Nuprl Lemma : decidable__alle-between2

es:EO. ∀e1,e2:E.
  ∀[P:{e:E| loc(e) loc(e1) ∈ Id}  ⟶ ℙ]. ∀e@loc(e1).Dec(P[e])  Dec(∀e∈[e1,e2].P[e]) supposing loc(e2) loc(e1) ∈ Id


Proof




Definitions occuring in Statement :  alle-between2: e∈[e1,e2].P[e] alle-at: e@i.P[e] es-loc: loc(e) es-E: E event_ordering: EO Id: Id decidable: Dec(P) uimplies: supposing a uall: [x:A]. B[x] prop: so_apply: x[s] all: x:A. B[x] 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] uimplies: supposing a member: t ∈ T implies:  Q alle-between2: e∈[e1,e2].P[e] prop: so_lambda: λ2x.t[x] so_apply: x[s] alle-le: e≤e'.P[e] subtype_rel: A ⊆B alle-at: e@i.P[e] decidable: Dec(P) or: P ∨ Q guard: {T} not: ¬A false: False

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



Date html generated: 2016_05_16-AM-09_44_55
Last ObjectModification: 2015_12_28-PM-09_40_32

Theory : new!event-ordering


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