Nuprl Lemma : eo-strict-forward-pred?

[Info:Type]. ∀[eo:EO+(Info)]. ∀[e:E].
  ∀e1:E. (es-pred?(eo>e;e1) if loc(e) loc(e1) ∧b (es-eq(eo) pred(e1) e) then inr ⋅  else es-pred?(eo;e1) fi  ∈ (E?))


Proof




Definitions occuring in Statement :  eo-strict-forward: eo>e event-ordering+: EO+(Info) es-pred?: es-pred?(es;e) es-pred: pred(e) es-eq: es-eq(es) es-loc: loc(e) es-E: E eq_id: b band: p ∧b q ifthenelse: if then else fi  it: uall: [x:A]. B[x] all: x:A. B[x] unit: Unit apply: a inr: inr  union: left right universe: Type equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T all: x:A. B[x] subtype_rel: A ⊆B implies:  Q top: Top prop: and: P ∧ Q uimplies: supposing a not: ¬A false: False so_lambda: λ2x.t[x] or: P ∨ Q so_apply: x[s] decidable: Dec(P) guard: {T} es-locl: (e <loc e') exposed-bfalse: exposed-bfalse bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) band: p ∧b q ifthenelse: if then else fi  deq: EqDecider(T) bfalse: ff iff: ⇐⇒ Q rev_implies:  Q label: ...$L... t exists: x:A. B[x] sq_type: SQType(T) bnot: ¬bb assert: b es-eq-E: e'

Latex:
\mforall{}[Info:Type].  \mforall{}[eo:EO+(Info)].  \mforall{}[e:E].
    \mforall{}e1:E
        (es-pred?(eo>e;e1)
        =  if  loc(e)  =  loc(e1)  \mwedge{}\msubb{}  (es-eq(eo)  pred(e1)  e)  then  inr  \mcdot{}    else  es-pred?(eo;e1)  fi  )



Date html generated: 2016_05_16-PM-01_17_41
Last ObjectModification: 2015_12_29-PM-02_05_01

Theory : event-ordering


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