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Proof step 31 from proof diff-primes-neg (previous step)

¬(n→i(n) + n→i(m) < j ∧ 0 < n→i(n) + n→i(m)), prime(j), 0 ≤ j, m < i→n(1 + (j - 1) / 2), n < i→n(1 + (j - 1) / 2), prime(j), n→i(m) ≤ (j - 1) / 2, n→i(n) ≤ (j - 1) / 2, j | n→i(n) - n→i(m) ∨ j | n→i(n) + n→i(m), 0 < j ⊦ countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j) = [], j = 2, m = n, ~1 = (j - 1) / 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
0 < j, n→i(n) ≤ (j - 1) / 2, n→i(m) ≤ (j - 1) / 2, prime(j), n < i→n(1 + (j - 1) / 2), m < i→n(1 + (j - 1) / 2), 0 ≤ j, j | n→i(n) - n→i(m) ∨ j | n→i(n) + n→i(m) ⊦ ~1 = (j - 1) / 2, m = n, j = 2, countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j) = [], n→i(n) + n→i(m) < j ∧ 0 < n→i(n) + n→i(m)

Proof step 31 from proof diff-primes-neg (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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