Theorems · Theorem · order theory
IsLowerSet.smul_subset
∀ {α : Type u_1} [inst : CommMonoid α] [inst_1 : Preorder α] [IsOrderedMonoid α] {s : Set α} {x : α},
IsLowerSet s → x ≤ 1 → x • s ⊆ s- Defined in
- Mathlib.Algebra.Order.UpperLower
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext, Quot.sound
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Cites8
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
- CommMonoidstatement and proof · cited by 2,264
- Set.smulSetstatement · cited by 608
- IsOrderedMonoidstatement and proof · cited by 577
- IsLowerSetstatement and proof · cited by 167
- Set.smul_set_subset_iffproof · cited by 7
- mul_le_of_le_one_left'proof · cited by 4
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