Theorems · Theorem · logic and foundations
HasCardinalLT.of_injective
∀ {X : Type u} {κ : Cardinal.{v}},
HasCardinalLT X κ → ∀ {Y : Type u'} (f : Y → X), Function.Injective f → HasCardinalLT Y κ- Defined in
- Mathlib.SetTheory.Cardinal.HasCardinalLT
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkproof · cited by 942
- Cardinal.liftproof · cited by 583
- lt_of_le_of_ltproof · cited by 432
- HasCardinalLTstatement and proof · cited by 99
- Cardinal.lift_liftproof · cited by 53
- Cardinal.lift_ltproof · cited by 39
- Cardinal.mk_le_of_injectiveproof · cited by 12
- ULift.down_injectiveproof · cited by 6
- ULift.up_injectiveproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- hasCardinalLT_iff_of_equivproof · cited by 12
- CategoryTheory.hasCardinalLT_of_hasCardinalLT_arrowproof · cited by 4
- CategoryTheory.CardinalDirectedPoset.isCardinalPresentable_iffproof · cited by 3
- hasCardinalLT_sum_iffproof · cited by 3
- HasCardinalLT.exists_regular_cardinal_forallproof · cited by 1
- CategoryTheory.Subobject.hasCardinalLT_of_monoproof · cited by 0