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Proof step 11 from proof uint2bits-len-01 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
j = i1 * 2 + j1 ∧ 0 ≤ j1 ∧ j1 < 2 ∧ 0 < 2 ∧ 0 ≤ j, ~1 ≤ i0, 0 < j, 2 * 2 ^ (i0 + 1) ≤ j, j < 3 * 2 ^ (i0 + 1), 0 < 2 ^ (i0 + 1), ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ j0 < 3 * 2 ^ i ∧ 2 * 2 ^ i ≤ j0 ∧ 0 < 2 ^ i → # uint2bits(j0) = i→n(i + 3) ⊦ # uint2bits(i1) + 1 = i→n(4 + i0), j = 1, ~1 ≠ i0 ∧ ~1 ≠ i0 ∧ ¬ 3 * 2 ^ i0 ≤ i1 ∧ ¬ i1 < 2 * 2 ^ i0

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [j, 2, i1, j1] rotate: T spec: int-div inst: name: div-elim-pos

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;%⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j); (elim) Used terms: j, 2, i1, j1