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Proof step 20 from proof band-min (previous step)

1 = # int2bits(j), i0 < 0, i0 ≤ ~2, j < i0, j < ~2, j < 0, ∀ i0, j, i1. i→n(i1) < i→n(~1) → # int2bits(i1) = # int2bits(j) ∧ bits2int(bitsand(int2bits(i1), int2bits(j))) < i0 ∧ i1 ≤ 0 ∧ j ≤ 0 ∧ i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ j < ~1 → int2bits(j) = int2bits((j - 1) / 2) + int2bits(j % 2) subst: [j] → [j] rotate: F spec: int2bits inst: name: int2bits-rec-neg-01

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1); Used terms: j