{ [A:Type]. [eq:EqDecider(A)]. [B:A  Type]. [P:A  ].
  [f:x:A fp-B[x]].
    (fpf-vals(eq;P;f)  (x:{a:A| (P a)}   B[x]) List) }

{ Proof }



Definitions occuring in Statement :  fpf-vals: fpf-vals(eq;P;f) fpf: a:A fp-B[a] assert: b bool: uall: [x:A]. B[x] so_apply: x[s] member: t  T set: {x:A| B[x]}  apply: f a function: x:A  B[x] product: x:A  B[x] list: type List universe: Type deq: EqDecider(T)
Definitions :  so_lambda: x.t[x] pi2: snd(t) pi1: fst(t) let: let fpf-vals: fpf-vals(eq;P;f) member: t  T so_apply: x[s] uall: [x:A]. B[x] bfalse: ff btrue: tt implies: P  Q all: x:A. B[x] ifthenelse: if b then t else f fi  prop: ycomb: Y reduce: reduce(f;k;as) map: map(f;as) filter: filter(P;l) zip: zip(as;bs) fpf: a:A fp-B[a] and: P  Q iff: P  Q unit: Unit bool: it:
Lemmas :  deq_wf bool_wf fpf_wf assert_of_bnot eqff_to_assert uiff_transitivity eqtt_to_assert iff_weakening_uiff bnot_wf not_wf assert_wf

\mforall{}[A:Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[f:x:A  fp->  B[x]].
    (fpf-vals(eq;P;f)  \mmember{}  (x:\{a:A|  \muparrow{}(P  a)\}    \mtimes{}  B[x])  List)


Date html generated: 2011_08_10-AM-08_03_18
Last ObjectModification: 2011_06_18-AM-08_21_01

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