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Proof step 3 from proof mod-ngez-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < j ∧ i < 0 → (0 ≤ i % j ↔ i % j = 0)

Rule argument

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

Additional information

Used simplifier rules: pot2-pos: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s) Used terms: 2 ^ i, j