Theorems · Theorem · order theory
Order.succ_eq_csInf
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] [inst_1 : SuccOrder α] [NoMaxOrder α] (a : α),
Order.succ a = sInf (Set.Ioi a)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Ioistatement · cited by 1,463
- le_of_ltproof · cited by 1,175
- InfSet.sInfstatement · cited by 935
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- LE.le.antisymmproof · cited by 507
- ConditionallyCompleteLatticestatement and proof · cited by 364
- NoMaxOrderstatement and proof · cited by 340
- csInf_leproof · cited by 51
- Order.lt_succproof · cited by 45
- Order.succ_le_of_ltproof · cited by 42
- le_csInfproof · cited by 36
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.succ_defproof · cited by 0