Nuprl Lemma : es-interface-history-pred

[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A List)]. ∀[e:E].
  es-interface-history(es;X;e)
  if e ∈b then es-interface-history(es;X;pred(e)) X(e) else es-interface-history(es;X;pred(e)) fi 
  ∈ (A List) 
  supposing ¬↑first(e)


Proof




Definitions occuring in Statement :  es-interface-history: es-interface-history(es;X;e) eclass-val: X(e) in-eclass: e ∈b X eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-first: first(e) es-pred: pred(e) es-E: E append: as bs list: List assert: b ifthenelse: if then else fi  uimplies: supposing a uall: [x:A]. B[x] not: ¬A universe: Type equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a es-interface-history: es-interface-history(es;X;e) es-le-before: loc(e) top: Top prop: subtype_rel: A ⊆B so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] es-before: before(e) not: ¬A implies:  Q false: False all: x:A. B[x] bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) and: P ∧ Q ifthenelse: if then else fi  bfalse: ff mapfilter: mapfilter(f;P;L) concat: concat(ll) squash: T in-eclass: e ∈b X eq_int: (i =z j) bag-size: #(bs) length: ||as|| list_ind: list_ind es-E-interface: E(X) true: True

Latex:
\mforall{}[Info:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[A:Type].  \mforall{}[X:EClass(A  List)].  \mforall{}[e:E].
    es-interface-history(es;X;e)
    =  if  e  \mmember{}\msubb{}  X
        then  es-interface-history(es;X;pred(e))  @  X(e)
        else  es-interface-history(es;X;pred(e))
        fi   
    supposing  \mneg{}\muparrow{}first(e)



Date html generated: 2016_05_16-PM-10_59_59
Last ObjectModification: 2016_01_17-PM-07_17_44

Theory : event-ordering


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