Nuprl Lemma : fpf-join-list-ap-disjoint

[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[L:a:A fp-> B[a] List]. ∀[x:A].
  (∀[f:a:A fp-> B[a]]. (⊕(L)(x) f(x) ∈ B[x]) supposing ((↑x ∈ dom(f)) and (f ∈ L))) supposing 
     ((∀f,g∈L.  ∀x:A. ((↑x ∈ dom(f)) ∧ (↑x ∈ dom(g))))) and 
     (↑x ∈ dom(⊕(L))))


Definitions occuring in Statement :  fpf-join-list: (L) fpf-ap: f(x) fpf-dom: x ∈ dom(f) fpf: a:A fp-> B[a] deq: EqDecider(T) pairwise: (∀x,y∈L.  P[x; y]) l_member: (x ∈ l) list: List assert: b uimplies: supposing a uall: [x:A]. B[x] so_apply: x[s] all: x:A. B[x] not: ¬A and: P ∧ Q function: x:A ─→ B[x] universe: Type equal: t ∈ T
Lemmas :  fpf-join-list-ap assert_wf fpf-dom_wf subtype-fpf2 top_wf subtype_top l_member_wf fpf_wf pairwise_wf2 all_wf not_wf fpf-join-list_wf subtype_rel_list list_wf equal_wf fpf-ap_wf decidable__lt deq_wf true_wf squash_wf assert_functionality_wrt_uiff length_wf lelt_wf le_weakening less_than_transitivity2 sq_stable__le less_than_wf le_wf select_wf
\mforall{}[A:Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[L:a:A  fp->  B[a]  List].  \mforall{}[x:A].
    (\mforall{}[f:a:A  fp->  B[a]].  (\moplus{}(L)(x)  =  f(x))  supposing  ((\muparrow{}x  \mmember{}  dom(f))  and  (f  \mmember{}  L)))  supposing 
          ((\mforall{}f,g\mmember{}L.    \mforall{}x:A.  (\mneg{}((\muparrow{}x  \mmember{}  dom(f))  \mwedge{}  (\muparrow{}x  \mmember{}  dom(g)))))  and 
          (\muparrow{}x  \mmember{}  dom(\moplus{}(L))))

Date html generated: 2015_07_17-AM-09_21_17
Last ObjectModification: 2015_07_16-AM-09_51_28

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