Nuprl Lemma : num-antecedents-property
[Info:Type]. [es:EO+(Info)]. [Sys:EClass(Top)]. [f:sys-antecedent(es;Sys)]. [e:E(Sys)].
{((f (f^#f(e) e)) = (f^#f(e) e)) 
([i:
#f(e)]. (
((f (f^i e)) = (f^i e))))}
Proof not projected
Definitions occuring in Statement :
num-antecedents: #f(e),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
int_seg: {i..j
},
uall: [x:A]. B[x],
top: Top,
guard: {T},
not: A,
and: P Q,
apply: f a,
natural_number: $n,
universe: Type,
equal: s = t,
fun_exp: f^n
Definitions :
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
le: A 
B,
ge: i 
j ,
so_lambda: 
x y.t[x; y],
false: False,
not: A,
and: P Q,
uall: [x:A]. B[x],
ycomb: Y,
prop: 
,
implies: P 
Q,
nat: ,
member: t 
T,
all: x:A. B[x],
num-antecedents: #f(e),
guard: {T},
es-E-interface: E(X),
so_lambda: x.t[x],
sys-antecedent: sys-antecedent(es;Sys),
label: ...$L... t,
eq_int: (i =
j),
primrec: primrec(n;b;c),
fun_exp: f^n,
uiff: uiff(P;Q),
uimplies: b supposing a,
unit: Unit,
bool: 
,
so_apply: x[s1;s2],
lelt: i j < k,
exists: 
x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
int_seg: {i..j},
cand: A c B,
so_apply: x[s],
sq_type: SQType(T),
or: P 
Q,
decidable: Dec(P),
it: 
,
subtype: S 
T
Lemmas :
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
assert-es-eq-E-2,
eqtt_to_assert,
uiff_transitivity,
ge_wf,
nat_properties,
event-ordering+_wf,
top_wf,
eclass_wf,
sys-antecedent_wf,
num-antecedents_wf,
int_seg_wf,
fun_exp_wf,
not_wf,
bnot_wf,
equal_wf,
bool_wf,
in-eclass_wf,
assert_wf,
es-E_wf,
es-eq-E_wf,
es-causl_wf,
less_than_wf,
es-E-interface_wf,
le_wf,
nat_wf,
event-ordering+_inc,
es-causl-swellfnd,
es-causle_wf,
all_wf,
int_subtype_base,
subtype_base_sq,
decidable__equal_int
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[Sys:EClass(Top)]. \mforall{}[f:sys-antecedent(es;Sys)]. \mforall{}[e:E(Sys)].
\{((f (f\^{}\#f(e) e)) = (f\^{}\#f(e) e)) \mwedge{} (\mforall{}[i:\mBbbN{}\#f(e)]. (\mneg{}((f (f\^{}i e)) = (f\^{}i e))))\}
Date html generated:
2012_01_23-PM-12_23_44
Last ObjectModification:
2011_12_13-AM-10_35_06
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