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Proof step 18 from proof uint2bits-len-01 (previous step)

0 ≤ i0, 0 ≤ i1, j1 < 2, 0 ≤ j1, i1 * 2 + j1 < 6 * 2 ^ i0, 4 * 2 ^ i0 ≤ i1 * 2 + j1, 0 < i1 * 2 + j1, 0 < 2 ^ i0, ∀ j0, i. i→n(j0) < i→n(i1 * 2 + j1) → 0 ≤ i ∧ j0 < 3 * 2 ^ i ∧ 2 * 2 ^ i ≤ j0 ∧ 0 < 2 ^ i → # uint2bits(j0) = i→n(i + 3) ⊦ ~1 = i0, i1 * 2 + j1 = 1, # uint2bits(i1) + 1 = i→n(4 + i0), ¬ i1 < 2 * 2 ^ i0 ∧ ¬ 3 * 2 ^ i0 ≤ i1

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: j * i ≤ j * i0 + j0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [2, 2 * 2 ^ i0, i1, j1] rotate: F spec: int-mult inst: name: modlep-01

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ 0 ≤ i → abs(i) = i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 2, 2 * 2 ^ i0, i1, j1