Nuprl Lemma : num-antecedents-fun_exp
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[Sys:EClass(Top)]. ∀[f:sys-antecedent(es;Sys)]. ∀[n:ℕ]. ∀[e:E(Sys)].
#f(f^n e) = (#f(e) - n) ∈ ℤ supposing n ≤ #f(e)
Proof
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),
fun_exp: f^n,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
le: A ≤ B,
apply: f a,
subtract: n - m,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
le_wf,
num-antecedents_wf,
es-E-interface_wf,
fun_exp0_lemma,
minus-zero,
add-zero,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel,
es-eq-E_wf,
event-ordering+_subtype,
bool_wf,
eqtt_to_assert,
assert-es-eq-E-2,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-E_wf,
nat_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
event-ordering+_wf,
not-le-2,
le_antisymmetry_iff,
squash_wf,
true_wf,
fun_exp1_lemma,
fun_exp_add_sq,
fun_exp_wf,
le_weakening2
\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:
2015_07_17-PM-00_55_07
Last ObjectModification:
2015_01_27-PM-10_49_15
Home
Index