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Proof step 4 from proof sub-def-01 (previous step)

0 < j1, 0 < j2 ⊦ rational (rational(i1, j1).num * rational(i2, j2).denom - rational(i1, j1).denom * rational(i2, j2).num, rational(i1, j1).denom * rational(i2, j2).denom) = rational(i1, j1) + rational(~ i2, j2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ri + rj = rational(ri.num * rj.denom + ri.denom * rj.num, ri.denom * rj.denom)
Proof step 6:
0 < j1, 0 < j2 ⊦ rational (rational(i1, j1).num * rational(i2, j2).denom - rational(i1, j1).denom * rational(i2, j2).num, rational(i1, j1).denom * rational(i2, j2).denom) = rational (rational(i1, j1).num * rational(~ i2, j2).denom + rational(i1, j1).denom * rational(~ i2, j2).num, rational(i1, j1).denom * rational(~ i2, j2).denom)

Rule argument

name: add-def rotate: F subst: [rj, ri] → [rational(~ i2, j2), rational(i1, j1)]

Additional information

Used terms: rational(~ i2, j2), rational(i1, j1)