Theorems · Theorem · number theory
Irrational.mul_ratCast
∀ {x : ℝ}, Irrational x → ∀ {q : ℚ}, q ≠ 0 → Irrational (x * ↑q)- Defined in
- Mathlib.NumberTheory.Real.Irrational
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- mul_inv_cancel₀proof · cited by 210
- Irrationalstatement and proof · cited by 139
- Rat.cast_oneproof · cited by 52
- Rat.cast_mulproof · cited by 19
- Irrational.of_mul_ratCastproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Irrational.ratCast_mulproof · cited by 4
- Irrational.mul_intCastproof · cited by 2
- Irrational.div_ratCastproof · cited by 1