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Step * 1 2 1 1 of Lemma free-dl-basis


1. T : Type
2. eq : EqDecider(T)
3. x : Point(free-dist-lattice(T; eq))
4. x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice(T; eq))
5. deq-fset(deq-fset(eq)) ∈ EqDecider(Point(free-dist-lattice(T; eq)))
6. x ∈ fset(fset(T))
⊢ λs./\(λx.free-dl-inc(x)"(s))"(x) = λs.{s}"(x) ∈ fset(Point(free-dist-lattice(T; eq)))
BY
{ (Assert (λs./\(λx.free-dl-inc(x)"(s))) = (λs.{s}) ∈ (fset(T) ⟶ Point(free-dist-lattice(T; eq))) BY
         (EqCD THEN Try (BLemma `lattice-fset-meet-free-dl-inc`) THEN Auto)) }

1
1. T : Type
2. eq : EqDecider(T)
3. x : Point(free-dist-lattice(T; eq))
4. x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice(T; eq))
5. deq-fset(deq-fset(eq)) ∈ EqDecider(Point(free-dist-lattice(T; eq)))
6. x ∈ fset(fset(T))
7. (λs./\(λx.free-dl-inc(x)"(s))) = (λs.{s}) ∈ (fset(T) ⟶ Point(free-dist-lattice(T; eq)))
⊢ λs./\(λx.free-dl-inc(x)"(s))"(x) = λs.{s}"(x) ∈ fset(Point(free-dist-lattice(T; eq)))

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Latex:

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Latex:

1.  T  :  Type
2.  eq  :  EqDecider(T)
3.  x  :  Point(free-dist-lattice(T;  eq))
4.  x  =  \mbackslash{}/(\mlambda{}s.\{s\}"(x))
5.  deq-fset(deq-fset(eq))  \mmember{}  EqDecider(Point(free-dist-lattice(T;  eq)))
6.  x  \mmember{}  fset(fset(T))
\mvdash{}  \mlambda{}s./\mbackslash{}(\mlambda{}x.free-dl-inc(x)"(s))"(x)  =  \mlambda{}s.\{s\}"(x)


By

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Latex:
(Assert  (\mlambda{}s./\mbackslash{}(\mlambda{}x.free-dl-inc(x)"(s)))  =  (\mlambda{}s.\{s\})  BY
              (EqCD  THEN  Try  (BLemma  `lattice-fset-meet-free-dl-inc`)  THEN  Auto))

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