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Proof step 24 from proof middle-coef-max_exp-big-primes (previous step)

2 * i < 3 * j, j ≤ i, prime(j), 2 < i, 0 < i, 2 * i < j ^ 3, j * j ≤ 2 * i, 0 ≤ i, j * j < 3 * j, j * j < j ^ 3 ⊦ (2 * i) / j + (2 * i) / (j * j) = 2 * i / j + 2 * i / (j * j), j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: numls-10 seq: ⊦ 0 < i → ((* i) * j < (* i) * j0 ↔ j < j0) subst: [j0, j, i] → [3, j, j] flags: rewrite

Additional information

Used simplifier rules: lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%prime-not-neg: ⊦ j < 0 → ¬ prime(j); from specification int-gcd%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 3, j, j