Theorems · Theorem · order theory
Order.pred_covBy_of_not_isMin
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] {a : α}, ¬IsMin a → Order.pred a ⋖ a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 19 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.
- Preorderstatement and proof · cited by 7,952
- PredOrderstatement and proof · cited by 334
- CovBystatement · cited by 290
- IsMinstatement and proof · cited by 277
- Order.predstatement · cited by 273
- Order.pred_lt_of_not_isMinproof · cited by 9
- WCovBy.covBy_of_ltproof · cited by 6
- Order.pred_wcovByproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Order.IsPredPrelimit.isMinproof · cited by 7
- Order.pred_covByproof · cited by 4
- Order.not_isPredPrelimit_iff_pred_eqproof · cited by 3
- PredOrder.nhdsLTproof · cited by 3
- OrderIso.map_predproof · cited by 1
- Order.succ_pred_of_not_isMinproof · cited by 1
- PredOrder.isOpen_singleton_of_not_isPredPrelimitproof · cited by 1
- SimpleGraph.hasse_preconnected_of_predproof · cited by 0