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Theorem diff-primes-dups

⊦ prime(j) ∧ j ≠ 2 → dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j) + countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 15
Proof steps: 27
Used lemmas: mod-le-same, mod-pos,
Used spec theorems:
Used simplifier rules:
- list-dup/intlista/a
- int-gcd/prime-not-neg
- nat-basic2/c
- nat-basic2/a
- intnat/n2i-add
- list/intlista/len
- list/intlista/a
- list/intlista/in-append
- int-mult/add-mult-two
- intnat/ini2-abs
- int-abs/forward-lele
- int-abs/forward-le-04
- int-abs/forward-le-03
- int-abs/forward-lels
- int-abs/numlsledel-01
- int-abs/numle-03
- int-div/div-ls-mone
- int-abs/numls-03
- int-abs/ler
- int-abs/succ-02
- int-abs/numsub
- int-abs/sub-add-01
- int-mult/commutativity
- int-mult/associativity
- int-gcd/prime-odd-01
- int-basic2/add-c
- int-basic2/add-a
- int-abs/sub-le-01
- int-div/div-two-zero-01
- int-abs/zero-gels-01
- int-abs/forward-le-02
- int-abs/forward-lsle
- int-abs/lels-01
- int-abs/forward-le-01
- int-abs/lels
- int-abs/anti
- int-abs/zero-gels-04
- int-gcd/prime-not-neg-01