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Step * of Lemma on-loc-class-program_wf

∀[Info,B:Type]. ∀[X:Id ⟶ EClass(B)]. ∀[pr:∀i:Id. LocalClass(X i)].
  on-loc-class-program(pr) ∈ LocalClass(on-loc-class(X)) supposing valueall-type(B)
BY
{ (Auto
   THEN RepUR ``on-loc-class-program`` 0
   THEN MemTypeCD
   THEN Auto
   THEN Try (Complete ((DoSubsume THEN Auto)))
   THEN (Assert ⌜pr loc(e) ∈ LocalClass(X loc(e))⌝⋅ THENA Auto)
   THEN Reduce 0
   THEN (MemTypeHD (-1) THENA Auto)
   THEN (RWO "-1<" 0 THENA Auto)
   THEN RepUR ``on-loc-class class-ap`` 0
   THEN Auto
   THEN DoSubsume
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[Info,B:Type].  \mforall{}[X:Id  {}\mrightarrow{}  EClass(B)].  \mforall{}[pr:\mforall{}i:Id.  LocalClass(X  i)].
    on-loc-class-program(pr)  \mmember{}  LocalClass(on-loc-class(X))  supposing  valueall-type(B)


By

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Latex:
(Auto
  THEN  RepUR  ``on-loc-class-program``  0
  THEN  MemTypeCD
  THEN  Auto
  THEN  Try  (Complete  ((DoSubsume  THEN  Auto)))
  THEN  (Assert  \mkleeneopen{}pr  loc(e)  \mmember{}  LocalClass(X  loc(e))\mkleeneclose{}\mcdot{}  THENA  Auto)
  THEN  Reduce  0
  THEN  (MemTypeHD  (-1)  THENA  Auto)
  THEN  (RWO  "-1<"  0  THENA  Auto)
  THEN  RepUR  ``on-loc-class  class-ap``  0
  THEN  Auto
  THEN  DoSubsume
  THEN  Auto)

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