Nuprl Lemma : simple-comb-2-classrel
[Info,A,B,C:Type]. [f:A 
B C]. [X:EClass(A)]. [Y:EClass(B)]. [es:EO+(Info)]. [e:E]. [v:C].
uiff(v 
lifting-2(f)|X, Y|(e);
a:A. b:B. ((v = (f a b)) 
b Y(e) a X(e)))
Proof not projected
Definitions occuring in Statement :
simple-comb-2: F|X, Y|,
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
exists: x:A. B[x],
squash: T,
and: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t,
lifting-2: lifting-2(f)
Definitions :
uall: [x:A]. B[x],
so_lambda: 
x y.t[x; y],
so_lambda: x.t[x],
bag-member: x bs,
true: True,
uimplies: b supposing a,
member: t T,
and: P Q,
squash: T,
lifting-2: lifting-2(f),
simple-comb-2: F|X, Y|,
classrel: v X(e),
uiff: uiff(P;Q),
cand: A c B,
prop: 
,
exists: x:A. B[x],
btrue: tt,
bfalse: ff,
lt_int: i <z j,
bnot: 
b,
le_int: i 
z j,
ifthenelse: if b then t else f fi ,
ycomb: Y,
label: ...$L... t,
ge: i 
j ,
lelt: i j < k,
length: ||as||,
false: False,
implies: P 
Q,
not: A,
le: A B,
int_seg: {i..j
},
nat: 
,
select: l[i],
so_apply: x[s1;s2],
all: x:A. B[x],
so_apply: x[s],
simple-comb2: x,y.F[x; y]|X;Y|,
guard: {T},
sq_type: SQType(T),
or: P 
Q,
decidable: Dec(P),
subtype: S 
T
Lemmas :
eclass_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
equal_wf,
and_wf,
exists_wf,
squash_wf,
classrel_wf,
simple-comb2-classrel,
bag_wf,
lelt_wf,
lifting2_wf,
int_subtype_base,
subtype_base_sq,
decidable__equal_int,
int_seg_wf,
length_wf_nat,
non_neg_length,
length_cons,
length_wf_nil,
length_nil,
length_wf,
select_wf,
le_wf,
simple-comb_wf
\mforall{}[Info,A,B,C:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[v:C].
uiff(v \mmember{} lifting-2(f)|X, Y|(e);\mdownarrow{}\mexists{}a:A. \mexists{}b:B. ((v = (f a b)) \mwedge{} b \mmember{} Y(e) \mwedge{} a \mmember{} X(e)))
Date html generated:
2012_01_23-PM-01_11_42
Last ObjectModification:
2011_12_14-AM-00_31_24
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