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Proof step 7 from proof middle-coef-larger-stronger (previous step)

0 ≤ 4 ^ i ∧ 0 < 2 * i, binom_coef(2 * i, i) * 2 * i ≤ 4 ^ i ∧ binom_coef(2 * i, i) ≠ 4 ^ i / (2 * i), 0 < i, 4 ^ i ≤ binom_coef(2 * i, i) * 2 * i ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: le-pos-01: ⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i ^ j ≤ i0 ^ j ↔ i ≤ i0); from specification int-pot%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); 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-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult