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Step * 1 of Lemma free-dl-basis


1. T : Type
2. eq : EqDecider(T)
3. x : Point(free-dist-lattice(T; eq))
⊢ x = \/(λs./\(λx.free-dl-inc(x)"(s))"(x)) ∈ Point(free-dist-lattice(T; eq))
BY
{ Assert ⌜x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice(T; eq))⌝⋅ }

1
.....assertion..... 
1. T : Type
2. eq : EqDecider(T)
3. x : Point(free-dist-lattice(T; eq))
⊢ x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice(T; eq))

2
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))
⊢ x = \/(λs./\(λx.free-dl-inc(x)"(s))"(x)) ∈ 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))
\mvdash{}  x  =  \mbackslash{}/(\mlambda{}s./\mbackslash{}(\mlambda{}x.free-dl-inc(x)"(s))"(x))


By

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Latex:
Assert  \mkleeneopen{}x  =  \mbackslash{}/(\mlambda{}s.\{s\}"(x))\mkleeneclose{}\mcdot{}

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