Nuprl Lemma : es-prior-fixedpoints-causle
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:E(X) ─→ E(X).
((∀x:E(X). f x c≤ x) ⇒ (∀e,e':E(X). ((e' ∈ prior-f-fixedpoints(e)) ⇒ e' c≤ e)))
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',
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
member_append,
es-E-interface_wf,
es-prior-fixedpoints_wf,
eclass-val_wf2,
es-prior-interface_wf,
subtype_rel_list,
es-E_wf,
event-ordering+_subtype,
cons_wf,
nil_wf,
member_singleton,
or_wf,
l_member_wf,
es-causle_weakening_eq,
es-causle_wf,
and_wf,
equal_wf,
es-prior-interface-locl,
es-causl_weakening,
es-causle_transitivity,
es-causle_weakening_locl,
es-le_weakening,
es-fix-causle,
es-fix_wf2,
es-fix-equal-E-interface,
es-E-interface-property,
assert_wf,
in-eclass_wf
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:E(X) {}\mrightarrow{} E(X).
((\mforall{}x:E(X). f x c\mleq{} x) {}\mRightarrow{} (\mforall{}e,e':E(X). ((e' \mmember{} prior-f-fixedpoints(e)) {}\mRightarrow{} e' c\mleq{} e)))
Date html generated:
2015_07_21-PM-03_52_51
Last ObjectModification:
2015_01_27-PM-06_03_17
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