Theorems · Theorem · group theory

MulAction.Supports.smul

∀ {G : Type u_1} {H : Type u_2} {α : Type u_3} {β : Type u_4} [inst : Group H] [inst_1 : SMul G α] [inst_2 : SMul G β]
  [inst_3 : MulAction H α] [inst_4 : SMul H β] [SMulCommClass G H β] [SMulCommClass G H α] {s : Set α} {b : β} (g : H),
  MulAction.Supports G s b → MulAction.Supports G (g • s) (g • b)

Defined in: Mathlib.GroupTheory.GroupAction.Support
Cited by: 0 results in Mathlib
Foundations: Depth 18 from the axioms · uses propext, Quot.sound
Assumes: Group SMul SMul MulAction SMul SMulCommClass SMulCommClass

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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
Groupstatement and proof · cited by 6,238
SMulCommClassstatement and proof · cited by 1,927
MulActionstatement and proof · cited by 1,294
Set.smulSetstatement · cited by 608
SMulCommClass.smul_commproof · cited by 143
Set.forall_mem_imageproof · cited by 65
smul_left_cancel_iffproof · cited by 10
MulAction.Supportsstatement and proof · cited by 3

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