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Step * of Lemma free-dlwc-basis

∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[Cs:T ⟶ fset(fset(T))]. ∀[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
{ (Auto THEN Assert ⌜x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))⌝⋅) }

1
.....assertion..... 
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]))
⊢ x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))

2
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]))

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Latex:

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


By

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

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