Theorems · Theorem · logic and foundations

Set.ncard_le_ncard

∀ {α : Type u_1} {s t : Set α}, s ⊆ t → autoParam t.Finite Set.ncard_le_ncard._auto_1 → s.ncard ≤ t.ncard

Defined in: Mathlib.Data.Set.Card
Cited by: 15 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

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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
ENatproof · cited by 4,985
Set.Finitestatement and proof · cited by 1,814
Set.ncardstatement and proof · cited by 344
Set.encardproof · cited by 327
Set.Finite.subsetproof · cited by 285
Nat.cast_leproof · cited by 159
Set.Finite.cast_ncard_eqproof · cited by 28
Set.encard_monoproof · cited by 8

Cited by15

Results whose statement or proof uses this declaration.

Set.sdiff_nonempty_of_ncard_lt_ncardproof · cited by 3
MulAction.IsMultiplyPretransitive.index_of_fixingSubgroup_mulproof · cited by 2
Set.ncard_le_cardproof · cited by 2
alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1
Set.ncard_sdiff_singleton_leproof · cited by 1
MulAction.IsPreprimitive.of_card_ltproof · cited by 1
Equiv.Perm.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1
MulAction.IsMultiplyPretransitive.index_of_fixingSubgroup_eqproof · cited by 0
AddAction.IsPreprimitive.of_card_ltproof · cited by 0
ProbabilityTheory.ae_le_of_hasLaw_binomialproof · cited by 0
Set.ncard_monoproof · cited by 0
Matroid.existsMaximalSubsetProperty_of_bddproof · cited by 0