---

Step * 2 1 1 2 1 1 1 1 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]))
6. deq-fset(deq-fset(eq)) ∈ EqDecider(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])))
7. x ∈ fset(fset(T))
8. y : fset({s:fset(T)| s ∈ x} )
9. x = y ∈ fset({s:fset(T)| s ∈ x} )
10. s : fset(T)
11. s ∈ x
⊢ ↑fset-contains-none(eq;s;x.Cs[x])
BY
{ ((RWO "free-dlwc-point" 4 THENA Auto) THEN D 4 THEN Unhide THEN Auto) }

1
1. T : Type
2. eq : EqDecider(T)
3. Cs : T ⟶ fset(fset(T))
4. x : fset(fset(T))
5. ↑fset-antichain(eq;x)
6. fset-all(x;a.fset-contains-none(eq;a;x.Cs[x]))
7. x = \/(λs.{s}"(x)) ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
8. deq-fset(deq-fset(eq)) ∈ EqDecider(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])))
9. x ∈ fset(fset(T))
10. y : fset({s:fset(T)| s ∈ x} )
11. x = y ∈ fset({s:fset(T)| s ∈ x} )
12. s : fset(T)
13. s ∈ x
⊢ ↑fset-contains-none(eq;s;x.Cs[x])

---

Latex:

---

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))
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))
8.  y  :  fset(\{s:fset(T)|  s  \mmember{}  x\}  )
9.  x  =  y
10.  s  :  fset(T)
11.  s  \mmember{}  x
\mvdash{}  \muparrow{}fset-contains-none(eq;s;x.Cs[x])


By

---

Latex:
((RWO  "free-dlwc-point"  4  THENA  Auto)  THEN  D  4  THEN  Unhide  THEN  Auto)

---

Home Index