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Proof step 16 from proof add-eq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ j1 ≠ 0 ∧ j2 ≠ 0 → rational(i1, j1) + rational(i2, j2) = rational(i1 * j2 + j1 * i2, j1 * j2)
Proof step 18:
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: add-def-03 rotate: F subst: [j2, i2, j1, i1] → [j1, i1, j, i]

Additional information

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