---

Step * of Lemma loop-classrel

∀[Info,B:Type]. ∀[X:EClass(B ⟶ bag(B))]. ∀[init:Id ⟶ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].
  uiff(v ∈ loop-class(X;init)(e);↓∃f:B ⟶ bag(B). ∃b:B. (f ∈ X(e) ∧ b ∈ Prior(loop-class(X;init))?init(e) ∧ v ↓∈ f b))
BY
{ ((UnivCD THENA Auto)
   THEN RW (AddrC [1] (RecUnfoldC `loop-class`)) 0
   THEN InstLemma `eclass2-classrel` [⌜Info⌝;⌜B⌝;⌜B⌝;⌜X⌝;⌜Prior(loop-class(X;init))?init⌝;⌜es⌝;⌜e⌝;⌜v⌝]⋅
   THEN Auto) }

---

Latex:

---

Latex:
\mforall{}[Info,B:Type].  \mforall{}[X:EClass(B  {}\mrightarrow{}  bag(B))].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:B].
    uiff(v  \mmember{}  loop-class(X;init)(e);\mdownarrow{}\mexists{}f:B  {}\mrightarrow{}  bag(B)
                                                                      \mexists{}b:B
                                                                        (f  \mmember{}  X(e)  \mwedge{}  b  \mmember{}  Prior(loop-class(X;init))?init(e)  \mwedge{}  v  \mdownarrow{}\mmember{}  f  b))


By

---

Latex:
((UnivCD  THENA  Auto)
  THEN  RW  (AddrC  [1]  (RecUnfoldC  `loop-class`))  0
  THEN  InstLemma  `eclass2-classrel`  [\mkleeneopen{}Info\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}Prior(loop-class(X;init))?init\mkleeneclose{};\mkleeneopen{}es\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}v\mkleeneclose{}
  ]\mcdot{}
  THEN  Auto)

---

Home Index