{ [B:Type]. [n:]. [m:n + 1]. [A:n  Type]. [bags:k:n  bag(A k)].
  [g:funtype(n - m;x.(A (x + m));B)].
    (lifting-gen-list-rev(n;bags) m g  bag(B)) }

{ Proof }



Definitions occuring in Statement :  lifting-gen-list-rev: lifting-gen-list-rev(n;bags) int_seg: {i..j} nat: uall: [x:A]. B[x] member: t  T apply: f a lambda: x.A[x] function: x:A  B[x] subtract: n - m add: n + m natural_number: $n universe: Type bag: bag(T) funtype: funtype(n;A;T)
Definitions :  apply: f a funtype: funtype(n;A;T) universe: Type prop: bag: bag(T) member: t  T so_lambda: x.t[x] uall: [x:A]. B[x] isect: x:A. B[x] int_seg: {i..j} function: x:A  B[x] lifting-gen-list-rev: Error :lifting-gen-list-rev,  axiom: Ax lambda: x.A[x] add: n + m bool: natural_number: $n set: {x:A| B[x]}  all: x:A. B[x] subtype: S  T rationals: real: le: A  B not: A false: False implies: P  Q void: Void less_than: a < b minus: -n lelt: i  j < k and: P  Q subtype_rel: A r B uiff: uiff(P;Q) product: x:A  B[x] uimplies: b supposing a ge: i  j  strong-subtype: strong-subtype(A;B) grp_car: |g| limited-type: LimitedType subtract: n - m int: equal: s = t nat: exists: x:A. B[x] sq_type: SQType(T) guard: {T} iff: P  Q rev_implies: P  Q label: ...$L... t sqequal: s ~ t ycomb: Y top: Top union: left + right unit: Unit bnot: b assert: b eq_int: (i = j) bor: p q band: p  q bimplies: p  q es-ble: e loc e' es-bless: e <loc e' es-eq-E: e = e' eq_lnk: a = b eq_id: a = b name_eq: name_eq(x;y) deq-all-disjoint: deq-all-disjoint(eq;ass;bs) deq-disjoint: deq-disjoint(eq;as;bs) deq-member: deq-member(eq;x;L) q_le: q_le(r;s) q_less: q_less(r;s) qeq: qeq(r;s) eq_atom: eq_atom$n(x;y) eq_type: eq_type(T;T') b-exists: (i<n.P[i])_b bl-exists: (xL.P[x])_b bl-all: (xL.P[x])_b dcdr-to-bool: [d] infix_ap: x f y grp_blt: a < b set_blt: a < b null: null(as) eq_atom: x =a y btrue: tt bfalse: ff le_int: i z j lt_int: i <z j single-bag: {x} primrec: primrec(n;b;c) fpf: a:A fp-B[a] eclass: EClass(A[eo; e]) bag-combine: xbs.f[x] intensional-universe: IType l_member: (x  l) or: P  Q so_apply: x[s] ifthenelse: if b then t else f fi  fpf-cap: f(x)?z pair: <a, b> squash: T true: True
Lemmas :  squash_wf true_wf subtype_rel-equal primrec_wf bool_subtype_base bool_cases intensional-universe_wf bag-combine_wf single-bag_wf eq_int_wf bnot_wf not_functionality_wrt_uiff assert_of_bnot eqff_to_assert assert_wf assert_of_eq_int eqtt_to_assert uiff_transitivity bool_wf ycomb-unroll ge_wf subtype_rel_wf nat_ind_tp rev_implies_wf iff_wf int_subtype_base subtype_base_sq uall_wf bag_wf funtype_wf nat_properties int_seg_properties int_seg_wf nat_wf member_wf le_wf not_wf false_wf

\mforall{}[B:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[m:\mBbbN{}n  +  1].  \mforall{}[A:\mBbbN{}n  {}\mrightarrow{}  Type].  \mforall{}[bags:k:\mBbbN{}n  {}\mrightarrow{}  bag(A  k)].
\mforall{}[g:funtype(n  -  m;\mlambda{}x.(A  (x  +  m));B)].
    (lifting-gen-list-rev(n;bags)  m  g  \mmember{}  bag(B))


Date html generated: 2011_08_17-PM-05_58_18
Last ObjectModification: 2011_06_22-AM-11_30_21

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