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Proof step 22 from proof uint2bits-div2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ 0 < i → j ^ i = j ^ i -1 * j

Rule argument

seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [i0 + 1, 2] rotate: F spec: int-pot inst: name: Pot-pos

Additional information

Used simplifier rules: ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ (i + 1)-1 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i * j = j * i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i0 + 1, 2