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Proof step 2 from proof mod-ngez-01 (previous step)

j < i, j < 0, 0 < i, j + 1 < i ⊦ 0 ≤ j % 2 ^ i ↔ j % 2 ^ i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j ∧ i < 0 → (0 ≤ i % j ↔ i % j = 0)

Rule argument

spec: int-div inst: name: mod-ngez seq: ⊦ 0 < j ∧ i < 0 → (0 ≤ i % j ↔ i % j = 0) subst: [j, i] → [2 ^ i, j] flags: rewrite

Additional information

Used simplifier rules: pot2-pos: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: 2 ^ i, j