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Proof step 40 from proof add-def-02 (previous step)

0 < i, 1 < i, 0 < j2, 0 < i3, ∀ j2, j1, i4, i3. i→n(i3) + i→n(i4) < i→n(i * i0) + i→n(i2) → 0 < j1 ∧ 0 < j2 → rational(i3, j1) + rational(i4, j2) = rational(i3 * j2 + j1 * i4, j1 * j2) ⊦ rational(i2, j2) + rational(i0, i3) = rational(i3 * i2 + i0 * j2, i3 * j2), i = 0, i3 = 0, j2 = 0

User applied rule apply induction

And obtained the following new goals

Rule argument

subst: [j2, j1, i4, i3] → [i3, j2, i0, i2]

Additional information

Used simplifier rules: add-comm: ⊦ ri + rj = rj + ri;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i; Used terms: i3, j2, i0, i2