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Proof step 14 from proof est-4-big-02 (previous step)

(i0 * j) * 2 + i0 * j < (i0 * j) * 2 + j0 * 2, 0 ≤ i0, 1 < j, 0 < j, 0 < i0, 0 < j0, 0 ≤ j0, j ≤ 2 * j0, 2 < i0 * j + j0, j ≤ i0 * j + j0, (i0 * j) * 2 + j0 * 2 < 3 * j, j0 < j, 0 < i0 * j + j0, i0 * j < 2 * j0 ⊦ (i0 * j) * 2 + i0 * j < 3 * j, j = 3, j = 2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: oelem inst: intlista name: transitivity seq: ⊦ i < i0 ∧ i0 < i1 → i < i1 subst: [i0, i1, i] → [(i0 * j) * 2 + j0 * 2, 3 * j, (i0 * j) * 2 + i0 * j] flags: rewrite

Additional information

Used simplifier rules: numsucc: ⊦ (* i0) * i + i = (i0 + 1) * 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%numls-01: ⊦ (* i2) * i < (* i1) * i + j0 ↔ (i2 - i1) * i < j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%ls-pos: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0); from specification int-mult%ls-same: ⊦ 0 < i → (i * j < i ↔ j < 1); from specification int-mult%bet-01: ⊦ 0 ≤ i → (i < 1 ↔ i = 0); from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: (i0 * j) * 2 + j0 * 2, 3 * j, (i0 * j) * 2 + i0 * j