Theorems · Theorem · order theory
IsMin.not_lt
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, IsMin a → ¬b < a- Defined in
- Mathlib.Order.Max
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Preorder
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
- LT.lt.leproof · cited by 2,189
- LT.lt.not_geproof · cited by 305
- IsMinstatement and proof · cited by 277
Cited by8
Results whose statement or proof uses this declaration.
- not_lt_botproof · cited by 19
- not_isMin_of_ltproof · cited by 5
- isMin_iff_forall_not_ltproof · cited by 4
- Order.IsNormal.of_succ_ltproof · cited by 4
- Set.Ioc_pred_right_eq_Iooproof · cited by 3
- IsMax.not_isMinproof · cited by 2
- Set.Icc_succ_pred_eq_Iooproof · cited by 2
- CategoryTheory.Limits.hasColimitsOfShape_of_initialSegproof · cited by 1