hasSMul — Mathlib

English

For any R-algebra A and set s ⊆ A, the lifted cardinality of adjoin R s is bounded by the max of lift(#R), lift(#s) and aleph0.

Русский

Для любой R-алгебры A и множества s внутри A, лифтированная мощность адьойна ограничена максимумом lift(#R), lift(#s) и aleph0.

LaTeX

$$lift.{u} #(adjoin R s) ≤ lift.{v} #R ⊔ lift.{u} #s ⊔ ℵ₀$$

Lean4

/-- Scalar multiplication defined as multiplication by the image of elements from `R`.
Note: Used for notation only.
-/
def hasSMul : SMul R (Pre R X) :=
  ⟨fun r m ↦ mul (ofScalar r) m⟩

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