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Proof step 1 from proof middle-coef-max_exp-big-primes (conclusion)

⊦ (2 * i) / 3 < j ∧ j ≤ i ∧ prime(j) ∧ 2 < i → max_exp(j, binom_coef(2 * i, i)) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 < i, 2 < i, prime(j), j ≤ i, (2 * i) / 3 < j ⊦ max_exp(j, binom_coef(2 * i, i)) = 0

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%less-mult-div-01: ⊦ 0 < i ∧ 0 < j ∧ 0 < j1 ∧ i1 < j → (i * i1) / j < i; from specification int-div%numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs