Nuprl Lemma : es-interface-predecessors-iseg
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(Top). ∀e,e':E(X).  (≤(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' 
, 
iseg: l1 ≤ l2
, 
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, 
es-E-interface_wf, 
equal_wf, 
all_wf, 
int_seg_subtype-nat, 
iff_wf, 
iseg_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, 
es-E_wf, 
event-ordering+_wf, 
decidable__equal_es-E-interface, 
es-le-self, 
iseg_weakening, 
assert_witness, 
in-eclass_wf, 
es-le-prior-interface-val, 
assert_elim, 
subtype_base_sq, 
bool_wf, 
bool_subtype_base, 
assert_wf, 
es-prior-interface_wf0, 
eclass-val_wf2, 
es-prior-interface_wf, 
es-is-prior-interface, 
es-locl_wf, 
es-prior-interface-val, 
eclass-val_wf, 
es-locl_transitivity1, 
es-le_weakening, 
es-interface-subtype_rel2, 
subtype_top, 
equal-wf-T-base, 
bnot_wf, 
not_wf, 
squash_wf, 
true_wf, 
list_wf, 
es-interface-predecessors-step, 
iff_weakening_equal, 
eqtt_to_assert, 
uiff_transitivity, 
eqff_to_assert, 
assert_of_bnot, 
es-prior-interface-causl, 
iseg_append_iff, 
cons_wf, 
nil_wf, 
append_wf, 
or_wf, 
exists_wf, 
length_wf, 
length-append, 
null_wf3, 
null_append, 
list-cases, 
length_of_nil_lemma, 
null_nil_lemma, 
product_subtype_list, 
length_of_cons_lemma, 
null_cons_lemma, 
assert_of_null, 
bool_cases_sqequal, 
assert-bnot, 
not_assert_elim, 
and_wf, 
btrue_wf, 
btrue_neq_bfalse, 
last_wf, 
es-interface-predecessors-last, 
last_append, 
cons_iseg, 
iseg_length, 
non_neg_length, 
length_wf_nat, 
length_cons, 
iseg_member, 
es-interface-predecessors-member, 
member_singleton
Latex:
\mforall{}[Info:Type].  \mforall{}es:EO+(Info).  \mforall{}X:EClass(Top).  \mforall{}e,e':E(X).    (\mleq{}(X)(e')  \mleq{}  \mleq{}(X)(e)  \mLeftarrow{}{}\mRightarrow{}  e'  \mleq{}loc  e  )
Date html generated:
2015_07_21-PM-03_35_06
Last ObjectModification:
2015_02_04-PM-06_16_19
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