Theorems · Theorem · order theory
Order.succ_pred_of_not_isMin
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : SuccOrder α] [inst_2 : PredOrder α] {a : α},
¬IsMin a → Order.succ (Order.pred a) = a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement · cited by 273
- Order.pred_covBy_of_not_isMinproof · cited by 8
- CovBy.succ_eqproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Order.succ_pred_iterate_of_not_isMinproof · cited by 0