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Proof step 4 from proof diff-primes-neg (previous step)

prime(j), ∃ m, n. m < # countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j) ∧ n < # countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j) ∧ m ≠ n ∧ countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)[m] = countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)[n] ⊦ j = 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)[m] = countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)[n], n < # countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j), m < # countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j), prime(j) ⊦ m = n, j = 2, countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j) = []

Rule argument

Additional information

Used simplifier rules: l: ⊦ # ints = 0 ↔ ints = []; from specification list-data[intlista]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1