Nuprl Lemma : member-es-fix-prior-fixedpoints
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:E(X) ─→ E(X). ((∀x:E(X). f x c≤ x) ⇒ (∀e:E(X). (f**(e) ∈ prior-f-fixedpoints(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-fix: f**(e),
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 :
es-prior-fixedpoints-fix,
es-E-interface_wf,
all_wf,
es-causle_wf,
event-ordering+_subtype,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_wf,
es-fix_wf2,
es-eq-E_wf,
assert_wf,
bnot_wf,
not_wf,
equal_wf,
assert_elim,
btrue_neq_bfalse,
es-fix_wf,
subtype_rel-equal,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert-es-eq-E-2,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
subtype_top,
es-prior-fixedpoints_wf,
eclass-val_wf2,
es-prior-interface_wf,
subtype_rel_list,
cons_wf,
nil_wf,
l_member_wf,
member_append,
member_singleton,
es-fix_property,
equal_functionality_wrt_subtype_rel2
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(X). (f**(e) \mmember{} prior-f-fixedpoints(e))))
Date html generated:
2015_07_21-PM-03_52_16
Last ObjectModification:
2015_01_27-PM-06_02_09
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