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Theorem bertrand-small-primes

∀ j. j ∈ ints → j ≤ sqrt(2 * i), all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0, 2 < i ⊦ Π ints ≤ (2 * i) ^ (sqrt(2 * i) - 1)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 18
Used lemmas: max_exp-def, max_exp-pos, middle-coef-max_exp-stronger, product-pot-no-dups,
Used spec theorems:
- int-pot/ls-pos
- intlist/nodups-interval-size
Used simplifier rules:
- int-basic1/numlslsdel-01
- int-abs/forward-le-01
- int-abs/lels-01
- int-gcd/prime-not-neg-01
- int-abs/bet
- int-pot/one-01
- int-basic1/forward-pos
- intnat/nat2int-04
- nat-basic1/f
- int-abs/forward-lels
- list-perm/intlista/in-05
- list-perm/intlista/ocappend
- intnat/n2i-add
- nat-basic2/a
- nat-basic2/c
- nat-basic2/l-02
- int-abs/forward-lsle
- int-square/square-not-neg-03
- list-data/intlista/l
- nat-basic1/zero
- intnat/num-n2i-ls-02
- int-abs/forward-le-05
- int-abs/forward-le
- int-abs/succ-02
- int-abs/sub-ls
- int-abs/leone
- int-mult/commutativity
- int-mult/associativity
- int-div/nummult-ls-02
- int-abs/sub-le-01
- int-abs/succ-01
- int-abs/lenls
- int-basic2/add-a
- int-basic2/add-c
- list-dup/intlista/rm-empty
- list-dup/intlista/rm-in-02
- list-dup/intlista/rm-nodups
- int-abs/forward-lele
- int-abs/lels
- list/intlista/in-11
- list/intlista/a
- intlist/all_prime_divisors-in-01
- int-gcd/prime-one