Theorems · Theorem · logic and foundations
Set.finite_of_encard_eq_coe
∀ {α : Type u_1} {s : Set α} {k : ℕ}, s.encard = ↑k → s.Finite- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENatstatement · cited by 4,985
- Set.Finitestatement · cited by 1,814
- Eq.leproof · cited by 605
- Set.encardstatement and proof · cited by 327
- Set.finite_of_encard_le_coeproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Set.powersetCard.exists_mem_notMemproof · cited by 2
- measurable_encardproof · cited by 1
- Equiv.Perm.has_swap_mem_of_lt_stabilizerproof · cited by 1
- Submodule.FG.exists_span_finset_card_eq_spanFinrankproof · cited by 1
- MulAction.isMultiplyPreprimitive_of_isMultiplyPretransitive_succproof · cited by 1
- AddAction.isMultiplyPreprimitive_of_isMultiplyPretransitive_succproof · cited by 1
- SimpleGraph.vertexCoverNum_topproof · cited by 0
- Convex.helly_theorem_set_compactproof · cited by 0