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Proof step 30 from proof uint2bits-falsein-01 (previous step)

2 ^ i = i0 + 1, 0 < i0, ∀ i. 2 ^ i ≠ 2 * (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) = 2 * (i0 + 1), i0 = 0, false ∈ uint2bits(i0).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [i, 2] rotate: F spec: int-pot inst: name: succ

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < 0 → 2 ^ i = 0;% ⊦ 0 < i ∧ 0 < j → 0 ≠ i + j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i, 2