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Theorem middle-coef-max_exp

i | binom_coef(2 * j, j), prime(i), 0 < j ⊦ i ^ max_exp(i, binom_coef(2 * j, j)) ≤ 2 * j

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment: Claim 2.1
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 21
Proof steps: 34
Used lemmas: max_exp-fac-gen-stronger, max_exp-mult, fac-le-zero, fac-pos-01, max_exp-div, fac-divides, binom-def, max_exp-pos-02,
Used spec theorems:
Used simplifier rules:
- int-mult/le-same-01
- int-mult/eq-pos
- int-abs/sub-eq
- int-mult/add-mult-two
- int-mult/ls-same
- oelem/intlista/transitivity
- int-abs/lels-03
- int-abs/zero-gels
- int-abs/ler
- int-abs/succ-02
- int-pot/ls-pos
- int-basic1/forward-pos
- int-abs/forward-lels
- int-abs/sub-ls-01
- int-abs/zero-gels-04
- int-pot/grz
- int-abs/numle-02
- int-abs/numleledel-01
- int-abs/lels-01
- int-basic1/ls-01
- int-abs/forward-le
- int-mult/one
- int-abs/numsub
- intnat/i2i-pos
- oelem/intlista/irreflexivity
- intnat/nat2int
- int-abs/forward-le-01
- int-abs/forward-le-05
- int-abs/forward-lsle
- list-data/intlista/l
- nat-basic1/zero
- intnat/num-n2i-ls-02
- int-pot/Pot-zero
- int-basic2/add-zero
- int-pot/one
- int-basic2/add-c
- int-basic2/add-a
- oelem/intlista/lel
- int-abs/anti
- int-abs/leone
- int-mult/zero-gr
- int-mult/associativity
- int-mult/commutativity
- int-abs/lels
- int-gcd/prime-one