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import Adam.Metadata
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import Mathlib.Algebra.Module.Submodule.Lattice
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import Mathlib.Data.Real.Basic -- definiert `ℝ`
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import Mathlib.Data.Fin.VecNotation -- Importiert Matrix/Vektor-Notation
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--import Mathlib.LinearAlgebra.FinSupp -- contains `top_le_span_range_iff_forall_exists_fun`
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import Mathlib.Tactic.FinCases
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import Mathlib.Algebra.BigOperators.Finsupp -- default?
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import Mathlib.LinearAlgebra.Span
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import Mathlib
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open Submodule
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Game "Adam"
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World "Module2"
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Level 2
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Title "Lineare Abbildung"
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Introduction
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"
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(Verpackungswahn)
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If `f` is a function and `M` a subset of its domain, then
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`f '' M` or `set.image f M` is the notation for the image, which is
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usally denoted `f(M) = {y | ∃ x ∈ M, f(x) = y}` in mathematical texts.
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"
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-- TODO: This is blocked by
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-- https://github.com/leanprover/lean4/issues/2074
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set_option autoImplicit false
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-- set_option pp.all true
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Statement
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"" : True := by
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sorry
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-- example {K V W : Type} [Field K] [AddCommMonoid V] [AddCommMonoid W]
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-- [Module K V] [Module K W] (M : Set V) (f : V →ₗ[K] W) :
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-- f '' span K M = @span K (f '' M) := by
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-- sorry
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-- example {K V : Type} [Field K] [AddCommMonoid V]
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-- [Module K V] (M : Set V) (f : V →ₗ[K] V) : f '' M = f '' M = := by
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-- rfl
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