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Proof step 6 from proof uint2bits-2pot-01 (previous step)

0 < j, 0 ≤ i, 0 < 2 ^ i, ∀ i0, j. i→n(i0) < i→n(i) → 0 ≤ i0 ∧ 0 < j → uint2bits(j * 2 ^ i0) = uint2bits(j) + mklist(false, i→n(i0)) ⊦ j * 2 ^ i = 1, uint2bits((j * 2 ^ i) / 2) + ((j * 2 ^ i) % 2 = 1)' = uint2bits(j) + mklist(false, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 0 ≤ i ∧ 0 < j → (i * 2 ^ j) / 2 = i * 2 ^ (j - 1)
Proof step 8:
¬(0 ≤ j ∧ 0 < i), 0 < j, 0 ≤ i, 0 < 2 ^ i, ∀ i0, j. i→n(i0) < i→n(i) → 0 ≤ i0 ∧ 0 < j → uint2bits(j * 2 ^ i0) = uint2bits(j) + mklist(false, i→n(i0)) ⊦ j * 2 ^ i = 1, uint2bits((j * 2 ^ i) / 2) + ((j * 2 ^ i) % 2 = 1)' = uint2bits(j) + mklist(false, i→n(i))
Proof step 11:
0 ≤ j ∧ 0 < i, 0 < j, 0 ≤ i, 0 < 2 ^ i, ∀ i0, j. i→n(i0) < i→n(i) → 0 ≤ i0 ∧ 0 < j → uint2bits(j * 2 ^ i0) = uint2bits(j) + mklist(false, i→n(i0)) ⊦ j * 2 ^ i = 1, uint2bits(j * 2 ^ (i - 1)) + ((j * 2 ^ i) % 2 = 1)' = uint2bits(j) + mklist(false, i→n(i))

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 < j → (i * 2 ^ j) / 2 = i * 2 ^ (j - 1) subst: [j, i] → [i, j] rotate: F spec: int-pot inst: name: div2-2pot-02

Additional information

Used terms: i, j