Theorems · Theorem · logic and foundations
ZFSet.card_insert
∀ {x y : ZFSet.{u}}, x ∉ y → (insert x y).card = y.card + 1- Defined in
- Mathlib.SetTheory.ZFC.Cardinal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 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 · cited by 2,598
- Cardinal.mkproof · cited by 942
- Iff.notproof · cited by 489
- SetLike.mem_coeproof · cited by 302
- ZFSetstatement and proof · cited by 259
- Cardinal.lift_injproof · cited by 38
- Cardinal.lift_oneproof · cited by 33
- Cardinal.lift_addproof · cited by 18
- ZFSet.cardstatement and proof · cited by 16
- Cardinal.mk_insertproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ZFSet.card_singletonproof · cited by 1
- ZFSet.card_pair_of_neproof · cited by 0