Theorems · Theorem · order theory
Order.pred_lt_iff_not_isMin
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] {a : α}, Order.pred a < a ↔ ¬IsMin a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
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
- IsMinstatement and proof · cited by 277
- Order.predstatement and proof · cited by 273
- LE.le.lt_of_not_geproof · cited by 21
- Order.pred_leproof · cited by 19
- not_isMin_of_ltproof · cited by 5
- Order.min_of_le_predproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Order.pred_lt_of_not_isMinproof · cited by 9
- Order.pred_lt_iff_ne_botproof · cited by 1
- Order.Ici_subset_Ioi_predproof · cited by 0
- Order.Ioo_eq_empty_iff_pred_leproof · cited by 0