Theorems · Theorem · number theory
irrational_div_ratCast_iff
∀ {q : ℚ} {x : ℝ}, Irrational (x / ↑q) ↔ q ≠ 0 ∧ Irrational x- Defined in
- Mathlib.NumberTheory.Real.Irrational
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- div_eq_mul_invproof · cited by 715
- Irrationalstatement and proof · cited by 139
- Rat.cast_invproof · cited by 22
- inv_eq_zeroproof · cited by 15
- irrational_mul_ratCast_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- irrational_div_intCast_iffproof · cited by 0
- irrational_div_natCast_iffproof · cited by 0