{ [A:Type]
    eq:EqDecider(A)
      [B:A  Type]
        L:a:A fp-B[a] List. x:A.
          (fL. (x  dom(f))  ((L)(x) = f(x))) supposing x  dom((L)) }

{ Proof }



Definitions occuring in Statement :  fpf-join-list: (L) fpf-ap: f(x) fpf-dom: x  dom(f) fpf: a:A fp-B[a] assert: b uimplies: b supposing a uall: [x:A]. B[x] so_apply: x[s] all: x:A. B[x] and: P  Q function: x:A  B[x] list: type List universe: Type equal: s = t l_exists: (xL. P[x]) deq: EqDecider(T)
Definitions :  uall: [x:A]. B[x] all: x:A. B[x] so_apply: x[s] uimplies: b supposing a assert: b fpf-dom: x  dom(f) fpf-join-list: (L) reduce: reduce(f;k;as) fpf-empty: deq-member: deq-member(eq;x;L) pi1: fst(t) bfalse: ff ifthenelse: if b then t else f fi  false: False member: t  T so_lambda: x.t[x] subtype: S  T and: P  Q prop: cand: A c B or: P  Q rev_implies: P  Q iff: P  Q implies: P  Q btrue: tt guard: {T} l_exists: (xL. P[x]) exists: x:A. B[x] true: True decidable: Dec(P) not: A bool: unit: Unit sq_type: SQType(T) it:
Lemmas :  false_wf assert_witness fpf-dom_wf fpf-join_wf top_wf fpf-trivial-subtype-top fpf-join-list_wf fpf_wf assert_wf deq_wf l_exists_cons fpf-ap_wf fpf-join-dom decidable__assert l_exists_wf l_member_wf fpf-join-ap bool_wf not_wf bnot_wf iff_weakening_uiff eqtt_to_assert uiff_transitivity eqff_to_assert assert_of_bnot not_assert_elim subtype_base_sq bool_subtype_base assert_elim

\mforall{}[A:Type]
    \mforall{}eq:EqDecider(A)
        \mforall{}[B:A  {}\mrightarrow{}  Type]
            \mforall{}L:a:A  fp->  B[a]  List.  \mforall{}x:A.
                (\mexists{}f\mmember{}L.  (\muparrow{}x  \mmember{}  dom(f))  \mwedge{}  (\moplus{}(L)(x)  =  f(x)))  supposing  \muparrow{}x  \mmember{}  dom(\moplus{}(L))


Date html generated: 2011_08_10-AM-08_01_13
Last ObjectModification: 2011_06_18-AM-08_19_53

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