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Proof step 8 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 (rational(i1, j1).num * rational(i2, j2).denom + rational(i1, j1).denom * rational(~ i2, j2).num, rational(i1, j1).denom * rational(i2, j2).denom)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: num-neg-01 rotate: F subst: [j, i] → [j2, i2]

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ ~ i * j = ~(i * j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + ~ j = i - j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: j2, i2