---

Step * 1 1 of Lemma free-dlwc-1-join-irreducible

.....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]))
5. y : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
6. {} ∈ x ∨ y
⊢ {} ∈ x ∨ {} ∈ y
BY
{ ((RWO "free-dlwc-join" (-1) THENA Auto) THEN (All (RWO "free-dlwc-point") THENA Auto)) }

1
1. T : Type
2. eq : EqDecider(T)
3. Cs : T ⟶ fset(fset(T))
4. x : {ac:fset(fset(T))| (↑fset-antichain(eq;ac)) ∧ fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))} 
5. y : {ac:fset(fset(T))| (↑fset-antichain(eq;ac)) ∧ fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))} 
6. {} ∈ lub(λs.fset-contains-none(eq;s;x.Cs[x]);x;y)
⊢ {} ∈ x ∨ {} ∈ y

---

Latex:

---

Latex:
.....assertion..... 
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.  y  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
6.  \{\}  \mmember{}  x  \mvee{}  y
\mvdash{}  \{\}  \mmember{}  x  \mvee{}  \{\}  \mmember{}  y


By

---

Latex:
((RWO  "free-dlwc-join"  (-1)  THENA  Auto)  THEN  (All  (RWO  "free-dlwc-point")  THENA  Auto))

---

Home Index