Theorems · Theorem · number theory
Irrational.ratCast_add
∀ (q : ℚ) {x : ℝ}, Irrational x → Irrational (↑q + x)- Defined in
- Mathlib.NumberTheory.Real.Irrational
- Cited by
- 6 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.
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
- neg_add_cancel_leftproof · cited by 84
- Rat.cast_negproof · cited by 25
- Irrational.of_ratCast_addproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Irrational.ratCast_subproof · cited by 3
- Irrational.intCast_addproof · cited by 3
- Irrational.add_ratCastproof · cited by 2
- exists_irrational_btwnproof · cited by 1
- irrational_ratCast_add_iffproof · cited by 0
- Real.goldenRatio_irrationalproof · cited by 0