You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
|
|
|
|
|
import Adam.Metadata
|
|
|
|
|
|
|
|
|
|
|
|
import Mathlib.Algebra.Module.Submodule.Lattice
|
|
|
|
|
|
import Mathlib.LinearAlgebra.Span
|
|
|
|
|
|
|
|
|
|
|
|
open Submodule
|
|
|
|
|
|
|
|
|
|
|
|
Game "Adam"
|
|
|
|
|
|
World "Module2"
|
|
|
|
|
|
Level 5
|
|
|
|
|
|
|
|
|
|
|
|
Title "Lineare Abbildung"
|
|
|
|
|
|
|
|
|
|
|
|
Introduction
|
|
|
|
|
|
"
|
|
|
|
|
|
Die interne Summe von Untermodulen wird in Lean mit `⊔` (`\\sup`) geschrieben.
|
|
|
|
|
|
"
|
|
|
|
|
|
|
|
|
|
|
|
Statement
|
|
|
|
|
|
"
|
|
|
|
|
|
Zeige, dass `V₁ ⊔ V₂` tatsächlich die interne Summe `⟨V₁ ∪ V₂⟩` ist.
|
|
|
|
|
|
"
|
|
|
|
|
|
{K V : Type _} [Field K] [AddCommMonoid V] [Module K V] (V₁ V₂ : Submodule K V) :
|
|
|
|
|
|
V₁ ⊔ V₂ = span K ( (V₁ : Set V) ∪ V₂ ) := by
|
|
|
|
|
|
rw [span_union]
|
|
|
|
|
|
simp
|
