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Proof step 15 from proof coef-product-le (previous step)

0 < Π ints, 0 < j, 2 * j + 1 < j, ∀ i. i ∈ ints → prime(i) ∧ j + 2 ≤ i ∧ i ≤ j * 2 + 1 ⊦ dups(ints)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: ls-add seq: ⊦ 0 ≤ j1 ∧ j1 < j → (i0 * j + j1 < j ↔ i0 ≤ 0) subst: [j1, j, i0] → [1, j, 2] flags: rewrite

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * 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%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1 Used terms: 1, j, 2