English
The technical identity expresses compatibility of the lifted action with inverses and products in Units M under the given conditions.
Русский
Техническое тождество выражает совместимость повышенного действия с обратными и произведениями в Units M при заданных условиях.
LaTeX
$$$ \\text{mulAction' } _\\text{proof} \\Rightarrow \\text{compatibility with inverses and products}$$$
Lean4
/-- Transfer `SMulCommClass G H M` to `SMulCommClass G H Mˣ`. -/
@[to_additive /-- Transfer `VAddCommClass G H M` to `VAddCommClass G H (AddUnits M)`. -/
]
instance smulCommClass' [Group G] [Group H] [Monoid M] [MulAction G M] [SMulCommClass G M M] [MulAction H M]
[SMulCommClass H M M] [IsScalarTower G M M] [IsScalarTower H M M] [SMulCommClass G H M] : SMulCommClass G H Mˣ where
smul_comm g h m := Units.ext <| smul_comm g h (m : M)
