Theorems · Theorem · order theory
Order.IsNormal.dirSupClosed_range
∀ {α : Type u_1} [inst : LinearOrder α] [WellFoundedLT α] {f : α → α}, Order.IsNormal f → DirSupClosed (Set.range f)- Defined in
- Mathlib.Order.IsNormal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderWellFoundedLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- LE.le.transproof · cited by 3,151
- Set.Nonemptyproof · cited by 2,627
- OrderBotproof · cited by 1,055
- SupSet.sSupproof · cited by 954
- WellFoundedLTstatement and proof · cited by 491
- Set.mem_range_selfproof · cited by 328
- IsLUBproof · cited by 280
Cited by2
Results whose statement or proof uses this declaration.
- Order.isNormal_enum_iff_dirSupClosedproof · cited by 0
- Order.IsNormal.isClub_rangeproof · cited by 0