Nuprl Lemma : es-local-le-pred-property
∀[Info:Type]
∀P:es:EO+(Info) ─→ E ─→ 𝔹. ∀es:EO+(Info). ∀e:E.
((↑e ∈b ≤(P) ⇐⇒ ∃a:E. (a ≤loc e ∧ (↑(P es a))))
∧ ≤(P)(e) ≤loc e ∧ (↑(P es ≤(P)(e))) ∧ (∀e'':E. (e'' ≤loc e ⇒ (≤(P)(e) <loc e'') ⇒ (¬↑(P es e''))))
supposing ↑e ∈b ≤(P))
Proof
Definitions occuring in Statement :
es-local-le-pred: ≤(P),
eclass-val: X(e),
in-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
es-causl-swellfnd,
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,
bool_wf,
eqtt_to_assert,
bag_size_single_lemma,
bag_only_single_lemma,
es-le_weakening_eq,
es-le_wf,
assert_wf,
true_wf,
exists_wf,
es-le-self,
es-locl_transitivity2,
es-locl_irreflexivity,
es-locl_wf,
uiff_transitivity,
equal-wf-T-base,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
equal_wf,
all_wf,
int_seg_subtype-nat,
iff_wf,
in-eclass_wf,
es-local-le-pred_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
subtype_top,
eclass-val_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,
event-ordering+_wf,
es-first_wf2,
bag_size_empty_lemma,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
and_wf,
subtype_base_sq,
bool_subtype_base,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
es-locl_transitivity1,
es-le_weakening,
es-le-pred,
not_assert_elim,
assert_witness,
es-le-iff
Latex:
\mforall{}[Info:Type]
\mforall{}P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbB{}. \mforall{}es:EO+(Info). \mforall{}e:E.
((\muparrow{}e \mmember{}\msubb{} \mleq{}(P) \mLeftarrow{}{}\mRightarrow{} \mexists{}a:E. (a \mleq{}loc e \mwedge{} (\muparrow{}(P es a))))
\mwedge{} \mleq{}(P)(e) \mleq{}loc e
\mwedge{} (\muparrow{}(P es \mleq{}(P)(e)))
\mwedge{} (\mforall{}e'':E. (e'' \mleq{}loc e {}\mRightarrow{} (\mleq{}(P)(e) <loc e'') {}\mRightarrow{} (\mneg{}\muparrow{}(P es e''))))
supposing \muparrow{}e \mmember{}\msubb{} \mleq{}(P))
Date html generated:
2015_07_20-PM-04_08_11
Last ObjectModification:
2015_01_27-PM-10_01_05
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