Theorems · Theorem · order theory
Order.pred_le
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] (a : α), Order.pred a ≤ a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 19 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.pred_leproof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- Order.pred_eq_iff_isMinproof · cited by 8
- Order.pred_iterate_leproof · cited by 6
- Order.pred_le_predproof · cited by 5
- Order.pred_lt_iff_not_isMinproof · cited by 4
- Pred.recstatement and proof · cited by 4
- Order.pred_wcovByproof · cited by 3
- strictMonoOn_of_pred_ltproof · cited by 3
- Order.le_pred_iff_isMinproof · cited by 3
- Set.Ioc_pred_right_eq_Iooproof · cited by 3
- toZ_strictMonoproof · cited by 3
- monotoneOn_of_pred_leproof · cited by 3
- Order.IsPredPrelimit.lt_pred_iffproof · cited by 2