Theorems · Theorem · logic and foundations
Set.ncard_lt_ncard
∀ {α : Type u_1} {s t : Set α}, s ⊂ t → autoParam t.Finite Set.ncard_lt_ncard._auto_1 → s.ncard < t.ncard- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 100 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.
- 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_ltproof · cited by 80
- Set.Finite.cast_ncard_eqproof · cited by 28
- LT.lt.subsetproof · cited by 20
- Set.Finite.encard_lt_encardproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- MulAction.IsPreprimitive.is_two_motive_of_is_motiveproof · cited by 2
- Ideal.ncard_primesOver_lt_of_not_leproof · cited by 1
- Set.ncard_lt_cardproof · cited by 1
- Set.Finite.ncard_strictMonoOnproof · cited by 0
- Set.ncard_strictMonoproof · cited by 0