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Step * 2 of Lemma free-dlwc-basis


1. T : Type
2. eq : EqDecider(T)
3. Cs : T ⟶ fset(fset(T))
4. x : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
5. x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
⊢ x = \/(λs./\(λx.free-dlwc-inc(eq;a.Cs[a];x)"(s))"(x)) ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
BY
{ (NthHypEq (-1) THEN RepeatFor 2 ((EqCD THEN Auto))) }

1
.....subterm..... T:t
2:n
1. T : Type
2. eq : EqDecider(T)
3. Cs : T ⟶ fset(fset(T))
4. x : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
5. x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
⊢ λs./\(λx.free-dlwc-inc(eq;a.Cs[a];x)"(s))"(x)
= λs.{s}"(x)
∈ fset(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])))

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Latex:

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Latex:

1.  T  :  Type
2.  eq  :  EqDecider(T)
3.  Cs  :  T  {}\mrightarrow{}  fset(fset(T))
4.  x  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
5.  x  =  \mbackslash{}/(\mlambda{}s.\{s\}"(x))
\mvdash{}  x  =  \mbackslash{}/(\mlambda{}s./\mbackslash{}(\mlambda{}x.free-dlwc-inc(eq;a.Cs[a];x)"(s))"(x))


By

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Latex:
(NthHypEq  (-1)  THEN  RepeatFor  2  ((EqCD  THEN  Auto)))

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