{ [A,B:Type]. [f:A  bag(B)].  (MapFilterComb(A;B;f)  CombinatorDef) }

{ Proof }



Definitions occuring in Statement :  MapFilterComb: MapFilterComb(A;B;f) combinator-def: CombinatorDef uall: [x:A]. B[x] member: t  T function: x:A  B[x] universe: Type bag: bag(T)
Definitions :  bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o} void: Void fpf-sub: f  g squash: T sq_stable: SqStable(P) top: Top true: True fpf-cap: f(x)?z filter: filter(P;l) IdLnk: IdLnk Id: Id rationals: append: as @ bs locl: locl(a) Knd: Knd false: False lt_int: i <z j le_int: i z j limited-type: LimitedType bfalse: ff btrue: tt eq_atom: x =a y null: null(as) set_blt: a < b grp_blt: a < b infix_ap: x f y dcdr-to-bool: [d] bl-all: (xL.P[x])_b bl-exists: (xL.P[x])_b b-exists: (i<n.P[i])_b eq_type: eq_type(T;T') eq_atom: eq_atom$n(x;y) qeq: qeq(r;s) q_less: q_less(r;s) q_le: q_le(r;s) deq-member: deq-member(eq;x;L) deq-disjoint: deq-disjoint(eq;as;bs) deq-all-disjoint: deq-all-disjoint(eq;ass;bs) eq_id: a = b eq_lnk: a = b es-eq-E: e = e' es-bless: e <loc e' es-ble: e loc e' bimplies: p  q band: p  q bor: p q bnot: b unit: Unit bool: so_apply: x[s] implies: P  Q union: left + right or: P  Q guard: {T} l_member: (x  l) assert: b es-E-interface: E(X) sq_type: SQType(T) permutation: permutation(T;L1;L2) list: type List real: grp_car: |g| int: quotient: x,y:A//B[x; y] subtype: S  T suptype: suptype(S; T) eclass: EClass(A[eo; e]) pair: <a, b> fpf: a:A fp-B[a] strong-subtype: strong-subtype(A;B) le: A  B ge: i  j  not: A less_than: a < b uimplies: b supposing a product: x:A  B[x] and: P  Q uiff: uiff(P;Q) natural_number: $n apply: f a nat: ifthenelse: if b then t else f fi  empty-bag: {} bag-only: only(bs) eq_int: (i = j) bag-size: bag-size(bs) prop: subtype_rel: A r B set: {x:A| B[x]}  lambda: x.A[x] so_lambda: x.t[x] SimpleComb1: SimpleComb1(T1.P1[T1];T.F[T];a.H[a]) all: x:A. B[x] bag: bag(T) combinator-def: CombinatorDef MapFilterComb: MapFilterComb(A;B;f) function: x:A  B[x] axiom: Ax universe: Type isect: x:A. B[x] member: t  T equal: s = t uall: [x:A]. B[x]
Lemmas :  bag_wf member_wf subtype_rel_wf SimpleComb1_wf ifthenelse_wf eq_int_wf bag-size_wf nat_wf bag-only_wf empty-bag_wf permutation_wf subtype_base_sq bool_wf uiff_transitivity eqtt_to_assert assert_of_eq_int assert_wf not_wf eqff_to_assert assert_of_bnot not_functionality_wrt_uiff bnot_wf subtype_rel_bag sq_stable__subtype_rel

\mforall{}[A,B:Type].  \mforall{}[f:A  {}\mrightarrow{}  bag(B)].    (MapFilterComb(A;B;f)  \mmember{}  CombinatorDef)


Date html generated: 2011_08_17-PM-06_27_28
Last ObjectModification: 2011_06_18-AM-11_50_12

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