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Proof step 1 from proof diff-primes-dups (conclusion)

⊦ 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
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)), dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j)), dups(countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%a: ⊦ ¬ dups(ints + ints0) → ¬ dups(ints) ∧ ¬ dups(ints0); (forward) from specification list-dup[intlista]