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Step * of Lemma simple-loc-comb-2-concat-classrel

∀[Info,A,B,C:Type]. ∀[f:Id ─→ A ─→ B ─→ bag(C)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
  uiff(v ∈ f@Loc o (Loc,X, Y)(e);↓∃a:A. ∃b:B. (a ∈ X(e) ∧ b ∈ Y(e) ∧ v ↓∈ f loc(e) a b))
BY
{ ((UnivCD THENA Auto)
   THEN Unfold `concat-lifting-loc-2` 0
   THEN Unfold `simple-loc-comb-2` 0
   THEN Reduce 0
   THEN (InstLemma `simple-loc-comb2-concat-classrel` [⌈Info⌉; ⌈A⌉; ⌈B⌉; ⌈C⌉; ⌈f⌉; ⌈X⌉; ⌈Y⌉; ⌈es⌉; ⌈e⌉; ⌈v⌉]⋅
         THENA Auto
         )
   THEN Unfold `simple-loc-comb2` (-1)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[Info,A,B,C:Type].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  bag(C)].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].
\mforall{}[e:E].  \mforall{}[v:C].
    uiff(v  \mmember{}  f@Loc  o  (Loc,X,  Y)(e);\mdownarrow{}\mexists{}a:A.  \mexists{}b:B.  (a  \mmember{}  X(e)  \mwedge{}  b  \mmember{}  Y(e)  \mwedge{}  v  \mdownarrow{}\mmember{}  f  loc(e)  a  b))


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  Unfold  `concat-lifting-loc-2`  0
  THEN  Unfold  `simple-loc-comb-2`  0
  THEN  Reduce  0
  THEN  (InstLemma  `simple-loc-comb2-concat-classrel`  [\mkleeneopen{}Info\mkleeneclose{};  \mkleeneopen{}A\mkleeneclose{};  \mkleeneopen{}B\mkleeneclose{};  \mkleeneopen{}C\mkleeneclose{};  \mkleeneopen{}f\mkleeneclose{};  \mkleeneopen{}X\mkleeneclose{};  \mkleeneopen{}Y\mkleeneclose{};  \mkleeneopen{}es\mkleeneclose{};  \mkleeneopen{}e\mkleeneclose{}
              ;  \mkleeneopen{}v\mkleeneclose{}]\mcdot{}
              THENA  Auto
              )
  THEN  Unfold  `simple-loc-comb2`  (-1)
  THEN  Auto)

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