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Proof step 4 from proof band-min-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 ≤ i → ¬ band(i, j) < 0
Proof step 6:
¬ 0 ≤ i, band(i, j) < i0, i0 + 2 ^ (n→i(# int2bits(i)) - 1) ≤ 0, i0 + 2 ^ (n→i(# int2bits(j)) - 1) ≤ 0, band(i, j) < 0 ⊦

Rule argument

name: band-notneg rotate: F subst: [j, i] → [j, i]

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i); Used terms: j, i