Theorems · Theorem · order theory
Order.min_of_le_pred
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] {a : α}, a ≤ Order.pred a → IsMin a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 3 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.
Cites5
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 · cited by 277
- Order.predstatement · cited by 273
- PredOrder.min_of_le_predproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Order.pred_eq_iff_isMinproof · cited by 8
- Order.pred_lt_iff_not_isMinproof · cited by 4
- Order.le_pred_iff_isMinproof · cited by 3