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Proof step 26 from proof uint2bits-div2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ 0 ≤ i ∧ 0 ≤ j → (j / 2) / 2 ^ i = j / 2 ^ (i + 1)

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 ≤ j → (j / 2) / 2 ^ i = j / 2 ^ (i + 1) subst: [i, j] → [i0, j] rotate: F spec: int-pot inst: name: div2-2pot-01

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i < j → ¬ j < i; Used terms: i0, j