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Proof step 22 from proof band-min (previous step)

j < ~1, 1 = #(int2bits((j - 1) / 2) + int2bits(j % 2)), 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 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
1 = # int2bits((j - 1) / 2) + # int2bits(j % 2), 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 ⊦

Rule argument

Additional information

Used simplifier rules: j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;