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Step * 1 3 1 of Lemma permutation-s-group_wf

.....subterm..... T:t
1:n
1. rv : SeparationSpace
2. <λx.x, λx.x> ∈ Point(permutation-ss(rv))
3. λfg.let f,g = fg 
       in <g, f> ∈ Point(permutation-ss(rv)) ⟶ Point(permutation-ss(rv))
4. λfg,fg'. let f,g = fg in let f',g' = fg' in <f o f', g' o g> ∈ Point(permutation-ss(rv))
   ⟶ Point(permutation-ss(rv))
   ⟶ Point(permutation-ss(rv))
5. sepw : x:Point(rv) ⟶ y:{y:Point(rv)| x # y}  ⟶ x # y
⊢ permutation-ss(rv) ∈ SeparationSpace
BY
{ Auto }

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Latex:

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Latex:
.....subterm.....  T:t
1:n
1.  rv  :  SeparationSpace
2.  <\mlambda{}x.x,  \mlambda{}x.x>  \mmember{}  Point(permutation-ss(rv))
3.  \mlambda{}fg.let  f,g  =  fg 
              in  <g,  f>  \mmember{}  Point(permutation-ss(rv))  {}\mrightarrow{}  Point(permutation-ss(rv))
4.  \mlambda{}fg,fg'.  let  f,g  =  fg  in  let  f',g'  =  fg'  in  <f  o  f',  g'  o  g>  \mmember{}  Point(permutation-ss(rv))
      {}\mrightarrow{}  Point(permutation-ss(rv))
      {}\mrightarrow{}  Point(permutation-ss(rv))
5.  sepw  :  x:Point(rv)  {}\mrightarrow{}  y:\{y:Point(rv)|  x  \#  y\}    {}\mrightarrow{}  x  \#  y
\mvdash{}  permutation-ss(rv)  \mmember{}  SeparationSpace


By

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Latex:
Auto

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