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Step * of Lemma rv-isometry-inverse

No Annotations
∀[rv:InnerProductSpace]. ∀[f,g:Point(rv) ⟶ Point(rv)].
  (Isometry(f)) supposing (Isometry(g) and (∀x:Point(rv). g (f x) ≡ x))
BY
{ (Auto
   THEN (InstLemma `rv-isometry-injective` [⌜rv⌝;⌜g⌝]⋅ THENA Auto)
   THEN InstLemma `rv-isometry-implies-functional` [⌜rv⌝;⌜g⌝]⋅
   THEN Auto) }

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

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Latex:

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Latex:
No  Annotations
\mforall{}[rv:InnerProductSpace].  \mforall{}[f,g:Point(rv)  {}\mrightarrow{}  Point(rv)].
    (Isometry(f))  supposing  (Isometry(g)  and  (\mforall{}x:Point(rv).  g  (f  x)  \mequiv{}  x))


By

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

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