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Step * 1 1 of Lemma generated-subspace-contains


1. K : Rng
2. vs : VectorSpace(K)
3. P : Point(vs) ⟶ ℙ
4. v : Point(vs)
5. p : P[v]
⊢ v = vs-tree-val(vs;l_tree_node(1;l_tree_leaf(<v, p>);l_tree_node(0;l_tree_leaf(<v, p>);l_tree_leaf(<v, p>)))) ∈ Point(\000Cvs)
BY
{ (RepUR ``vs-tree-val`` 0 THEN GenConclTerm ⌜v + v⌝⋅ THEN Auto) }

1
1. K : Rng
2. vs : VectorSpace(K)
3. P : Point(vs) ⟶ ℙ
4. v : Point(vs)
5. p : P[v]
6. v1 : Point(vs)
7. v + v = v1 ∈ Point(vs)
⊢ v = 1 * v + 0 * v1 ∈ Point(vs)

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Latex:

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Latex:

1.  K  :  Rng
2.  vs  :  VectorSpace(K)
3.  P  :  Point(vs)  {}\mrightarrow{}  \mBbbP{}
4.  v  :  Point(vs)
5.  p  :  P[v]
\mvdash{}  v  =  vs-tree-val(vs;l\_tree\_node(1;l\_tree\_leaf(<v,  p>);l\_tree\_node(0;l\_tree\_leaf(<v,  p>);l\_tree\_leaf\000C(<v,  p>))))


By

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Latex:
(RepUR  ``vs-tree-val``  0  THEN  GenConclTerm  \mkleeneopen{}v  +  v\mkleeneclose{}\mcdot{}  THEN  Auto)

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