Step
*
1
1
1
of Lemma
vs-iso-iff-kernel-0
1. K : Rng
2. A : VectorSpace(K)
3. B : VectorSpace(K)
4. f : A ⟶ B
5. ∃g:B ⟶ A. ((∀a:Point(A). ((g (f a)) = a ∈ Point(A))) ∧ (∀b:Point(B). ((f (g b)) = b ∈ Point(B))))
6. a : Point(A)
7. a ∈ Ker(f)
⊢ a = 0 ∈ Point(A)
BY
{ ExRepD }
1
1. K : Rng
2. A : VectorSpace(K)
3. B : VectorSpace(K)
4. f : A ⟶ B
5. g : B ⟶ A
6. ∀a:Point(A). ((g (f a)) = a ∈ Point(A))
7. ∀b:Point(B). ((f (g b)) = b ∈ Point(B))
8. a : Point(A)
9. a ∈ Ker(f)
⊢ a = 0 ∈ Point(A)
Latex:
Latex:
1. K : Rng
2. A : VectorSpace(K)
3. B : VectorSpace(K)
4. f : A {}\mrightarrow{} B
5. \mexists{}g:B {}\mrightarrow{} A. ((\mforall{}a:Point(A). ((g (f a)) = a)) \mwedge{} (\mforall{}b:Point(B). ((f (g b)) = b)))
6. a : Point(A)
7. a \mmember{} Ker(f)
\mvdash{} a = 0
By
Latex:
ExRepD
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