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Proof step 7 from proof add-def-03 (previous step)

j1 < 0 ⊦ j1 = 0, j2 = 0, rational(i1, j1) + rational(i2, j2) = rational(i1 * j2 + j1 * i2, j1 * j2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ j < 0 → rational(i, j) = rational(~ i, abs(j))
Proof step 9:
j1 < 0, j1 < 0 ⊦ j1 = 0, j2 = 0, rational(~ i1, abs(j1)) + rational(i2, j2) = rational(i1 * j2 + j1 * i2, j1 * j2)

Rule argument

name: denom-neg rotate: F subst: [j, i] → [j1, i1]

Additional information

Used terms: j1, i1