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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: estimate-add1-le-right seq: ⊦ j0 ≤ i + j ∧ i ≤ i0 → j0 ≤ i0 + j subst: [i, j, i0, j0] → [n→i(m), (j - 1) / 2, (j - 1) / 2, j] flags: rewrite

Additional information

Used simplifier rules: add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: n→i(m), (j - 1) / 2, (j - 1) / 2, j