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Proof step 12 from proof add-eq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: equal-same rotate: F subst: [i0, j, i] → [i1 * j0, j0 * j1, i0 * j1]

Additional information

Used simplifier rules: factor-rat-03: ⊦ 0 < j ∧ 0 < i1 → rational(i1 * i, i1 * j) = rational(i, j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i1 * j0, j0 * j1, i0 * j1