Nuprl Lemma : fpf-join-list-ap2

[A:Type]
  ∀eq:EqDecider(A)
    ∀[B:A ─→ Type]
      ∀L:a:A fp-> B[a] List. ∀x:A.  ((x ∈ fpf-domain(⊕(L)))  (∃f∈L. (↑x ∈ dom(f)) ∧ (⊕(L)(x) f(x) ∈ B[x])))


Proof




Definitions occuring in Statement :  fpf-join-list: (L) fpf-ap: f(x) fpf-domain: fpf-domain(f) fpf-dom: x ∈ dom(f) fpf: a:A fp-> B[a] deq: EqDecider(T) l_exists: (∃x∈L. P[x]) l_member: (x ∈ l) list: List assert: b uall: [x:A]. B[x] so_apply: x[s] all: x:A. B[x] implies:  Q and: P ∧ Q function: x:A ─→ B[x] universe: Type equal: t ∈ T
Lemmas :  fpf-join-list-ap list_wf fpf_wf deq_wf l_member_wf fpf-domain_wf fpf-join-list_wf top_wf subtype_rel_list subtype-fpf2 subtype_top member-fpf-domain
\mforall{}[A:Type]
    \mforall{}eq:EqDecider(A)
        \mforall{}[B:A  {}\mrightarrow{}  Type]
            \mforall{}L:a:A  fp->  B[a]  List.  \mforall{}x:A.
                ((x  \mmember{}  fpf-domain(\moplus{}(L)))  {}\mRightarrow{}  (\mexists{}f\mmember{}L.  (\muparrow{}x  \mmember{}  dom(f))  \mwedge{}  (\moplus{}(L)(x)  =  f(x))))



Date html generated: 2015_07_17-AM-09_21_13
Last ObjectModification: 2015_01_28-AM-07_46_54

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