Theorems · Theorem · logic and foundations
Cardinal.cantorFunction_injective
∀ {c : ℝ}, 0 < c → c < 1 / 2 → Function.Injective (Cardinal.cantorFunction c)cantorFunction c is injective if 0 < c < 1/2.
- Defined in
- Mathlib.Analysis.Real.Cardinality
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- ne_of_gtproof · cited by 637
- ne_of_ltproof · cited by 203
- Nat.findproof · cited by 139
- Nat.find_specproof · cited by 74
- of_not_notproof · cited by 51
- Function.ne_iffproof · cited by 40
- Nat.find_minproof · cited by 30
- Cardinal.cantorFunctionstatement and proof · cited by 4
- Bool.eq_true_of_not_eq_falseproof · cited by 1
- Bool.eq_false_of_not_eq_trueproof · cited by 1
- Cardinal.increasing_cantorFunctionproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.mk_realproof · cited by 11