Theorems · Theorem · logic and foundations
Cardinal.mk_le_mk_of_subset
∀ {α : Type u_1} {s t : Set α}, s ⊆ t → Cardinal.mk ↑s ≤ Cardinal.mk ↑t- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 7,166
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Set.embeddingOfSubsetproof · cited by 9
Cited by37
Results whose statement or proof uses this declaration.
- Nat.card_monoproof · cited by 5
- HahnSeries.cardSupp_monoproof · cited by 5
- HahnSeries.cardSupp_mul_leproof · cited by 4
- HahnSeries.cardSupp_single_leproof · cited by 3
- Cardinal.card_lt_of_card_iUnion_ltproof · cited by 2
- Cardinal.le_mk_sdiff_add_mkproof · cited by 2
- Cardinal.mk_Icc_realproof · cited by 2
- Matroid.cRk_le_cardinalMkproof · cited by 2
- IsClosed.two_pow_mk_le_two_pow_mk_denseproof · cited by 2
- Cardinal.mk_subtype_le_of_countable_eventually_mem_auxproof · cited by 1
- Ordinal.lift_card_sInf_compl_leproof · cited by 1
- ZFSet.card_monoproof · cited by 1