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Proof step 12 from proof uint2bits-2pot-02 (previous step)

2 ^ i % 2 = 0, 0 ≤ 2 ^ i, 0 < 2 ^ i, 1 < 2 ^ 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) + ((2 ^ i - 1) % 2 = 1)' = false ' + mklist(true, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ 1 < i → (2 ^ i - 1) % 2 = 1
Proof step 14:
1 < i, 2 ^ i % 2 = 0, 0 ≤ 2 ^ i, 0 < 2 ^ i, 1 < 2 ^ 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) + (1 = 1)' = false ' + mklist(true, i→n(i))

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 ↔ j < i);% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i