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


1. T : Type
2. eq : EqDecider(T)
3. Cs : T ⟶ fset(fset(T))
4. x : {ac:fset(fset(T))| (↑fset-antichain(eq;ac)) ∧ fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))} 
5. y : {ac:fset(fset(T))| (↑fset-antichain(eq;ac)) ∧ fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))} 
6. {} ∈ fset-minimals(xs,ys.f-proper-subset-dec(eq;xs;ys); x ⋃ y)
⊢ {} ∈ x ∨ {} ∈ y
BY
{ ((FLemma `member-fset-minimals` [-1] THENA Auto) THEN FLemma `member-fset-union` [-1] THEN Auto) }

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Latex:

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Latex:

1.  T  :  Type
2.  eq  :  EqDecider(T)
3.  Cs  :  T  {}\mrightarrow{}  fset(fset(T))
4.  x  :  \{ac:fset(fset(T))| 
                (\muparrow{}fset-antichain(eq;ac))  \mwedge{}  fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))\} 
5.  y  :  \{ac:fset(fset(T))| 
                (\muparrow{}fset-antichain(eq;ac))  \mwedge{}  fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))\} 
6.  \{\}  \mmember{}  fset-minimals(xs,ys.f-proper-subset-dec(eq;xs;ys);  x  \mcup{}  y)
\mvdash{}  \{\}  \mmember{}  x  \mvee{}  \{\}  \mmember{}  y


By

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Latex:
((FLemma  `member-fset-minimals`  [-1]  THENA  Auto)  THEN  FLemma  `member-fset-union`  [-1]  THEN  Auto)

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