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Theorem coprimes-prime

⊦ prime(i) → coprimes(i) = count-i2j(1, i - 1)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 12
Used lemmas: count-i2j-in, filterFun-all, filterFun-base, counti2j-empty, filterFun-one, filterFun-append, counti2j-rec, coprimes-def,
Used spec theorems:
- int-gcd/gcd-com
- int-gcd/gcd-prime
Used simplifier rules:
- int-gcd/prime-not-neg-01
- list/intlista/Last
- int-gcd/gcd-same-01
- list/intlista/Nil
- list/intlista/e
- int-gcd/prime-one
- list/intlista/a
- list/intlista/app
- int-abs/forward-le-05
- int-basic1/forward-pos
- int-basic2/add-c
- int-basic2/add-a
- int-abs/succ-01
- int-abs/sub-le-01
- int-abs/leone
- int-abs/lels
- int-abs/bet
- oelem/intlista/lel
- int-gcd/gcd-one-01
- int-gcd/gcd-com