English
If SMulCommClass M N α holds, then SMulCommClass N M α also holds; commutativity of actions is symmetric.
Русский
Если SMulCommClass M N α выполняется, то SMulCommClass N M α тоже выполняется; коммутativity действий симметрична.
LaTeX
$$$ \forall M,N,\; \alpha,\; [SMul M \alpha],[SMul N \alpha],[SMulCommClass M N \alpha] \Rightarrow SMulCommClass N M \alpha. $$$
Lean4
/-- Commutativity of actions is a symmetric relation. This lemma can't be an instance because this
would cause a loop in the instance search graph. -/
@[to_additive]
theorem symm (M N α : Type*) [SMul M α] [SMul N α] [SMulCommClass M N α] : SMulCommClass N M α where
smul_comm a' a b := (smul_comm a a' b).symm
