Nuprl Lemma : rec-comb_wf2
[Info:Type]. [n,m:
]. [A:{m..n
} 
Type]. [X:i:{m..n} EClass(A i)]. [T:Type]. [f:Id
i:{m..n} bag(A i)
bag(T)
bag(T)].
[init:Id bag(T)].
(rec-comb(X;f;init) 
EClass(T))
Proof not projected
Definitions occuring in Statement :
rec-comb: rec-comb(X;f;init),
eclass: EClass(A[eo; e]),
Id: Id,
int_seg: {i..j},
nat: ,
uall: [x:A]. B[x],
member: t T,
apply: f a,
function: x:A B[x],
universe: Type,
bag: bag(T)
Definitions :
uall: [x:A]. B[x],
nat: ,
eclass: EClass(A[eo; e]),
member: t T,
rec-comb: rec-comb(X;f;init),
top: Top,
ycomb: Y,
primed-class-opt: Prior(X)?b,
all: x:A. B[x],
implies: P 
Q,
ge: i 
j ,
le: A 
B,
not: 
A,
false: False,
squash: 
T,
true: True,
sq_exists: 
x:{A| B[x]},
and: P 
Q,
so_lambda: 
x y.t[x; y],
strongwellfounded: SWellFounded(R[x; y]),
exists: x:A. B[x],
prop: 
,
or: P 
Q,
so_apply: x[s1;s2],
es-locl: (e <loc e'),
subtype: S 
T,
guard: {T}
Lemmas :
top_wf,
es-causl-swellfnd,
event-ordering+_inc,
nat_properties,
ge_wf,
less_than_wf,
nat_wf,
le_wf,
es-causl_wf,
es-local-pred_wf2,
lt_int_wf,
bag-size_wf,
es-locl_wf,
equal_wf,
es-E_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
int_seg_wf,
eclass_wf
\mforall{}[Info:Type]. \mforall{}[n,m:\mBbbN{}]. \mforall{}[A:\{m..n\msupminus{}\} {}\mrightarrow{} Type]. \mforall{}[X:i:\{m..n\msupminus{}\} {}\mrightarrow{} EClass(A i)]. \mforall{}[T:Type].
\mforall{}[f:Id {}\mrightarrow{} i:\{m..n\msupminus{}\} {}\mrightarrow{} bag(A i) {}\mrightarrow{} bag(T) {}\mrightarrow{} bag(T)]. \mforall{}[init:Id {}\mrightarrow{} bag(T)].
(rec-comb(X;f;init) \mmember{} EClass(T))
Date html generated:
2012_01_23-PM-12_26_41
Last ObjectModification:
2011_12_19-PM-04_53_29
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