Theorems · Theorem · order theory
Order.le_pred_of_lt
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] {a b : α}, b < a → b ≤ Order.pred a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Order.predstatement · cited by 273
- PredOrder.le_pred_of_ltproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- Order.le_pred_iff_of_not_isMinproof · cited by 14
- Order.pred_le_predproof · cited by 5
- Order.pred_wcovByproof · cited by 3
- Order.le_of_pred_ltproof · cited by 2
- LT.lt.le_predproof · cited by 2
- Set.insert_Ico_pred_right_eq_Icoproof · cited by 2
- IsPredArchimedean.isAtom_findAtomproof · cited by 1
- Order.pred_eq_of_covByproof · cited by 1
- Set.Ici.coe_pred_of_not_isMinproof · cited by 1
- Order.pred_eq_sSupproof · cited by 1
- Order.le_and_pred_le_iffproof · cited by 1
- StrictMono.not_bddBelow_range_of_isPredArchimedeanproof · cited by 1