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Theorem Extsimple

⊦ i1 ≠ 0 ∧ i2 ≠ 0 ∧ j1 ≠ 0 ∧ j2 ≠ 0 → ( rational(i1, j1) = rational(i2, j2) ↔ abs(i1) / gcd(i1, j1) = abs(i2) / gcd(i2, j2) ∧ abs(j1) / gcd(i1, j1) = abs(j2) / gcd(i2, j2) ∧ ( (0 < i1 ∧ 0 < j1 ∨ i1 < 0 ∧ j1 < 0) ∧ (0 < i2 ∧ 0 < j2 ∨ i2 < 0 ∧ j2 < 0) ∨ (0 < i1 ∧ j1 < 0 ∨ i1 < 0 ∧ 0 < j1) ∧ (0 < i2 ∧ j2 < 0 ∨ i2 < 0 ∧ 0 < j2)))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

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Infos about the proof

Proved?: Yes
Interactions: 38
Proof steps: 71
Used lemmas: numerator-neg2, numerator-neg1, numerator-pos, denominator-pos, Equality,
Used spec theorems:
Used simplifier rules: