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Proof step 18 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 ^ 2 ≤ 2 * i, j ^ 2 < j ^ 3 ⊦ (2 * i) / j + (2 * i) / j ^ 2 = 2 * i / j + 2 * i / j ^ 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0)
Proof step 20:
0 < 3 ∧ 0 ≤ 2 * i, 2 * i < 3 * j, j ≤ i, prime(j), 2 < i, 0 < i, 2 * i < j ^ 3, j ^ 2 ≤ 2 * i, j ^ 2 < j ^ 3 ⊦ (2 * i) / j + (2 * i) / j ^ 2 = 2 * i / j + 2 * i / j ^ 2

Rule argument

spec: int-div inst: name: num-ls seq: ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0) subst: [j0, j, i] → [j, 3, 2 * i] flags: rewrite

Additional information

Used simplifier rules: zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j, 3, 2 * i