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Proof step 8 from proof middle-coef-largest (previous step)

0 ≤ j, j ≤ 2 * i, binom_coef(2 * i, i) < binom_coef(2 * i, 2 * i - j), 0 ≤ i, i ≤ j ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 9:
⊦ j < i ∧ 0 ≤ j → ¬ binom_coef(2 * i, i) < binom_coef(2 * i, j)
Proof step 10:
2 * i - j < i ∧ 0 ≤ 2 * i - j → ¬ binom_coef(2 * i, i) < binom_coef(2 * i, 2 * i - j), 0 ≤ j, j ≤ 2 * i, binom_coef(2 * i, i) < binom_coef(2 * i, 2 * i - j), 0 ≤ i, i ≤ j ⊦

Rule argument

spec: inst: name: middle-coef-largest-01 seq: ⊦ j < i ∧ 0 ≤ j → ¬ binom_coef(2 * i, i) < binom_coef(2 * i, j) subst: [j, i] → [2 * i - j, i] flags: current, []

Additional information

Used terms: 2 * i - j, i