Theorems · Theorem · group theory
SetLike.smul_subset_self
∀ {S : Type u_1} {R : Type u_2} {M : Type u_3} [inst : SetLike S M] [inst_1 : SMul R M] [SMulMemClass S R M] (r : R)
(s : S), r • ↑s ⊆ ↑s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- SetLikeSMulSMulMemClass
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.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- SetLikestatement and proof · cited by 1,084
- Set.smulSetstatement · cited by 608
- SMulMemClassstatement and proof · cited by 77
- SMulMemClass.smul_memproof · cited by 55
Cited by1
Results whose statement or proof uses this declaration.
- SetLike.units_smulproof · cited by 1