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Step * 1 2 of Lemma rename-one-comp


1. I : Cname List
2. z : Cname
3. z1 : Cname
4. z2 : Cname
5. ¬(z2 ∈ I)
6. ¬(z1 ∈ I)
7. ¬(z ∈ I)
8. (rename-one-name(z;z1) o rename-one-name(z1;z2))
= (rename-one-name(z;z1) o rename-one-name(z1;z2))
∈ name-morph([z / I];[z2 / I])
⊢ name-morph([z / I];[z2 / I]) ⊆r (nameset([z / I]) ⟶ extd-nameset([z2 / I]))
BY
{ Auto }

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Latex:

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Latex:

1.  I  :  Cname  List
2.  z  :  Cname
3.  z1  :  Cname
4.  z2  :  Cname
5.  \mneg{}(z2  \mmember{}  I)
6.  \mneg{}(z1  \mmember{}  I)
7.  \mneg{}(z  \mmember{}  I)
8.  (rename-one-name(z;z1)  o  rename-one-name(z1;z2))
=  (rename-one-name(z;z1)  o  rename-one-name(z1;z2))
\mvdash{}  name-morph([z  /  I];[z2  /  I])  \msubseteq{}r  (nameset([z  /  I])  {}\mrightarrow{}  extd-nameset([z2  /  I]))


By

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Latex:
Auto

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