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Proof step 29 from proof div-def-01 (previous step)

rational(i0, j0) = rational(0, 1), rational(i, j) / ~ rational(0, 1) = ~ rational(i * j0, i0 * j), 0 < j, 0 < j0, 0 < i, i0 < 0 ⊦ rational(i, j) / rational(0, 1) = rational(i * j0, j * i0), i0 = 0, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ 0 < j ∧ 0 < j0 → (rational(i, j) = rational(i0, j0) ↔ i * j0 = i0 * j)

Rule argument

name: equality-def rotate: F subst: [j0, i0, j, i] → [1, 0, j0, i0]

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i * 0 = 0; Used terms: 1, 0, j0, i0