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Step * of Lemma disjoint-union-classrel-ite-weak2

∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:A + B].
  (v ∈ X + Y(e) ⇐⇒ ↓((↑isl(v)) ∧ outl(v) ∈ X(e)) ∨ ((↑¬bisl(v)) ∧ outr(v) ∈ Y(e) ∧ (∀w:A. (¬w ∈ X(e)))))
BY
{ ((UnivCD THENA MaAuto)
   THEN InstLemma `disjoint-union-classrel-ite2` [⌜Info⌝;⌜A⌝;⌜B⌝;⌜X⌝;⌜Y⌝;⌜es⌝;⌜e⌝;⌜v⌝]⋅
   THEN MaAuto) }

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Latex:

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Latex:
\mforall{}[Info,A,B:Type].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:A  +  B].
    (v  \mmember{}  X  +  Y(e)
    \mLeftarrow{}{}\mRightarrow{}  \mdownarrow{}((\muparrow{}isl(v))  \mwedge{}  outl(v)  \mmember{}  X(e))  \mvee{}  ((\muparrow{}\mneg{}\msubb{}isl(v))  \mwedge{}  outr(v)  \mmember{}  Y(e)  \mwedge{}  (\mforall{}w:A.  (\mneg{}w  \mmember{}  X(e)))))


By

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Latex:
((UnivCD  THENA  MaAuto)
  THEN  InstLemma  `disjoint-union-classrel-ite2`  [\mkleeneopen{}Info\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}Y\mkleeneclose{};\mkleeneopen{}es\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}v\mkleeneclose{}]\mcdot{}
  THEN  MaAuto)

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