Theorems · Theorem · logic and foundations
Cardinal.card_lt_card_of_left_finite
∀ {α : Type u} {A B : Set α}, A.Finite → A ⊂ B → Cardinal.mk ↑A < Cardinal.mk ↑B- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 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.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Finiteproof · cited by 3,029
- Cardinalstatement · cited by 2,598
- Set.Finitestatement and proof · cited by 1,814
- Cardinal.mkstatement · cited by 942
- LT.lt.trans_leproof · cited by 678
- Infiniteproof · cited by 352
- finite_or_infiniteproof · cited by 50
- Cardinal.card_lt_card_of_right_finiteproof · cited by 3
- Cardinal.lt_aleph0_iff_subtype_finiteproof · cited by 2
- Cardinal.aleph0_le_mk_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.ord_mk_lt_typeproof · cited by 1