Theorems · Theorem · order theory
Set.card_lt_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
- 2 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- ssubset_iff_subset_neproof · cited by 7
- Fintype.card_lt_of_injective_not_surjectiveproof · cited by 2
- Set.eq_of_inclusion_surjectiveproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Set.eq_of_subset_of_card_leproof · cited by 7
- Set.Finite.card_lt_cardproof · cited by 4