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Proof step 2 from proof middle-coef-max_exp-stronger (previous step)

prime(i), 2 * j < i ^ max_exp(i, binom_coef(2 * j, j)), 0 < j ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 3:
∃ i0. 0 ≤ i0 ∧ i ^ i0 ≤ 2 * j ∧ 2 * j < i ^ (i0 + 1), prime(i), 2 * j < i ^ max_exp(i, binom_coef(2 * j, j)), 0 < j ⊦
Proof step 8:
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)

Rule argument

fma: ∃ i0. 0 ≤ i0 ∧ i ^ i0 ≤ 2 * j ∧ 2 * j < i ^ (i0 + 1)

Additional information

Used formulas: ∃ i0. 0 ≤ i0 ∧ i ^ i0 ≤ 2 * j ∧ 2 * j < i ^ (i0 + 1)