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Theorem coef-sub

⊦ 1 ≤ j ∧ j ≤ i → binom_coef(i, j) - binom_coef(i, j - 1) = (fac(i) * (i + 1 - 2 * j)) / (fac(j) * fac(i + 1 - j))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: middle-coef-largest-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: fac-zero-02, coef-sub-mult,
Used spec theorems:
- Used simplifier rules: