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Proof step 4 from proof middle-coef-max_exp-stronger (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), 0 ≤ i0, prime(i), 0 < j ⊦ max_exp(i, binom_coef(2 * j, j)) ≤ i0
Proof step 6:
max_exp(i, binom_coef(2 * j, j)) ≤ 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, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), i ^ i0 < i ^ max_exp(i, binom_coef(2 * j, j)) ⊦

Rule argument

spec: inst: name: middle-coef-max_exp-le seq: i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), 0 ≤ i0, prime(i), 0 < j ⊦ max_exp(i, binom_coef(2 * j, j)) ≤ i0 subst: [i, i0, j] → [i, i0, j] flags: current, []

Additional information

Used terms: i, i0, j