toSubgroupClass — Mathlib

English

Restriction of scalar multiplication to a subfield preserves SMulWithZero structure.

Русский

Ограничение скалярного умножения до подполя сохраняет структуру SMulWithZero.

LaTeX

$$$ [Zero X] [SMulWithZero K X] (F : Subfield K) : SMulWithZero F X$$

Lean4

/-- A subfield contains `1`, products and inverses.

Be assured that we're not actually proving that subfields are subgroups:
`SubgroupClass` is really an abbreviation of `SubgroupWithOrWithoutZeroClass`.
-/
instance (priority := 100) toSubgroupClass : SubgroupClass S K :=
  { h with }

Похожие утверждения