Nuprl Lemma : fpf-restrict_wf

[A:Type]. [B:A  Type]. [f:x:A fp-B[x]]. [P:A  ].  (fpf-restrict(f;P)  x:{x:A| (P x)}  fp-B[x])


Proof not projected




Definitions occuring in Statement :  fpf-restrict: fpf-restrict(f;P) 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] universe: Type
Definitions :  so_lambda: x.t[x] pi1: fst(t) pi2: snd(t) fpf-domain: fpf-domain(f) mk_fpf: mk_fpf(L;f) fpf-restrict: fpf-restrict(f;P) member: t  T so_apply: x[s] fpf: a:A fp-B[a] uall: [x:A]. B[x] prop: all: x:A. B[x] uimplies: b supposing a implies: P  Q and: P  Q iff: P  Q
Lemmas :  fpf_wf bool_wf l_member_wf assert_wf filter_type subtype_rel_self subtype_rel_dep_function l_member-settype member_filter

\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[f:x:A  fp->  B[x]].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbB{}].
    (fpf-restrict(f;P)  \mmember{}  x:\{x:A|  \muparrow{}(P  x)\}    fp->  B[x])


Date html generated: 2012_01_23-AM-11_55_59
Last ObjectModification: 2011_12_10-PM-12_50_09

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