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Proof step 44 from proof add-def-02 (previous step)

0 < i3, 0 < j2, 1 < i, 0 < i, ∀ j2, j1, i4, i3. i→n(i3) + i→n(i4) < i→n(i * 0) + i→n(i2) → 0 < j1 ∧ 0 < j2 → rational(i3, j1) + rational(i4, j2) = rational(i3 * j2 + j1 * i4, j1 * j2) ⊦ j2 = 0, i3 = 0, i = 0, rational(i2, j2) + rational(0, 1) = rational(i2, j2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ 0r = rational(0, 1)
Proof step 46:
0 < i3, 0 < j2, 1 < i, 0 < i, ∀ j2, j1, i4, i3. i→n(i3) + i→n(i4) < i→n(i * 0) + i→n(i2) → 0 < j1 ∧ 0 < j2 → rational(i3, j1) + rational(i4, j2) = rational(i3 * j2 + j1 * i4, j1 * j2) ⊦ j2 = 0, i3 = 0, i = 0, rational(i2, j2) + 0r = rational(i2, j2)

Rule argument

name: zero-def rotate: T subst:

Additional information

Used terms: