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Step * 1 of Lemma free-dl-le


1. [T] : Type
2. eq : EqDecider(T)@i
3. x : Point(free-dist-lattice(T; eq))@i
4. y : Point(free-dist-lattice(T; eq))@i
⊢ x ≤ y ⇐⇒ fset-ac-le(eq;x;y)
BY
{ ((RWO "free-dl-point" (-2) THENA Auto) THEN (RWO "free-dl-point" (-1) THENA Auto)) }

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 ≤ y ⇐⇒ 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  :  Point(free-dist-lattice(T;  eq))@i
4.  y  :  Point(free-dist-lattice(T;  eq))@i
\mvdash{}  x  \mleq{}  y  \mLeftarrow{}{}\mRightarrow{}  fset-ac-le(eq;x;y)


By

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Latex:
((RWO  "free-dl-point"  (-2)  THENA  Auto)  THEN  (RWO  "free-dl-point"  (-1)  THENA  Auto))

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