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Step * 1 1 of Lemma free-dl-le


1. [T] : Type
2. eq : EqDecider(T)@i
3. x : {ac:fset(fset(T))| ↑fset-antichain(eq;ac)} @i
4. y : {ac:fset(fset(T))| ↑fset-antichain(eq;ac)} @i
⊢ x ≤ y ⇐⇒ fset-ac-le(eq;x;y)
BY
{ ((RepUR ``lattice-le lattice-meet`` 0 THEN (RWO "free-dl-point" 0 THENA Auto))
   THEN RepUR ``free-dist-lattice mk-bounded-distributive-lattice`` 0
   THEN RepUR ``mk-bounded-lattice`` 0) }

1
1. [T] : Type
2. eq : EqDecider(T)@i
3. x : {ac:fset(fset(T))| ↑fset-antichain(eq;ac)} @i
4. y : {ac:fset(fset(T))| ↑fset-antichain(eq;ac)} @i
⊢ x = fset-ac-glb(eq;x;y) ∈ {ac:fset(fset(T))| ↑fset-antichain(eq;ac)}  ⇐⇒ fset-ac-le(eq;x;y)

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Latex:

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Latex:

1.  [T]  :  Type
2.  eq  :  EqDecider(T)@i
3.  x  :  \{ac:fset(fset(T))|  \muparrow{}fset-antichain(eq;ac)\}  @i
4.  y  :  \{ac:fset(fset(T))|  \muparrow{}fset-antichain(eq;ac)\}  @i
\mvdash{}  x  \mleq{}  y  \mLeftarrow{}{}\mRightarrow{}  fset-ac-le(eq;x;y)


By

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Latex:
((RepUR  ``lattice-le  lattice-meet``  0  THEN  (RWO  "free-dl-point"  0  THENA  Auto))
  THEN  RepUR  ``free-dist-lattice  mk-bounded-distributive-lattice``  0
  THEN  RepUR  ``mk-bounded-lattice``  0)

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