Theorems · Theorem · order theory
Set.card_le_card
∀ {α : Type u} {s t : Set α} [inst : Fintype ↑s] [inst_1 : Fintype ↑t], s ⊆ t → Fintype.card ↑s ≤ Fintype.card ↑t- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Fintype.cardstatement · cited by 1,386
- Set.inclusionproof · cited by 145
- Set.inclusion_injectiveproof · cited by 28
- Fintype.card_le_of_injectiveproof · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- SimpleGraph.card_commonNeighbors_le_degree_leftproof · cited by 2
- Setoid.card_classes_ker_leproof · cited by 1
- SimpleGraph.degree_le_of_leproof · cited by 1
- SimpleGraph.Subgraph.degree_leproof · cited by 0
- SimpleGraph.Subgraph.degree_le'proof · cited by 0