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Proof step 13 from proof uint2bits-falsein-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ 1 < i → (2 ^ i - 1) % 2 = 1

Rule argument

seq: ⊦ 1 < i → (2 ^ i - 1) % 2 = 1 subst: [i] → [i] rotate: F spec: int-pot inst: name: two-mod-01

Additional information

Used simplifier rules: ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ 2 ^ i = 2 ↔ i = 1;% ⊦ ¬ i < j → (i ≠ j ↔ j < i);% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ 1 < 2 ^ i ↔ 0 < i;% ⊦ i ≤ j → ¬ j < i; Used terms: i