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Proof step 5 from proof num-div-denom-01 (previous step)

i1 < 0 ⊦ i = 0, i1 = 0, j = 0, (rational(i, i1).num * j) / i1 / gcd(i, i1) + (i * j) / i1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < i ∧ j < 0 → rational(i, j).num = ~(i / gcd(i, j))
Proof step 7:
¬(0 < i ∧ i1 < 0), i1 < 0 ⊦ i = 0, i1 = 0, j = 0, (rational(i, i1).num * j) / i1 / gcd(i, i1) + (i * j) / i1 = 0
Proof step 10:
0 < i ∧ i1 < 0, i1 < 0 ⊦ i = 0, i1 = 0, j = 0, (~(i / gcd(i, i1)) * j) / i1 / gcd(i, i1) + (i * j) / i1 = 0

Rule argument

name: numerator-neg1 rotate: F subst: [j, i] → [i1, i]

Additional information

Used terms: i1, i