---

Step * 1 2 of Lemma FormSafe-iff-FormSafe1'


1. C : Type
2. left : Form(C)
3. right : Form(C)
4. ∀vs:Atom List. (FormSafe1(left) vs ⇐⇒ FormSafe1'(left) vs)
5. ∀vs:Atom List. (FormSafe1(right) vs ⇐⇒ FormSafe1'(right) vs)
6. vs : Atom List
7. (∃theta:Atom List
     (l_subset(Atom;theta;vs-FormFvs(right)) ∧ (FormSafe1'(left) theta) ∧ (FormSafe1'(right) vs-theta)))
∨ (∃phi:Atom List. (l_subset(Atom;phi;vs-FormFvs(left)) ∧ (FormSafe1'(left) vs-phi) ∧ (FormSafe1'(right) phi)))
⊢ ∃as,bs:Atom List
   (set-equal(Atom;vs;as @ bs)
   ∧ (FormSafe1(left) as)
   ∧ (FormSafe1(right) bs)
   ∧ (l_disjoint(Atom;as;FormFvs(right)) ∨ l_disjoint(Atom;bs;FormFvs(left))))
BY
{ ((RWO "4< 5<" (-1) THENA Auto) THEN RepeatFor 2 (Thin 4) THEN D -1 THEN ExRepD) }

1
1. C : Type
2. left : Form(C)
3. right : Form(C)
4. vs : Atom List
5. theta : Atom List
6. l_subset(Atom;theta;vs-FormFvs(right))
7. FormSafe1(left) theta
8. FormSafe1(right) vs-theta
⊢ ∃as,bs:Atom List
   (set-equal(Atom;vs;as @ bs)
   ∧ (FormSafe1(left) as)
   ∧ (FormSafe1(right) bs)
   ∧ (l_disjoint(Atom;as;FormFvs(right)) ∨ l_disjoint(Atom;bs;FormFvs(left))))

2
1. C : Type
2. left : Form(C)
3. right : Form(C)
4. vs : Atom List
5. phi : Atom List
6. l_subset(Atom;phi;vs-FormFvs(left))
7. FormSafe1(left) vs-phi
8. FormSafe1(right) phi
⊢ ∃as,bs:Atom List
   (set-equal(Atom;vs;as @ bs)
   ∧ (FormSafe1(left) as)
   ∧ (FormSafe1(right) bs)
   ∧ (l_disjoint(Atom;as;FormFvs(right)) ∨ l_disjoint(Atom;bs;FormFvs(left))))

---

Latex:

---

Latex:

1.  C  :  Type
2.  left  :  Form(C)
3.  right  :  Form(C)
4.  \mforall{}vs:Atom  List.  (FormSafe1(left)  vs  \mLeftarrow{}{}\mRightarrow{}  FormSafe1'(left)  vs)
5.  \mforall{}vs:Atom  List.  (FormSafe1(right)  vs  \mLeftarrow{}{}\mRightarrow{}  FormSafe1'(right)  vs)
6.  vs  :  Atom  List
7.  (\mexists{}theta:Atom  List
          (l\_subset(Atom;theta;vs-FormFvs(right))
          \mwedge{}  (FormSafe1'(left)  theta)
          \mwedge{}  (FormSafe1'(right)  vs-theta)))
\mvee{}  (\mexists{}phi:Atom  List
        (l\_subset(Atom;phi;vs-FormFvs(left))  \mwedge{}  (FormSafe1'(left)  vs-phi)  \mwedge{}  (FormSafe1'(right)  phi)))
\mvdash{}  \mexists{}as,bs:Atom  List
      (set-equal(Atom;vs;as  @  bs)
      \mwedge{}  (FormSafe1(left)  as)
      \mwedge{}  (FormSafe1(right)  bs)
      \mwedge{}  (l\_disjoint(Atom;as;FormFvs(right))  \mvee{}  l\_disjoint(Atom;bs;FormFvs(left))))


By

---

Latex:
((RWO  "4<  5<"  (-1)  THENA  Auto)  THEN  RepeatFor  2  (Thin  4)  THEN  D  -1  THEN  ExRepD)

---

Home Index