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Step * of Lemma free-dlwc-point

∀[T,eq,Cs:Top].
  (Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])) ~ {ac:fset(fset(T))| 
                                                              (↑fset-antichain(eq;ac))
                                                              ∧ fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))} )
BY
{ (Auto
   THEN (RepUR ``lattice-point free-dist-lattice-with-constraints`` 0 THEN RepUR ``constrained-antichain-lattice`` 0)
   THEN RepUR ``mk-bounded-distributive-lattice mk-bounded-lattice`` 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T,eq,Cs:Top].
    (Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])) 
    \msim{}  \{ac:fset(fset(T))|  (\muparrow{}fset-antichain(eq;ac))  \mwedge{}  fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))\}  )


By

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Latex:
(Auto
  THEN  (RepUR  ``lattice-point  free-dist-lattice-with-constraints``  0
              THEN  RepUR  ``constrained-antichain-lattice``  0
              )
  THEN  RepUR  ``mk-bounded-distributive-lattice  mk-bounded-lattice``  0
  THEN  Auto)

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