Theorems · Theorem · logic and foundations
Set.ncard_sdiff_singleton_of_mem
∀ {α : Type u_1} {s : Set α} {a : α}, a ∈ s → (s \ {a}).ncard = s.ncard - 1- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 2 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.
Cites12
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.Finiteproof · cited by 1,814
- Set.ncardstatement · cited by 344
- Set.Infiniteproof · cited by 263
- ENat.toNatproof · cited by 143
- zero_tsubproof · cited by 100
- Set.finite_singletonproof · cited by 70
- eq_tsub_of_add_eqproof · cited by 11
- Set.Infinite.sdiffproof · cited by 10
- Set.infinite_or_finiteproof · cited by 6
- Set.Infinite.encard_eqproof · cited by 6
- Set.ncard_sdiff_singleton_add_oneproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Set.pred_ncard_le_ncard_sdiff_singletonproof · cited by 1
- Set.ncard_diff_singleton_of_memproof · cited by 0