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Proof step 5 from proof middle-coef-larger-stronger (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ i ∧ 0 < j → (i0 < i / j ↔ i0 * j ≤ i ∧ i0 ≠ i / j)
Proof step 7:
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 ⊦

Rule argument

spec: int-div inst: name: div-ls-modnotzero seq: ⊦ 0 ≤ i ∧ 0 < j → (i0 < i / j ↔ i0 * j ≤ i ∧ i0 ≠ i / j) subst: [j, i, i0] → [2 * i, 4 ^ i, binom_coef(2 * i, i)] flags: rewrite

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-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%notneg-02: ⊦ 0 < i → ¬ i ^ j < 0; from specification int-pot Used terms: 2 * i, 4 ^ i, binom_coef(2 * i, i)