Theorems · Theorem · order theory
CovBy.succ_eq
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : SuccOrder α] {a b : α}, a ⋖ b → Order.succ a = bAlias of Order.succ_eq_of_covBy.
See also Order.le_succ_of_wcovBy.
- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderSuccOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement · cited by 6,410
- Order.succstatement · cited by 633
- SuccOrderstatement · cited by 574
- CovBystatement · cited by 290
- Order.succ_eq_of_covByproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- OrderIso.map_succproof · cited by 4
- Order.succ_eq_iff_covByproof · cited by 3
- Order.not_isSuccPrelimit_iff_succ_eqproof · cited by 3
- Order.isSuccPrelimit_of_succ_ltproof · cited by 3
- InitialSeg.map_succproof · cited by 1
- Order.succ_pred_of_not_isMinproof · cited by 1
- Order.isSuccPrelimit_of_succ_neproof · cited by 1
- Order.succ_predproof · cited by 0