Theorems · Theorem · logic and foundations
Cardinal.mk_insert
∀ {α : Type u} {s : Set α} {a : α}, a ∉ s → Cardinal.mk ↑(insert a s) = Cardinal.mk ↑s + 1- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Elemstatement and proof · cited by 7,166
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Set.union_singletonproof · cited by 107
- Cardinal.mk_singletonproof · cited by 9
- Cardinal.mk_union_of_disjointproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.mk_Iic_ltproof · cited by 2
- ZFSet.card_insertproof · cited by 2
- Cardinal.mk_insert_leproof · cited by 1