Nuprl Lemma : es-fix-fun-exp
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X). ∀e:E(X). (↓∃n:ℕ. (f**(e) = (f^n e) ∈ E(X)))
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),
es-fix: f**(e),
fun_exp: f^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
apply: f a,
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,
int_seg_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-fix-cases,
es-eq-E_wf,
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,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-E-interface_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
event-ordering+_wf,
fun_exp0_lemma,
fun_exp_wf,
fun_exp_add_apply1,
iff_weakening_equal
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X). \mforall{}e:E(X). (\mdownarrow{}\mexists{}n:\mBbbN{}. (f**(e) = (f\^{}n e)))
Date html generated:
2015_07_17-PM-00_54_33
Last ObjectModification:
2015_02_04-PM-05_29_53
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