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Step * of Lemma State-loc-comb-exists

∀[Info,B,A:Type]. ∀[f:Id ─→ A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E].
  ↓∃v:B. v ∈ State-loc-comb(init;f;X)(e) supposing #(init loc(e)) > 0
BY
{ (Auto
   THEN (InstLemma `State-comb-exists` [⌈Info⌉;⌈B⌉;⌈A⌉;⌈f loc(e)⌉;⌈init⌉;⌈X⌉;⌈es⌉;⌈e⌉]⋅ THENA Auto)
   THEN SquashExRepD
   THEN (FLemma `State-loc-comb-classrel-non-loc` [-1] THENA Auto)
   THEN D 0
   THEN InstConcl [⌈v⌉]⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[Info,B,A:Type].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[X:EClass(A)].  \mforall{}[es:EO+(Info)].
\mforall{}[e:E].
    \mdownarrow{}\mexists{}v:B.  v  \mmember{}  State-loc-comb(init;f;X)(e)  supposing  \#(init  loc(e))  >  0


By

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Latex:
(Auto
  THEN  (InstLemma  `State-comb-exists`  [\mkleeneopen{}Info\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}f  loc(e)\mkleeneclose{};\mkleeneopen{}init\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}es\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  SquashExRepD
  THEN  (FLemma  `State-loc-comb-classrel-non-loc`  [-1]  THENA  Auto)
  THEN  D  0
  THEN  InstConcl  [\mkleeneopen{}v\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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