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Proof step 15 from proof uint2bits-len (previous step)

0 ≤ 2 ^ (2 + i0), 1 < 2 ^ (2 + i0), 0 < 2 ^ (2 + i0), 2 ^ (i0 + 1) < 2 ^ (2 + i0), 0 ≤ i0, 0 < j, j < 2 ^ (2 + i0), 2 ^ (i0 + 1) ≤ j, 0 ≤ j, 2 ^ (i0 + 1) ≤ j / 2, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i ≤ j0 ∧ j0 < 2 ^ (i + 1) → # uint2bits(j0) = i→n(i + 2) ⊦ ~1 = i0, j = 1, # uint2bits(j / 2) + 1 = i→n(3 + i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 ≤ j → (2 ^ i ≤ j / 2 ↔ 2 ^ (i + 1) ≤ j) subst: [j, i] → [j, i0 + 1] rotate: F spec: int-pot inst: name: le-2pot

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < j → ¬ j < i;% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) Used terms: j, i0 + 1