Nuprl Lemma : sys-antecedent-filter-image
[Info,A,B:Type]. [g:A 
bag(B)]. [es:EO+(Info)]. [X:EClass(A)]. [f:sys-antecedent(es;X)].
f 
sys-antecedent(es;g[X]) supposing a:E(X). ((
((f a) = a)) 
(bag-size(g X(a)) = 1) (bag-size(g X(f a)) = 1))
Proof not projected
Definitions occuring in Statement :
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
es-filter-image: f[X],
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
not: A,
implies: P Q,
member: t T,
apply: f a,
function: x:A B[x],
natural_number: $n,
int: 
,
universe: Type,
equal: s = t,
bag-size: bag-size(bs),
bag: bag(T)
Definitions :
true: True,
ifthenelse: if b then t else f fi ,
btrue: tt,
so_lambda: 
x y.t[x; y],
assert: 
b,
so_lambda: x.t[x],
prop: 
,
member: t T,
implies: P Q,
all: x:A. B[x],
uimplies: b supposing a,
uall: [x:A]. B[x],
suptype: suptype(S; T),
subtype: S 
T,
top: Top,
sys-antecedent: sys-antecedent(es;Sys),
guard: {T},
sq_type: SQType(T),
so_apply: x[s1;s2],
so_apply: x[s],
es-E-interface: E(X)
Lemmas :
in-eclass_wf,
assert_elim,
bag_wf,
eclass_wf,
sys-antecedent_wf,
es-interface-val_wf2,
nat_wf,
bool_subtype_base,
subtype_base_sq,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
eclass-val_wf,
bag-size_wf,
equal_wf,
not_wf,
es-interface-top,
es-E-interface_wf,
all_wf,
es-E-interface-subtype_rel,
es-causle_wf,
top_wf,
subtype_rel_bag,
es-filter-image_wf
\mforall{}[Info,A,B:Type]. \mforall{}[g:A {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(A)]. \mforall{}[f:sys-antecedent(es;X)].
f \mmember{} sys-antecedent(es;g[X])
supposing \mforall{}a:E(X). ((\mneg{}((f a) = a)) {}\mRightarrow{} (bag-size(g X(a)) = 1) {}\mRightarrow{} (bag-size(g X(f a)) = 1))
Date html generated:
2012_01_23-PM-12_29_50
Last ObjectModification:
2011_12_13-PM-02_59_27
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