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Proof step 7 from proof bertrand-middle-coef-smaller (previous step)

binom_coef(2 * i, i) = 0, 2 < i, 0 < i, (2 * i) ^ (sqrt(2 * i) - 1) * 4 ^ ((2 * i) / 3) < 0, (2 * i) ^ (sqrt(2 * i) - 1) * 4 ^ ((2 * i) / 3) < i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: coef-eq-zero seq: ⊦ binom_coef(i, j) = 0 ↔ j < 0 ∨ i < j subst: [j, i] → [i, 2 * i] flags: rewrite, current

Additional information

Used simplifier rules: ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%ls-same: ⊦ 0 < i → (i * j < i ↔ j < 1); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i, 2 * i