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Proof step 20 from proof middle-coef-max_exp-big-primes (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
2 * i < 3 * j, j ≤ i, prime(j), 2 < i, 0 < i, 2 * i < j ^ 3, j ^ 2 ≤ 2 * i, j ^ 2 < j ^ 3, j ^ 2 < 3 * j, 0 ≤ i ⊦ (2 * i) / j + (2 * i) / j ^ 2 = 2 * i / j + 2 * i / j ^ 2

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult