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Proof step 7 from proof mod2-2pot-02 (previous step)

j % (2 ^ i0 * 2) = 1, 0 ≤ j, 0 ≤ i0 ⊦ j % 2 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ j % (2 * i) = 1 ∧ 0 < i ∧ 0 ≤ j → j % 2 = 1

Rule argument

spec: int-div name: mod-twoodd-02 seq: ⊦ j % (2 * i) = 1 ∧ 0 < i ∧ 0 ≤ j → j % 2 = 1 subst: [j, i] → [j, 2 ^ i0] flags: <all paths>

Additional information

Used simplifier rules: two-lez: ⊦ 0 ≤ i → ¬ 2 ^ i ≤ 0;%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i < j ↔ ¬ j ≤ i; (ss) Used terms: j, 2 ^ i0