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Step * 2 1 1 3 of Lemma lattice-extend-meet

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1. T : Type
2. eq : EqDecider(T)
3. L : BoundedDistributiveLattice
4. eqL : EqDecider(Point(L))
5. f : T ⟶ Point(L)
6. a : {ac:fset(fset(T))| ↑fset-antichain(eq;ac)} 
7. b : {ac:fset(fset(T))| ↑fset-antichain(eq;ac)} 
8. ∀[s:fset(fset(T))]. (λls./\(ls)"(λxs.f"(xs)"(s)) = λx./\(f"(x))"(s) ∈ fset(Point(L)))
9. z : fset(fset(Point(L)))
⊢ \/(λls./\(ls)"(λxs.f"(xs)"(a))) ∧ \/(λls./\(ls)"(λxs.f"(xs)"(b))) ≤ \/(λls./\(ls)"(z)) ∈ Type
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Latex:

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Latex:
.....wf..... 
1.  T  :  Type
2.  eq  :  EqDecider(T)
3.  L  :  BoundedDistributiveLattice
4.  eqL  :  EqDecider(Point(L))
5.  f  :  T  {}\mrightarrow{}  Point(L)
6.  a  :  \{ac:fset(fset(T))|  \muparrow{}fset-antichain(eq;ac)\} 
7.  b  :  \{ac:fset(fset(T))|  \muparrow{}fset-antichain(eq;ac)\} 
8.  \mforall{}[s:fset(fset(T))].  (\mlambda{}ls./\mbackslash{}(ls)"(\mlambda{}xs.f"(xs)"(s))  =  \mlambda{}x./\mbackslash{}(f"(x))"(s))
9.  z  :  fset(fset(Point(L)))
\mvdash{}  \mbackslash{}/(\mlambda{}ls./\mbackslash{}(ls)"(\mlambda{}xs.f"(xs)"(a)))  \mwedge{}  \mbackslash{}/(\mlambda{}ls./\mbackslash{}(ls)"(\mlambda{}xs.f"(xs)"(b)))  \mleq{}  \mbackslash{}/(\mlambda{}ls./\mbackslash{}(ls)"(z))  \mmember{}  Type


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