Theorems · Theorem · logic and foundations
Set.ncard_image_le
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {f : α → β},
autoParam s.Finite Set.ncard_image_le._auto_1 → (f '' s).ncard ≤ s.ncard- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 99 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
- Set.imagestatement and proof · cited by 5,609
- 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
- Nat.cast_leproof · cited by 159
- Set.Finite.imageproof · cited by 96
- Set.Finite.cast_ncard_eqproof · cited by 28
- Set.encard_image_leproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- TensorProduct.spanFinrank_top_eq_of_residueFieldproof · cited by 1
- MulAction.IsPreprimitive.of_card_ltproof · cited by 1
- AddAction.IsPreprimitive.of_card_ltproof · cited by 0