Theorems · Theorem · order theory
succ_notMem_iff_isMax
∀ {α : Type u_3} [inst : PartialOrder α] {s : Set α} [s.OrdConnected] [inst_2 : SuccOrder α] [NoMaxOrder α] {a : ↑s},
Order.succ ↑a ∉ s ↔ IsMax a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- PartialOrderstatement and proof · cited by 6,410
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- NoMaxOrderstatement and proof · cited by 340
- Set.OrdConnectedstatement and proof · cited by 161
- IsMax.succ_eqproof · cited by 7
- coe_succ_of_memproof · cited by 2
- isMax_of_succ_notMemproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.