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Theorem middle-coef-divides-not

⊦ 2 * i < j ∧ prime(j) ∧ 0 < i → ¬ j | binom_coef(2 * i, i)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: bertrand-prime-factors,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 13
Used lemmas: prime-fac-divides-not, fac-not-zero, fac-divides, binom-def,
Used spec theorems:
- int-gcd/divides
- int-div/div-mult
Used simplifier rules: