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Proof step 4 from proof uint2bits-2pot-neg-mone (previous step)

0 < i, 0 < j, ∀ j, i0. i→n(i0) < i→n(i) → 0 < j ∧ 0 < i0 → uint2bits(j * 2 ^ i0 - 1) = uint2bits(j - 1) + mklist(true, i→n(i0)) ⊦ uint2bits(j * 2 ^ i - 1) = uint2bits(j - 1) + mklist(true, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 6:
0 < i, 0 < i, 0 < j, ∀ j, i0. i→n(i0) < i→n(i) → 0 < j ∧ 0 < i0 → uint2bits(j * 2 ^ i0 - 1) = uint2bits(j - 1) + mklist(true, i→n(i0)) ⊦ uint2bits(j * 2 ^ i -1 * 2 - 1) = uint2bits(j - 1) + mklist(true, i→n(i))

Rule argument

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

Additional information

Used terms: i, 2