Theorems · Theorem · number theory
irrational_ratCast_mul_iff
∀ {q : ℚ} {x : ℝ}, Irrational (↑q * x) ↔ q ≠ 0 ∧ Irrational x- Defined in
- Mathlib.NumberTheory.Real.Irrational
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Irrationalstatement and proof · cited by 139
- left_ne_zero_of_mulproof · cited by 27
- Irrational.ratCast_mulproof · cited by 4
- Rat.cast_ne_zeroproof · cited by 3
- Irrational.of_ratCast_mulproof · cited by 3
- Irrational.ne_zeroproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- irrational_mul_ratCast_iffproof · cited by 3
- irrational_intCast_mul_iffproof · cited by 0
- irrational_natCast_mul_iffproof · cited by 0