Nuprl Lemma : member-interface-predecessors
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(Top). ∀e:E. ∀e':E(X). ((e' ∈ ≤(X)(e)) ⇐⇒ e' ≤loc 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,
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
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,
equal_wf,
es-E_wf,
all_wf,
int_seg_subtype-nat,
es-E-interface_wf,
iff_wf,
l_member_wf,
es-interface-predecessors_wf,
subtype_rel_list,
Id_wf,
es-loc_wf,
es-le_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,
eclass_wf,
top_wf,
event-ordering+_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
subtype_top,
bool_wf,
member_append,
eclass-val_wf2,
es-prior-interface_wf,
eqtt_to_assert,
cons_wf,
assert_wf,
nil_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
append_wf,
or_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
list_ind_nil_lemma,
squash_wf,
true_wf,
list_wf,
es-interface-predecessors-general-step,
iff_weakening_equal,
uiff_transitivity,
assert_of_bnot,
es-prior-interface-causl,
es-loc-prior-interface,
es-locl_transitivity1,
es-le_weakening,
es-le-self,
and_wf,
es-le-prior-interface-val,
assert_elim,
member_singleton,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
not_assert_elim,
bool_cases,
nil_member,
es-is-prior-interface,
es-locl_wf
Latex:
\mforall{}[Info:Type]. \mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E. \mforall{}e':E(X). ((e' \mmember{} \mleq{}(X)(e)) \mLeftarrow{}{}\mRightarrow{} e' \mleq{}loc e )
Date html generated:
2015_07_21-PM-03_36_31
Last ObjectModification:
2015_02_04-PM-06_15_21
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