Theorems · Theorem · number theory
Irrational.of_mul_ratCast
∀ (q : ℚ) {x : ℝ}, Irrational (x * ↑q) → Irrational x- Defined in
- Mathlib.NumberTheory.Real.Irrational
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Irrational.mul_casesproof · cited by 3
- Rat.not_irrationalproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Irrational.of_ratCast_mulproof · cited by 3
- Irrational.mul_ratCastproof · cited by 3
- Irrational.of_mul_intCastproof · cited by 1