Nuprl Lemma : assert-member-eclass
[Info,T:Type]. [X:EClass(T)]. [es:EO+(Info)]. [e:E]. (
member-eclass(es;e;X) 
v:T. v 
X(e))
Proof not projected
Definitions occuring in Statement :
member-eclass: member-eclass(es;e;X),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
uall: [x:A]. B[x],
exists: x:A. B[x],
iff: P Q,
squash: T,
universe: Type
Definitions :
guard: {T},
so_lambda: 
x y.t[x; y],
all: x:A. B[x],
top: Top,
false: False,
rev_implies: P Q,
implies: P Q,
and: P 
Q,
so_lambda: x.t[x],
not: 
A,
member: t T,
classrel: v X(e),
exists: x:A. B[x],
member-eclass: member-eclass(es;e;X),
iff: P Q,
eclass: EClass(A[eo; e]),
so_apply: x[s1;s2],
uimplies: b supposing a,
so_apply: x[s],
nat: 
,
uall: [x:A]. B[x],
prop: 
,
subtype: S 
T
Lemmas :
bag-member-iff-size,
assert_of_eq_int,
not_functionality_wrt_uiff,
assert_of_bnot,
uiff_transitivity,
iff_weakening_uiff,
iff_functionality_wrt_iff,
eclass_wf,
classrel_wf,
top_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
dep-eclass_subtype_rel,
member-eclass_wf,
less_than_wf,
bag-member_wf,
exists_wf,
squash_wf,
equal_wf,
not_wf,
nat_wf,
bag-size_wf,
eq_int_wf,
bnot_wf,
assert_wf
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(\muparrow{}member-eclass(es;e;X) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}v:T. v \mmember{} X(e))
Date html generated:
2012_01_23-PM-12_22_33
Last ObjectModification:
2011_12_13-PM-12_56_21
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