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Proof step 33 from proof diff-primes (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
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(m) + n→i(n), 0 < n→i(m) + n→i(n), 0 ≤ n→i(m) + n→i(n), j | n→i(m) - n→i(n) ∨ j | n→i(m) + n→i(n) ⊦ ~1 = (j - 1) / 2, m = n, j = 2, countFun(0, (j - 1) / 2, λ i. i ^2 |%| j) = []

Rule argument

Additional information

Used simplifier rules: forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs