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Proof step 36 from proof diff-primes-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: divmult seq: j ≠ 0 ⊦ i % j = 0 → i / j * j = i subst: [j, i] → [2, j - 1] flags: rewrite

Additional information

Used simplifier rules: prime-odd-01: ⊦ prime(j) ∧ j ≠ 2 → (j - 1) % 2 = 0; from specification int-gcd%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%lep-01: ⊦ i + j ≤ i ↔ j ≤ 0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 2, j - 1