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Step * of Lemma existse-between3_wf

∀[es:EO]. ∀[e1,e2:E]. ∀[P:{e:E| (loc(e) = loc(e1) ∈ Id) ∧ (¬↑first(e))}  ─→ ℙ].
  ∃e∈(e1,e2].P[e] ∈ ℙ supposing loc(e2) = loc(e1) ∈ Id
BY
{ (Unfold `existse-between3` 0 THEN Auto THEN (RWO "es-locl-iff" (-2)) THEN Auto) }

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Latex:


\mforall{}[es:EO].  \mforall{}[e1,e2:E].  \mforall{}[P:\{e:E|  (loc(e)  =  loc(e1))  \mwedge{}  (\mneg{}\muparrow{}first(e))\}    {}\mrightarrow{}  \mBbbP{}].
    \mexists{}e\mmember{}(e1,e2].P[e]  \mmember{}  \mBbbP{}  supposing  loc(e2)  =  loc(e1)


By

(Unfold  `existse-between3`  0  THEN  Auto  THEN  (RWO  "es-locl-iff"  (-2))  THEN  Auto)

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