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) ∈ E(Sys)) ∧ (∀[i:ℕ#f(e)]. (¬((f (f^i e)) = (f^i e) ∈ E(Sys))))}
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,
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 ∈ T
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
fun_exp_wf,
int_seg_wf,
num-antecedents_wf,
int_seg_subtype-nat,
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,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
es-eq-E_wf,
es-E-interface_wf,
bool_wf,
eqtt_to_assert,
assert-es-eq-E-2,
fun_exp0_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-E_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
sys-antecedent_wf,
eclass_wf,
top_wf,
event-ordering+_wf,
and_wf,
in-eclass_wf,
assert_elim,
assert_wf,
all_wf,
es-causle_wf,
uall_wf,
not_wf,
squash_wf,
sq_stable__and,
sq_stable__equal,
sq_stable__uall,
sq_stable__not,
int_subtype_base,
fun_exp1_lemma,
fun_exp_add_sq,
equal_functionality_wrt_subtype_rel2,
true_wf,
minus-zero,
fun_exp_add_apply1,
iff_weakening_equal
\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:
2015_07_17-PM-00_54_58
Last ObjectModification:
2015_02_04-PM-05_30_56
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