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Step * 2 2 1 1 of Lemma fdl-1-join-irreducible


1. X : Type
2. y : Point(free-dl(X))
3. x : Point(free-dl(X))
⊢ λa.Ax ∈ (↑fdl-is-1(x)) ⇒ (↑fdl-is-1(x ∨ y))
BY
{ ((Subst' Point(free-dl(X)) ~ free-dl-type(X) -2 THENA Computation)
   THEN (Subst' Point(free-dl(X)) ~ free-dl-type(X) -1 THENA Computation)
   ) }

1
1. X : Type
2. y : free-dl-type(X)
3. x : free-dl-type(X)
⊢ λa.Ax ∈ (↑fdl-is-1(x)) ⇒ (↑fdl-is-1(x ∨ y))

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Latex:

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Latex:

1.  X  :  Type
2.  y  :  Point(free-dl(X))
3.  x  :  Point(free-dl(X))
\mvdash{}  \mlambda{}a.Ax  \mmember{}  (\muparrow{}fdl-is-1(x))  {}\mRightarrow{}  (\muparrow{}fdl-is-1(x  \mvee{}  y))


By

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Latex:
((Subst'  Point(free-dl(X))  \msim{}  free-dl-type(X)  -2  THENA  Computation)
  THEN  (Subst'  Point(free-dl(X))  \msim{}  free-dl-type(X)  -1  THENA  Computation)
  )

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