Nuprl Lemma : es-prior-fixedpoints-iseg
∀[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)) ⇒ prior-f-fixedpoints(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-causle: e c≤ e',
iseg: l1 ≤ l2,
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-causl-swellfnd,
event-ordering+_subtype,
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
decidable__es-E-equal,
equal_wf,
all_wf,
int_seg_subtype-nat,
l_member_wf,
es-prior-fixedpoints_wf,
subtype_rel_list,
es-E_wf,
iseg_wf,
decidable__lt,
not-equal-2,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add_functionality_wrt_le,
zero-add,
le-add-cancel-alt,
less-iff-le,
le-add-cancel,
set_wf,
less_than_wf,
primrec-wf2,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
add-mul-special,
zero-mul,
es-causle_wf,
es-E-interface_wf,
eclass_wf,
top_wf,
event-ordering+_wf,
assert_wf,
bool_subtype_base,
bool_wf,
subtype_base_sq,
assert_elim,
in-eclass_wf,
member_wf,
and_wf,
iseg_weakening,
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
eqff_to_assert,
assert-es-eq-E-2,
eqtt_to_assert,
bool_cases,
not_wf,
bnot_wf,
es-eq-E_wf,
uiff_transitivity,
equal-wf-T-base,
nil_wf,
cons_wf,
es-prior-interface_wf,
eclass-val_wf2,
append_wf,
subtype_top,
es-interface-subtype_rel2,
es-prior-interface_wf0,
member_append,
es-prior-interface-causl,
iseg_append,
equal_functionality_wrt_subtype_rel2,
member_singleton,
es-fix_wf2,
es-prior-fixedpoints-fix,
es-fix-causle,
es-E-interface-property,
es-fix-equal-E-interface
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{} prior-f-fixedpoints(e') \mleq{} prior-f-fixedpoints(e))))
Date html generated:
2015_07_21-PM-03_53_14
Last ObjectModification:
2015_07_16-AM-09_40_39
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