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Proof step 22 from proof uint2bits-falsein-01 (previous step)

2 ^ i = 2 * (i0 + 1), 0 < i0, false ∈ uint2bits(i0).rest, ∀ i. 2 ^ i ≠ i0 + 1, ∀ j0. i→n(j0) < i→n(i0 * 2 + 1) → 0 < j0 → (false ∈ uint2bits(j0).rest ↔ (∀ i. 2 ^ i ≠ j0 + 1)) ⊦ 2 ^ (i - 1) = i0 + 1, i0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 24:
¬ 0 < i, 2 ^ i = 2 * (i0 + 1), 0 < i0, false ∈ uint2bits(i0).rest, ∀ i. 2 ^ i ≠ i0 + 1, ∀ j0. i→n(j0) < i→n(i0 * 2 + 1) → 0 < j0 → (false ∈ uint2bits(j0).rest ↔ (∀ i. 2 ^ i ≠ j0 + 1)) ⊦ 2 ^ (i - 1) = i0 + 1, i0 = 0

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 simplifier rules: ⊦ i -1 = i - 1;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i, 2