### Nuprl Lemma : decidable__existse-between3

es:EO. ∀e1,e2:E.
∀[P:{e:E| (loc(e) loc(e1) ∈ Id) ∧ (¬↑first(e))}  ─→ ℙ]
∀e@loc(e1).Dec(P[e]) supposing ¬↑first(e)  Dec(∃e∈(e1,e2].P[e]) supposing loc(e2) loc(e1) ∈ Id

Proof

Definitions occuring in Statement :  existse-between3: e∈(e1,e2].P[e] alle-at: e@i.P[e] es-first: first(e) es-loc: loc(e) es-E: E event_ordering: EO Id: Id assert: b decidable: Dec(P) uimplies: supposing a uall: [x:A]. B[x] prop: so_apply: x[s] all: x:A. B[x] not: ¬A implies:  Q and: P ∧ Q set: {x:A| B[x]}  function: x:A ─→ B[x] equal: t ∈ T
Lemmas :  alle-at_wf Id_wf es-loc_wf es-E_wf isect_wf not_wf assert_wf es-first_wf2 decidable_wf equal_wf event_ordering_wf decidable__existse-le es-locl_wf es-locl-first assert_elim btrue_neq_bfalse decidable__cand decidable__es-locl es-le_wf exists_wf es-le-loc subtype_base_sq bool_wf bool_subtype_base false_wf
\mforall{}es:EO.  \mforall{}e1,e2:E.
\mforall{}[P:\{e:E|  (loc(e)  =  loc(e1))  \mwedge{}  (\mneg{}\muparrow{}first(e))\}    {}\mrightarrow{}  \mBbbP{}]
\mforall{}e@loc(e1).Dec(P[e])  supposing  \mneg{}\muparrow{}first(e)  {}\mRightarrow{}  Dec(\mexists{}e\mmember{}(e1,e2].P[e])  supposing  loc(e2)  =  loc(e1)

Date html generated: 2015_07_17-AM-08_48_27
Last ObjectModification: 2015_01_27-PM-02_26_57

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