Theorems · Theorem · order theory
IsUpperSet.mul_left
∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : Preorder α] [IsOrderedMonoid α] {s t : Set α},
IsUpperSet t → IsUpperSet (s * t)- Defined in
- Mathlib.Algebra.Order.UpperLower
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- IsOrderedMonoidstatement and proof · cited by 577
- smul_eq_mulproof · cited by 357
- Set.mulstatement · cited by 297
- IsUpperSetstatement and proof · cited by 148
- Set.iUnion_smul_setproof · cited by 7
- isUpperSet_iUnion₂proof · cited by 3
- IsUpperSet.smulproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsLowerSet.mul_leftproof · cited by 2
- IsUpperSet.mul_rightproof · cited by 2
- IsUpperSet.thickening'proof · cited by 1