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Proof step 5 from proof even-not (previous step)

(2 * i + 1) % 2 = 0, i < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: mod-add1-negpos-neg seq: ⊦ i % j = 0 ∧ i + i0 < 0 ∧ i < 0 ∧ 0 ≤ i0 ∧ i0 % j ≠ 0 ∧ 0 < j → (i + i0) % j = i0 % j - j subst: [j, i0, i] → [2, 1, 2 * i] flags: rewrite, current

Additional information

Used simplifier rules: mod-two-02: ⊦ (i * 2) % 2 = 0;%mod-two-02: ⊦ (i * 2) % 2 = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%modzero-02: ⊦ i < 0 ∧ j0 < j ∧ 0 < j → i * j + j0 < 0; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0); from specification int-mult%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs Used terms: 2, 1, 2 * i