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Step * 1 1 of Lemma free-dlwc-1-join-irreducible

.....assertion..... 
1. T : Type@i'
2. eq : EqDecider(T)@i
3. Cs : T ⟶ fset(fset(T))@i
4. x : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))@i
5. y : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))@i
6. {} ∈ x ∨ y
⊢ {} ∈ x ∨ {} ∈ y
BY
{ ((RWO "free-dlwc-join" (-1) THENA Auto) THEN (All (RWO "free-dlwc-point") THENA Auto)) }

1
1. T : Type@i'
2. eq : EqDecider(T)@i
3. Cs : T ⟶ fset(fset(T))@i
4. x : {ac:fset(fset(T))| (↑fset-antichain(eq;ac)) ∧ fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))} @i
5. y : {ac:fset(fset(T))| (↑fset-antichain(eq;ac)) ∧ fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))} @i
6. {} ∈ lub(λs.fset-contains-none(eq;s;x.Cs[x]);x;y)
⊢ {} ∈ x ∨ {} ∈ y

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Latex:

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Latex:
.....assertion..... 
1.  T  :  Type@i'
2.  eq  :  EqDecider(T)@i
3.  Cs  :  T  {}\mrightarrow{}  fset(fset(T))@i
4.  x  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))@i
5.  y  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))@i
6.  \{\}  \mmember{}  x  \mvee{}  y
\mvdash{}  \{\}  \mmember{}  x  \mvee{}  \{\}  \mmember{}  y


By

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Latex:
((RWO  "free-dlwc-join"  (-1)  THENA  Auto)  THEN  (All  (RWO  "free-dlwc-point")  THENA  Auto))

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