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Theorem coef-eq-zero

⊦ binom_coef(i, j) = 0 ↔ j < 0 ∨ i < j

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: bertrand-middle-coef-smaller, coef-neg, coef-product-le, coef-rec-add-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 7
Used lemmas: fac-zero-02, fac-divides, fac-not-zero, binom-def, binom-less,
Used spec theorems:
- int-gcd/div-eq
Used simplifier rules: