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Step * of Lemma equal-eo-strict-forward-E

∀[Info:Type]. ∀[eo:EO+(Info)]. ∀[e:E]. ∀[e1,e2:E].  uiff(e1 = e2 ∈ E;e1 = e2 ∈ E)
BY
{ (Auto
   THEN StrongHypSubst (-1) 0⋅
   THEN Auto
   THEN (InstLemma `eo-strict-forward-E-subtype2` [⌈Info⌉;⌈eo⌉;⌈e⌉]⋅ THENA Auto)
   THEN (Assert ⌈z ∈ {e':E| (loc(e') = loc(e) ∈ Id) ⇒ (e <loc e')} ⌉⋅ THENM (DoSubsume THEN Auto))
   THEN MemTypeCD
   THEN Auto
   THEN (HypSubst' (-3) 0 THENA Auto)
   THEN BLemma `eo-strict-forward-E-member`
   THEN Auto) }

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Latex:


\mforall{}[Info:Type].  \mforall{}[eo:EO+(Info)].  \mforall{}[e:E].  \mforall{}[e1,e2:E].    uiff(e1  =  e2;e1  =  e2)


By

(Auto
  THEN  StrongHypSubst  (-1)  0\mcdot{}
  THEN  Auto
  THEN  (InstLemma  `eo-strict-forward-E-subtype2`  [\mkleeneopen{}Info\mkleeneclose{};\mkleeneopen{}eo\mkleeneclose{};\mkleeneopen{}e\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (Assert  \mkleeneopen{}z  \mmember{}  \{e':E|  (loc(e')  =  loc(e))  {}\mRightarrow{}  (e  <loc  e')\}  \mkleeneclose{}\mcdot{}  THENM  (DoSubsume  THEN  Auto))
  THEN  MemTypeCD
  THEN  Auto
  THEN  (HypSubst'  (-3)  0  THENA  Auto)
  THEN  BLemma  `eo-strict-forward-E-member`
  THEN  Auto)

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