Nuprl Lemma : iseg-interface-predecessors
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀e:E(X). ∀L:E(X) List.
(L ≤ ≤(X)(e)
⇐⇒ (↑null(L)) ∨ ((¬↑null(L)) ∧ (∃p:E(X). (p ≤loc e ∧ (L = ≤(X)(p) ∈ (E(X) List)) ∧ (p = last(L) ∈ E)))))
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
iseg: l1 ≤ l2,
last: last(L),
null: null(as),
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
iseg_wf,
es-E-interface_wf,
es-interface-predecessors_wf,
subtype_rel_list,
Id_wf,
es-loc_wf,
event-ordering+_subtype,
or_wf,
assert_wf,
null_wf3,
top_wf,
not_wf,
exists_wf,
es-le_wf,
list_wf,
length_wf,
equal_wf,
es-E_wf,
last_wf,
eclass_wf,
event-ordering+_wf,
decidable__assert,
member-interface-predecessors,
last_member,
iseg_member,
es-interface-predecessors-sorted-by-locl,
iseg-sorted-by,
es-locl_wf,
sorted-by-strict-unique,
es-locl_transitivity2,
es-le_weakening,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
es-locl_irreflexivity,
l_member_wf,
member-iseg-sorted-by,
es-locl-antireflexive,
es-le_transitivity,
es-le-self,
and_wf,
list-cases,
null_nil_lemma,
nil_iseg,
product_subtype_list,
null_cons_lemma,
length_wf_nat,
nat_wf,
es-interface-predecessors-iseg
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E(X). \mforall{}L:E(X) List.
(L \mleq{} \mleq{}(X)(e)
\mLeftarrow{}{}\mRightarrow{} (\muparrow{}null(L)) \mvee{} ((\mneg{}\muparrow{}null(L)) \mwedge{} (\mexists{}p:E(X). (p \mleq{}loc e \mwedge{} (L = \mleq{}(X)(p)) \mwedge{} (p = last(L))))))
Date html generated:
2015_07_21-PM-03_39_00
Last ObjectModification:
2015_01_27-PM-06_33_56
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