Nuprl Lemma : num-antecedents-fun_exp
[Info:Type]. [es:EO+(Info)]. [Sys:EClass(Top)]. [f:sys-antecedent(es;Sys)]. [n:
]. [e:E(Sys)].
#f(f^n e) = (#f(e) - n) supposing n 
#f(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),
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
le: A B,
apply: f a,
subtract: n - m,
int: 
,
universe: Type,
equal: s = t,
fun_exp: f^n
Definitions :
uall: [x:A]. B[x],
es-E-interface: E(X),
uimplies: b supposing a,
num-antecedents: #f(e),
fun_exp: f^n,
member: t 
T,
prop: 
,
so_lambda: 
x y.t[x; y],
primrec: primrec(n;b;c),
ycomb: Y,
ifthenelse: if b then t else f fi ,
eq_int: (i =
j),
btrue: tt,
implies: P 
Q,
le: A B,
not: 
A,
false: False,
ge: i 
j ,
all: x:A. B[x],
bfalse: ff,
guard: {T},
squash: 
T,
true: True,
top: Top,
compose: f o g,
nat: ,
so_apply: x[s1;s2],
bool: 
,
unit: Unit,
uiff: uiff(P;Q),
and: P 
Q,
sys-antecedent: sys-antecedent(es;Sys),
subtype: S 
T,
it: 
Lemmas :
nat_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
le_wf,
num-antecedents_wf,
es-E-interface_wf,
es-eq-E_wf,
assert_wf,
in-eclass_wf,
bool_wf,
equal_wf,
bnot_wf,
not_wf,
nat_properties,
ge_wf,
uiff_transitivity,
eqtt_to_assert,
assert-es-eq-E-2,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
squash_wf,
true_wf,
fun_exp_add_sq,
fun_exp_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[Sys:EClass(Top)]. \mforall{}[f:sys-antecedent(es;Sys)]. \mforall{}[n:\mBbbN{}]. \mforall{}[e:E(Sys)].
\#f(f\^{}n e) = (\#f(e) - n) supposing n \mleq{} \#f(e)
Date html generated:
2012_01_23-PM-12_23_53
Last ObjectModification:
2011_12_31-AM-11_10_27
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