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Proof step 43 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))), 0 ≤ j, ∀ i0, j. i→n(i0) < i→n(i) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ j = ~1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
1 < i, 0 < i, 0 ≤ i, i < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', false ' + true ')), 1 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', false ' + true ')), 0 < bits2int(bitsand(int2bits(i / 2) + (i % 2 = 1)', false ' + true ')), ∀ i0, j. i→n(i0) < i→n(i) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ uint2bits(1) = false + true;%0 ≤ i ⊦ int2bits((* i)) = uint2bits(i);%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;