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Proof step 41 from proof diff-primes-neg (previous step)

n→i(n) + n→i(m) < j, n→i(n) + n→i(m) ≤ 0, 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, 0 < j, 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-abs inst: name: notle-pos seq: ⊦ 0 ≤ i ∧ ¬ i0 ≤ j → ¬ i + i0 ≤ j subst: [j, i0, i] → [0, n→i(m), n→i(n)] flags: rewrite

Additional information

Used simplifier rules: nat2int: ⊦ 0 ≤ n→i(n); from specification intnat%nat2int-10: ⊦ n→i(n) ≤ 0 ↔ n = 0; from specification intnat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic1%zero: ⊦ 0 < m ↔ m ≠ 0; from specification nat-basic1%abs-zero: ⊦ i→n(i) = 0 ↔ i = 0; from specification intnat%numadd-01: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; 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%div-two-zero-01: ⊦ 0 ≤ i / 2 ↔ ~1 ≤ i; from specification int-div%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%ax-04: ⊦ i + 0 = i; from specification int-basic2 Used terms: 0, n→i(m), n→i(n)