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Proof step 49 from proof middle-coef-max_exp (previous step)

i | binom_coef(2 * j, j), prime(i), 2 * j < i ^ max_exp(i, binom_coef(2 * j, j)), 0 < j ⊦ ∃ i0. 0 ≤ i0 ∧ i ^ i0 ≤ 2 * j ∧ 2 * j < i ^ (i0 + 1)

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: exinpot seq: 0 < j, 1 < i ⊦ ∃ i0. 0 ≤ i0 ∧ i ^ i0 ≤ j ∧ j < i ^ (i0 + 1) subst: [j, i] → [2 * j, i] flags: []

Additional information

Used simplifier rules: zero-gr: ⊦ 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: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%prime-one: ⊦ i ≤ 1 → ¬ prime(i); from specification int-gcd Used terms: 2 * j, i