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Proof step 91 from proof band-min (previous step)

# int2bits(i3) = # int2bits(i2), 0 ≤ i3 + j0, j0 ≤ 0, abs(j1) < 2, 2 ^ (n→i(# int2bits(i2)) + 1) + i0 ≤ 0, i2 * 2 + j1 < 0, i2 ≤ 0, j1 ≤ 0, i3 < 0, i3 * 2 + j0 < 0, abs(j0) < 2, i3 * 2 + j0 < ~1, i2 * 2 + j1 < ~1, bits2int(bitsand(int2bits(i3), int2bits(i2))) < i0 / 2, i0 < 0, ∀ i0, j, i1. i→n(i1) < i→n((i3 * 2 + j0) + 1) → # int2bits(i1) = # int2bits(j) ∧ bits2int(bitsand(int2bits(i1), int2bits(j))) < i0 ∧ i1 ≤ 0 ∧ j ≤ 0 ∧ i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 → false ⊦ ~2 = i3 * 2 + j0, ~2 = i2 * 2 + j1, i3 + j0 = ~1, ~1 = ((i3 * 2 + j0) + 1) % 2 ∧ ~1 = ((i2 * 2 + j1) + 1) % 2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < 0 ∧ j < 0 → ¬ 0 ≤ i + j subst: [j, i] → [j0, i3] rotate: F spec: int-abs inst: name: zero-ge-01

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i + 0 = i;% ⊦ 0 < i ∧ j < 0 → ((* i) * i0 < (* j) ↔ i0 < j / i);% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 < i → (i * j < 0 ↔ j < 0); Used terms: j0, i3