Nuprl Lemma : existse-between2_functionality_wrt_iff

es:EO. ∀e1:E. ∀e2:{e:E| loc(e) loc(e1) ∈ Id} .
  ∀[P,Q:{e:E| loc(e) loc(e1) ∈ Id}  ⟶ ℙ].
    ((∀e:{e:E| loc(e) loc(e1) ∈ Id} (P[e] ⇐⇒ Q[e]))  (∃e∈[e1,e2].P[e] ⇐⇒ ∃e∈[e1,e2].Q[e]))


Proof




Definitions occuring in Statement :  existse-between2: e∈[e1,e2].P[e] es-loc: loc(e) es-E: E event_ordering: EO Id: Id uall: [x:A]. B[x] prop: so_apply: x[s] all: x:A. B[x] iff: ⇐⇒ Q implies:  Q set: {x:A| B[x]}  function: x:A ⟶ B[x] equal: t ∈ T
Definitions unfolded in proof :  all: x:A. B[x] uall: [x:A]. B[x] implies:  Q iff: ⇐⇒ Q and: P ∧ Q existse-between2: e∈[e1,e2].P[e] exists: x:A. B[x] member: t ∈ T cand: c∧ B prop: so_apply: x[s] uimplies: supposing a subtype_rel: A ⊆B so_lambda: λ2x.t[x] rev_implies:  Q guard: {T}

Latex:
\mforall{}es:EO.  \mforall{}e1:E.  \mforall{}e2:\{e:E|  loc(e)  =  loc(e1)\}  .
    \mforall{}[P,Q:\{e:E|  loc(e)  =  loc(e1)\}    {}\mrightarrow{}  \mBbbP{}].
        ((\mforall{}e:\{e:E|  loc(e)  =  loc(e1)\}  .  (P[e]  \mLeftarrow{}{}\mRightarrow{}  Q[e]))  {}\mRightarrow{}  (\mexists{}e\mmember{}[e1,e2].P[e]  \mLeftarrow{}{}\mRightarrow{}  \mexists{}e\mmember{}[e1,e2].Q[e]))



Date html generated: 2016_05_16-AM-09_45_24
Last ObjectModification: 2015_12_28-PM-09_40_02

Theory : new!event-ordering


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