Nuprl Lemma : es-interface-predecessors-nil
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
(≤(X)(pred(e)) ~ []) supposing ((¬↑first(e)) and (¬↑e ∈b prior(X)))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-interface-predecessors: ≤(X)(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
nil: [],
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
universe: Type,
sqequal: s ~ t
Lemmas :
es-interface-predecessors_wf,
es-pred_wf,
list_wf,
es-E-interface_wf,
Id_wf,
es-loc_wf,
set_wf,
event-ordering+_subtype,
list-cases,
product_subtype_list,
is-prior-interface,
not_wf,
assert_wf,
es-first_wf2,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_wf,
top_wf,
subtype_top,
eclass_wf,
member-es-interface-events2,
es-le-before_wf2,
subtype_rel_list,
es-le_wf,
length_wf_nat,
equal_wf,
nat_wf,
cons_member,
l_member_wf,
es-locl_wf,
member-es-le-before,
es-pred-locl,
es-locl_transitivity1
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(\mleq{}(X)(pred(e)) \msim{} []) supposing ((\mneg{}\muparrow{}first(e)) and (\mneg{}\muparrow{}e \mmember{}\msubb{} prior(X)))
Date html generated:
2015_07_21-PM-02_44_13
Last ObjectModification:
2015_01_27-PM-09_42_48
Home
Index