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Proof step 5 from proof middle-coef-largest (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ j ∧ j ≤ i → binom_coef(i, j) = binom_coef(i, i - j)
Proof step 7:
0 ≤ j ∧ j ≤ 2 * i, i ≤ j, 0 ≤ i, binom_coef(2 * i, i) < binom_coef(2 * i, 2 * i - j), j ≤ 2 * i, 0 ≤ j ⊦

Rule argument

spec: inst: name: coef-switch seq: ⊦ 0 ≤ j ∧ j ≤ i → binom_coef(i, j) = binom_coef(i, i - j) subst: [j, i] → [j, 2 * i] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: j, 2 * i