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Proof step 18 from proof add-eq (previous step)

j ≠ 0 ∧ j1 ≠ 0, j ≠ 0 ∧ j0 ≠ 0, 0 < j0 * j1, rational(i * j0 + j * i0, j * j0) = rational(i * j1 + j * i1, j * j1), 0 < j, 0 < j0, 0 < j1 ⊦ i0 * j1 = i1 * j0, rational(i0, j0) = rational(i1, j1)

User applied rule insert lemma

And obtained the following new goals

Proof step 19:
rational(i, j) = rational(i0, j0), 0 < j, 0 < j0 ⊦ i * j0 = i0 * j
Proof step 20:
(i * j0 + j * i0) * j * j1 = (i * j1 + j * i1) * j * j0, j ≠ 0 ∧ j1 ≠ 0, j ≠ 0 ∧ j0 ≠ 0, 0 < j0 * j1, rational(i * j0 + j * i0, j * j0) = rational(i * j1 + j * i1, j * j1), 0 < j, 0 < j0, 0 < j1 ⊦ i0 * j1 = i1 * j0, rational(i0, j0) = rational(i1, j1)

Rule argument

name: equality-01 subst: [i, j, i0, j0] → [i * j0 + j * i0, j * j0, i * j1 + j * i1, j * j1]

Additional information

Used simplifier rules: ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i; Used terms: i * j0 + j * i0, j * j0, i * j1 + j * i1, j * j1