Theorems · Theorem · number theory
LiouvilleWith.mul_rat
∀ {p x : ℝ} {r : ℚ}, LiouvilleWith p x → r ≠ 0 → LiouvilleWith p (x * ↑r)The product of a Liouville number and a nonzero rational number is again a Liouville number.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Filter.atTopproof · cited by 2,405
- mul_commproof · cited by 2,262
- absproof · cited by 1,814
- le_of_ltproof · cited by 1,175
- DivisionRingproof · cited by 1,062
- ne_of_gtproof · cited by 637
- lt_of_lt_of_leproof · cited by 438
- Filter.Frequentlyproof · cited by 414
- Nat.cast_mulproof · cited by 309
- Nat.cast_pos'proof · cited by 219
- Filter.tendsto_idproof · cited by 180
Cited by2
Results whose statement or proof uses this declaration.
- LiouvilleWith.mul_rat_iffproof · cited by 3
- LiouvilleWith.irrationalproof · cited by 0