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Proof step 9 from proof band-min-02 (previous step)

¬ 0 ≤ j, band(i, j) < i0, i0 + 2 ^ (n→i(# int2bits(i)) - 1) ≤ 0, i0 + 2 ^ (n→i(# int2bits(j)) - 1) ≤ 0, band(i, j) < 0, i < 0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
band(i, j) < i0, i0 + 2 ^ (n→i(# int2bits(i)) - 1) ≤ 0, i0 + 2 ^ (n→i(# int2bits(j)) - 1) ≤ 0, band(i, j) < 0, i < 0, j < 0 ⊦

Rule argument

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ ¬ i ≤ j ↔ j < i;