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Step * 1 of Lemma rv-orthogonal-iff


1. rv : InnerProductSpace
2. f : Point(rv) ⟶ Point(rv)
3. Orthogonal(f)
⊢ f 0 ≡ 0 ∧ Isometry(f)
BY
{ (InstLemma `rv-orthogonal-isometry` [⌜rv⌝;⌜f⌝]⋅
   THEN Auto
   THEN InstLemma `rv-isometry-implies-functional` [⌜rv⌝;⌜f⌝]⋅
   THEN Auto) }

1
1. rv : InnerProductSpace
2. f : Point(rv) ⟶ Point(rv)
3. Orthogonal(f)
4. Isometry(f)
5. ∀x,y:Point(rv).  (x ≡ y ⇒ f x ≡ f y)
⊢ f 0 ≡ 0

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Latex:

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Latex:

1.  rv  :  InnerProductSpace
2.  f  :  Point(rv)  {}\mrightarrow{}  Point(rv)
3.  Orthogonal(f)
\mvdash{}  f  0  \mequiv{}  0  \mwedge{}  Isometry(f)


By

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Latex:
(InstLemma  `rv-orthogonal-isometry`  [\mkleeneopen{}rv\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  InstLemma  `rv-isometry-implies-functional`  [\mkleeneopen{}rv\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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