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Proof step 55 from proof uint2bits-add-low (previous step)

0 < 2 * (i1 + 2 ^ i2) + j0, 1 < 2 * (i1 + 1) + i2, 2 < 2 ^ (i2 + 2), 0 < 2 ^ i2, 0 < 2 ^ (i2 + 2), j0 + 1 < 2 ^ (i2 + 2), 0 < i1 * 2 + j0, 1 < (i1 * 2 + j0) + j0, 0 ≤ 2 ^ i2, i1 * 2 + j0 < 2 ^ (i2 + 2), 2 < 2 * (i1 + 1) + j0 + i2, i1 * 2 + j0 ≤ 1 + 2 ^ i2 * 2, 2 < 2 * (i1 + 2 ^ i2) + j0, i1 * 2 + j0 ≤ 2 ^ (i2 + 2), 2 < (i1 * 2 + j0) + 2 ^ (i2 + 2), i1 * 2 + j0 ≤ 2 ^ (i2 + 2) + 1, 2 ^ i2 < i1, 0 ≤ j0, j0 < 2, 1 < i1 * 2 + j0, 0 < (i1 * 2 + j0) + j0, 0 ≤ (i1 * 2 + j0) + j0, 0 ≤ 2 * (i1 + 1) + i2, 0 ≤ 2 ^ (i2 + 2), 0 < 2 * (i1 + 1) + j0 + i2, 0 ≤ 2 * (i1 + 1) + j0 + i2, 0 ≤ (i1 * 2 + j0) + 2 ^ (i2 + 2), j0 < 2 ^ (i2 + 2), 0 ≤ i2, 0 < 2 * (i1 + 1) + i2, 1 < i1, 0 ≤ i1 + 2 ^ i2, 0 < i1, 0 ≤ i1, ∀ i0, j. i→n(i0) < i→n(i2 + 2) → true → j < 0 ∧ 0 < i0 ∧ abs(j) ≤ 2 ^ (i0 - 1) → uint2bits(j + 2 ^ i0) = false ' + fillsgn(i→n(i0), int2bits(j)) ⊦ ~1 = i2, 1 = i1 * 2 + j0, uint2bits(2 ^ i2 * 2 - i1) + (~1 = (1 - i1 * 2 + j0) % 2)' = false ' + fillsgn(i→n(i2 + 2), int2bits(1 - i1 * 2 + j0))

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: j * i + j0 ≤ j * i0 + j1, 0 ≤ j0, j0 < j, abs(j1) < j ⊦ i ≤ i0 subst: [j, i, j0, i0, j1] → [2, i1, j0, 2 ^ i2, 1] rotate: F spec: int-mult inst: name: modlep-03

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i * j = j * i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 2, i1, j0, 2 ^ i2, 1