Theorems · Theorem · logic and foundations
ZFSet.IsOrdinal.isTransitive
∀ {x : ZFSet.{u_1}}, x.IsOrdinal → x.IsTransitiveAn ordinal is a transitive set.
- Defined in
- Mathlib.SetTheory.ZFC.Ordinal
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ZFSetstatement and proof · cited by 259
- ZFSet.IsOrdinalstatement and proof · cited by 34
- ZFSet.IsTransitivestatement · cited by 22
Cited by7
Results whose statement or proof uses this declaration.
- ZFSet.IsOrdinal.subset_of_memproof · cited by 4
- ZFSet.IsOrdinal.mem_transproof · cited by 4
- ZFSet.isOrdinal_iff_isTransproof · cited by 3
- ZFSet.isOrdinal_iff_trichotomousproof · cited by 1
- ZFSet.isOrdinal_iff_forall_mem_isTransitiveproof · cited by 1
- ZFSet.isOrdinal_iff_forall_mem_isOrdinalproof · cited by 0
- ZFSet.isOrdinal_iff_isWellOrderproof · cited by 0