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Proof step 15 from proof uint2bits-2pot-02 (previous step)

1 < i, 0 ≤ 2 ^ i, 0 < 2 ^ i, 1 < 2 ^ i, 0 < i, 0 ≤ i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 → uint2bits(2 ^ i0 - 1) = false ' + mklist(true, i→n(i0)) ⊦ i = 1, uint2bits(2 ^ i / 2 - 1) + true ' = false ' + mklist(true, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 2 ^ i / 2 = 2 ^ (i - 1)
Proof step 17:
1 < i, 0 ≤ 2 ^ i, 0 < 2 ^ i, 1 < 2 ^ i, 0 < i, 0 ≤ i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 → uint2bits(2 ^ i0 - 1) = false ' + mklist(true, i→n(i0)) ⊦ i = 1, uint2bits(2 ^ (i - 1) - 1) + true ' = false ' + mklist(true, i→n(i))

Rule argument

seq: ⊦ 2 ^ i / 2 = 2 ^ (i - 1) subst: [i] → [i] rotate: F spec: int-pot inst: name: div2

Additional information

Used terms: i