---

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

.....wf..... 
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]))
6. deq-fset(deq-fset(eq)) ∈ EqDecider(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])))
7. x ∈ fset(fset(T))
⊢ x ∈ fset({s:fset(T)| s ∈ x} )
BY
{ (BLemma `fset-subtype2`⋅ THENA Auto) }

---

Latex:

---

Latex:
.....wf..... 
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))
6.  deq-fset(deq-fset(eq))  \mmember{}  EqDecider(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])))
7.  x  \mmember{}  fset(fset(T))
\mvdash{}  x  \mmember{}  fset(\{s:fset(T)|  s  \mmember{}  x\}  )


By

---

Latex:
(BLemma  `fset-subtype2`\mcdot{}  THENA  Auto)

---

Home Index