Theorems · Theorem · order theory
Set.OrdConnected.smul
∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : Preorder α] [IsOrderedMonoid α] {s : Set α} {a : α},
s.OrdConnected → (a • s).OrdConnected- Defined in
- Mathlib.Algebra.Order.UpperLower
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- CommGroupstatement and proof · cited by 990
- Set.smulSetstatement · cited by 608
- IsOrderedMonoidstatement and proof · cited by 577
- Set.OrdConnectedstatement and proof · cited by 161
- upperClosureproof · cited by 84
- lowerClosureproof · cited by 83
- LowerSet.lowerproof · cited by 13
- UpperSet.upperproof · cited by 11
- Set.smul_set_interproof · cited by 11
- IsLowerSet.ordConnectedproof · cited by 5
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