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Proof step 55 from proof band-min (previous step)

# int2bits(i3) = # int2bits(i2), ~1 = ((i3 * 2 + j0) + 1) % 2, ~1 = ((i2 * 2 + j1) + 1) % 2, abs(j1) < 2, abs(j0) < 2, i3 * 2 + j0 < ~1, i2 * 2 + j1 < ~1, 2 * bits2int(bitsand(int2bits(i3), int2bits(i2))) < i0 - 1, j0 ≤ 0, i3 ≤ 0, i3 * 2 + j0 < 0, j1 ≤ 0, i2 ≤ 0, i2 * 2 + j1 < 0, 2 ^ (n→i(# int2bits(i2)) + 1) + 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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 < i, j < 0 ⊦ (* i) * i0 < (* j) ↔ i0 < j / i subst: [j, i0, i] → [i0 - 1, bits2int(bitsand(int2bits(i3), int2bits(i2))), 2] rotate: F spec: int-div inst: name: nummult-ls-01-01

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i + j < j ↔ i < 0;% ⊦ ¬ 2 ^ i < 0; Used terms: i0 - 1, bits2int(bitsand(int2bits(i3), int2bits(i2))), 2