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Proof step 34 from proof diff-primes-neg (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(n) + n→i(m), 0 < n→i(n) + n→i(m), 0 ≤ n→i(n) + n→i(m), 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) = []

User applied rule cut formula

And obtained the following new goals

Proof step 35:
j ≤ (j - 1) / 2 + (j - 1) / 2, 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), 0 < n→i(n) + n→i(m), 0 ≤ n→i(n) + n→i(m), 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) = []
Proof step 38:
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), 0 < n→i(n) + n→i(m), 0 ≤ n→i(n) + n→i(m), j | n→i(n) - n→i(m) ∨ j | n→i(n) + n→i(m) ⊦ j ≤ (j - 1) / 2 + (j - 1) / 2, ~1 = (j - 1) / 2, m = n, j = 2, countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j) = []

Rule argument

fma: j ≤ (j - 1) / 2 + (j - 1) / 2

Additional information

Used formulas: j ≤ (j - 1) / 2 + (j - 1) / 2