Nuprl Lemma : first-in-eclass_wf
[T:Type]. [X:EClass(Top)]. [es:EO+(T)]. [e:E]. (first-in-eclass(es;e;X) 
)
Proof not projected
Definitions occuring in Statement :
first-in-eclass: first-in-eclass(es;e;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
bool: ,
uall: [x:A]. B[x],
top: Top,
member: t T,
universe: Type
Definitions :
void: Void,
uimplies: b supposing a,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
es-E-interface: E(X),
es-prior-interface: prior(X),
in-eclass: e 
X,
member-eclass: member-eclass(es;e;X),
band: p 
q,
set: {x:A| B[x]} ,
assert: 
b,
lambda: 
x.A[x],
bnot: 
b,
bfalse: ff,
btrue: tt,
subtype: S 
T,
subtype_rel: A r B,
atom: Atom,
apply: f a,
es-base-E: es-base-E(es),
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
all: x:A. B[x],
bag: bag(T),
function: x:A 
B[x],
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
top: Top,
universe: Type,
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
uall: [x:A]. B[x],
event-ordering+: EO+(Info),
event_ordering: EO,
es-E: E,
isect: 
x:A. B[x],
axiom: Ax,
bool: ,
first-in-eclass: first-in-eclass(es;e;X),
member: t T,
equal: s = t
Lemmas :
subtype_rel_wf,
es-E-interface_wf,
top_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-base-E_wf,
es-E_wf,
es-prior-interface_wf,
es-interface-subtype_rel2,
member_wf,
eclass_wf,
es-prior-interface_wf1,
es-prior-interface_wf0,
in-eclass_wf,
bnot_wf,
member-eclass_wf,
band_wf
\mforall{}[T:Type]. \mforall{}[X:EClass(Top)]. \mforall{}[es:EO+(T)]. \mforall{}[e:E]. (first-in-eclass(es;e;X) \mmember{} \mBbbB{})
Date html generated:
2011_10_21-AM-00_01_00
Last ObjectModification:
2011_05_20-AM-11_06_22
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