Theorems · Theorem · number theory
Irrational.mul_intCast
∀ {x : ℝ}, Irrational x → ∀ {m : ℤ}, m ≠ 0 → Irrational (x * ↑m)- Defined in
- Mathlib.NumberTheory.Real.Irrational
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Rat.cast_intCastproof · cited by 74
- Int.cast_ne_zeroproof · cited by 17
- Irrational.mul_ratCastproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Irrational.intCast_mulproof · cited by 3
- Irrational.mul_natCastproof · cited by 0