits(i) = int2bits(i / 2) + (i % 2 = 1)
Proof step 36:
¬ 1 < j, 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))), ∀ i0, j. i→n(i0) < i→n(i) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦
Proof step 75:
1 < j, 0 < i, 1 < i, 0 ≤ i, i < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(j / 2) + (j % 2 = 1))), 1 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(j / 2) + (j % 2 = 1))), 0 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', int2bits(j / 2) + (j % 2 = 1))), ∀ i0, j. i→n(i0) < i→n(i) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦

Rule argument

seq: ⊦ 1 < i → int2bits(i) = int2bits(i / 2) + (i % 2 = 1) subst: [i] → [j] rotate: F spec: int2bits inst: name: int2bits-rec-pos

Additional information

Used terms: j