Theorems · Theorem · order theory
Order.pred_lt_of_le_of_not_isMin
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] {a b : α}, a ≤ b → ¬IsMin a → Order.pred a < b- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 273
- LE.le.trans_lt'proof · cited by 50
- Order.pred_lt_of_not_isMinproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Order.pred_le_predproof · cited by 5
- Set.insert_Ico_left_eq_Ico_pred_of_not_isMinproof · cited by 3
- Order.pred_lt_of_leproof · cited by 1
- Order.pred_lt_pred_of_not_isMinproof · cited by 0