Nuprl Lemma : es-prior-fixedpoints-fixed
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:E(X) ─→ E(X)].
∀[e,e':E(X)]. (f e') = e' ∈ E supposing (e' ∈ prior-f-fixedpoints(e)) supposing ∀x:E(X). f x c≤ x
Proof
Definitions occuring in Statement :
es-prior-fixedpoints: prior-f-fixedpoints(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-causle: e c≤ e',
es-E: E,
l_member: (x ∈ l),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
all_wf,
es-causle_wf,
event-ordering+_subtype,
es-E-interface_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_wf,
l_member_wf,
es-prior-fixedpoints_wf,
subtype_rel_list,
es-causl-swellfnd,
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,
property-from-l_member,
equal_wf,
sq_stable__equal,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)].
\mforall{}[e,e':E(X)]. (f e') = e' supposing (e' \mmember{} prior-f-fixedpoints(e)) supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2015_07_21-PM-03_53_50
Last ObjectModification:
2015_01_27-PM-05_58_44
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