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Step * 1 of Lemma free-dlwc-basis

.....assertion..... 
1. T : Type
2. eq : EqDecider(T)
3. Cs : T ⟶ fset(fset(T))
4. x : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
⊢ x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
BY
{ ((Assert x ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])) BY
          Declaration)
   THEN (RWO "free-dlwc-point" 4 THENA Auto)
   THEN DVar `x'
   THEN ExRepD
   THEN (Assert deq-fset(deq-fset(eq)) ∈ EqDecider(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))) BY
               (RWO "free-dlwc-point" 0 THEN Auto))) }

1
1. T : Type
2. eq : EqDecider(T)
3. Cs : T ⟶ fset(fset(T))
4. x : fset(fset(T))
5. ↑fset-antichain(eq;x)
6. fset-all(x;a.fset-contains-none(eq;a;x.Cs[x]))
7. x ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
8. deq-fset(deq-fset(eq)) ∈ EqDecider(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])))
⊢ x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))

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Latex:

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Latex:
.....assertion..... 
1.  T  :  Type
2.  eq  :  EqDecider(T)
3.  Cs  :  T  {}\mrightarrow{}  fset(fset(T))
4.  x  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
\mvdash{}  x  =  \mbackslash{}/(\mlambda{}s.\{s\}"(x))


By

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Latex:
((Assert  x  \mmember{}  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))  BY
                Declaration)
  THEN  (RWO  "free-dlwc-point"  4  THENA  Auto)
  THEN  DVar  `x'
  THEN  ExRepD
  THEN  (Assert  deq-fset(deq-fset(eq))
                            \mmember{}  EqDecider(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])))  BY
                          (RWO  "free-dlwc-point"  0  THEN  Auto)))

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