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Step * of Lemma Accum-loc-class-exists

∀[Info,B,A:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[init:Id ⟶ bag(B)]. ∀[X:EClass(A)].
  ((↓∃x:B. x ↓∈ init loc(e)) ⇒ (↓∃u:A. u ∈ X(e)) ⇒ (↓∃v:B. v ∈ Accum-loc-class(f;init;X)(e)))
BY
{ ((UnivCD THENA MaAuto)
   THEN (InstLemma `primed-class-opt-exists` [⌜Info⌝;⌜B⌝;⌜es⌝;⌜Accum-loc-class(f;init;X)⌝;⌜init⌝;⌜e⌝]⋅ THENA Auto)
   THEN SquashExRepD
   THEN D 0
   THEN (InstConcl [⌜f loc(e) u b⌝]⋅ THENA Auto)
   THEN RepeatFor 2 (MaUseClassRel' 0)
   THEN D 0
   THEN InstConcl [⌜u⌝;⌜b⌝]⋅
   THEN Auto
   THEN Try (Fold `Accum-loc-class` 0)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[Info,B,A:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].
\mforall{}[X:EClass(A)].
    ((\mdownarrow{}\mexists{}x:B.  x  \mdownarrow{}\mmember{}  init  loc(e))  {}\mRightarrow{}  (\mdownarrow{}\mexists{}u:A.  u  \mmember{}  X(e))  {}\mRightarrow{}  (\mdownarrow{}\mexists{}v:B.  v  \mmember{}  Accum-loc-class(f;init;X)(e)))


By

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Latex:
((UnivCD  THENA  MaAuto)
  THEN  (InstLemma  `primed-class-opt-exists`  [\mkleeneopen{}Info\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}es\mkleeneclose{};\mkleeneopen{}Accum-loc-class(f;init;X)\mkleeneclose{};\mkleeneopen{}init\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{}]\mcdot{}
              THENA  Auto
              )
  THEN  SquashExRepD
  THEN  D  0
  THEN  (InstConcl  [\mkleeneopen{}f  loc(e)  u  b\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  RepeatFor  2  (MaUseClassRel'  0)
  THEN  D  0
  THEN  InstConcl  [\mkleeneopen{}u\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  Try  (Fold  `Accum-loc-class`  0)
  THEN  Auto)

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