Theorems · Theorem · logic and foundations
Cardinal.inductionOn
∀ {motive : Cardinal.{u_1} → Prop} (c : Cardinal.{u_1}), (∀ (α : Type u_1), motive (Cardinal.mk α)) → motive c- Defined in
- Mathlib.SetTheory.Cardinal.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
Cited by19
Results whose statement or proof uses this declaration.
- Cardinal.lift_umaxproof · cited by 56
- Cardinal.lift_liftproof · cited by 53
- Cardinal.lift_id'proof · cited by 43
- Cardinal.card_ordproof · cited by 23
- Cardinal.sum_constproof · cited by 13
- Cardinal.mul_eq_selfproof · cited by 13
- Cardinal.cantorproof · cited by 12
- Cardinal.prod_constproof · cited by 8
- Cardinal.gc_ord_cardproof · cited by 6
- Cardinal.le_mk_iff_exists_setproof · cited by 6
- Cardinal.power_oneproof · cited by 4
- Cardinal.power_zeroproof · cited by 4