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Theorem coef-mult-rec

⊦ 0 < j ∧ j ≤ i → i * binom_coef(i - 1, j - 1) = j * binom_coef(i, j)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: coef-divides-rec, coef-gcd, coef-rec,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 14
Proof steps: 20
Used lemmas: fac-zero-02, fac-zero, fac-divides, fac-not-zero, fac-rec, binom-def,
Used spec theorems:
- int-gcd/div-mult-shift
- int-mult/commutativity
Used simplifier rules: