Theorems · Theorem · combinatorics
Infinite.of_injective
∀ {α : Sort u_4} {β : Sort u_5} [Infinite β] (f : β → α), Function.Injective f → Infinite α- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finiteproof · cited by 3,029
- Infinitestatement and proof · cited by 352
- Finite.of_injectiveproof · cited by 32
- Finite.falseproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- Cardinal.le_range_of_union_finset_eq_univproof · cited by 2
- FirstOrder.Language.Term.card_sigmaproof · cited by 1
- mk_eq_mk_of_basisproof · cited by 1
- Polynomial.dickson_one_one_zmod_pproof · cited by 1
- Transcendental.infiniteproof · cited by 1
- FirstOrder.Language.card_functions_sum_skolem₁proof · cited by 1
- Pi.infinite_of_exists_rightproof · cited by 0
- Cardinal.extend_function_of_ltproof · cited by 0
- DFinsupp.infinite_of_exists_rightproof · cited by 0
- Infinite.sigma_of_rightproof · cited by 0