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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < i ∧ i ≠ 1 → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1)
Proof step 4:
¬(0 < 2 ^ i - 1 ∧ 2 ^ i - 1 ≠ 1), 0 < i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 → uint2bits(2 ^ i0 - 1) = false ' + mklist(true, i→n(i0)) ⊦ uint2bits(2 ^ i - 1) = false ' + mklist(true, i→n(i))
Proof step 5:
0 < 2 ^ i - 1 ∧ 2 ^ i - 1 ≠ 1, 0 < i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 → uint2bits(2 ^ i0 - 1) = false ' + mklist(true, i→n(i0)) ⊦ uint2bits((2 ^ i - 1) / 2) + ((2 ^ i - 1) % 2 = 1) = false ' + mklist(true, i→n(i))

Rule argument

name: uint2bits-rec-01 rotate: F subst: [i] → [2 ^ i - 1]

Additional information

Used terms: 2 ^ i - 1