Nuprl Lemma : SM-gen-class_wf

[Info,S:Type]. [n:]. [m:{1..n + 1}]. [A:k:{m..n + 1}  Type].
[trXs:k:{m..n + 1}  (Id  A k  S  S  EClass(A k))]. [init:Id  bag(S)].
  (SM-gen-class(init;n;m;trXs)  EClass(S))


Proof not projected




Definitions occuring in Statement :  SM-gen-class: SM-gen-class(init;n;m;trXs) eclass: EClass(A[eo; e]) Id: Id int_seg: {i..j} nat_plus: uall: [x:A]. B[x] member: t  T apply: f a function: x:A  B[x] product: x:A  B[x] add: n + m natural_number: $n universe: Type bag: bag(T)
Definitions :  uall: [x:A]. B[x] member: t  T SM-gen-class: SM-gen-class(init;n;m;trXs) nat: le: A  B not: A implies: P  Q false: False so_lambda: x.t[x] so_lambda: x y.t[x; y] all: x:A. B[x] subtype: S  T top: Top nat_plus: int_seg: {i..j} lelt: i  j < k and: P  Q prop: so_apply: x[s] so_apply: x[s1;s2]
Lemmas :  rec-comb_wf2 le_wf pi2_wf Id_wf eclass_wf es-E_wf event-ordering+_inc event-ordering+_wf int_seg_wf SM-gen-tr_wf pi1_wf_top bag_wf nat_plus_wf

\mforall{}[Info,S:Type].  \mforall{}[n:\mBbbN{}\msupplus{}].  \mforall{}[m:\{1..n  +  1\msupminus{}\}].  \mforall{}[A:k:\{m..n  +  1\msupminus{}\}  {}\mrightarrow{}  Type].
\mforall{}[trXs:k:\{m..n  +  1\msupminus{}\}  {}\mrightarrow{}  (Id  {}\mrightarrow{}  A  k  {}\mrightarrow{}  S  {}\mrightarrow{}  S  \mtimes{}  EClass(A  k))].  \mforall{}[init:Id  {}\mrightarrow{}  bag(S)].
    (SM-gen-class(init;n;m;trXs)  \mmember{}  EClass(S))


Date html generated: 2012_01_23-PM-01_06_46
Last ObjectModification: 2011_12_30-PM-08_24_24

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