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Proof step 2 from proof even-or-succ-even (previous step)

0 ≤ i ⊦ i % 2 = 0, (i + 1) % 2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: even-not-ex seq: ⊦ i % 2 ≠ 0 ↔ (∃ i0. i = 2 * i0 + 1) subst: [i] → [i] flags: rewrite, current

Additional information

Used simplifier rules: mod-mult-pos-02: ⊦ 0 < j ∧ 0 ≤ i ∧ 0 ≤ i0 → (i * j + i0) % j = i0 % j;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i