Nuprl Lemma : sys-antecedent-fixedpoint
∀[Info:Type]
∀es:EO+(Info). ∀Sys:EClass(Top). ∀f:sys-antecedent(es;Sys). ∀e:E(Sys).
∃n:ℕ. (((f (f^n e)) = (f^n e) ∈ E(Sys)) ∧ ¬((f (f^n - 1 e)) = (f^n - 1 e) ∈ E(Sys)) supposing 0 < n)
Proof
Definitions occuring in Statement :
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,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
apply: f a,
subtract: n - m,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Lemmas :
num-antecedents-property,
num-antecedents_wf,
all_wf,
es-E-interface_wf,
es-causle_wf,
event-ordering+_subtype,
equal_wf,
fun_exp_wf,
subtract_wf,
decidable__le,
false_wf,
not-le-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,
le_wf,
less_than_wf,
not_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_wf,
subtract-is-less,
lelt_wf
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}Sys:EClass(Top). \mforall{}f:sys-antecedent(es;Sys). \mforall{}e:E(Sys).
\mexists{}n:\mBbbN{}. (((f (f\^{}n e)) = (f\^{}n e)) \mwedge{} \mneg{}((f (f\^{}n - 1 e)) = (f\^{}n - 1 e)) supposing 0 < n)
Date html generated:
2015_07_17-PM-00_55_15
Last ObjectModification:
2015_01_27-PM-10_49_47
Home
Index