Nuprl Lemma : es-closed-open-interval-decomp-mem
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e1,e2,e:E].
([e1;e2) = ([e1;e) @ [e;e2)) ∈ (E List)) supposing (e1 ≤loc e and e ≤loc e2 )
Proof
Definitions occuring in Statement :
event-ordering+: EO+(Info),
es-closed-open-interval: [e;e'),
es-le: e ≤loc e' ,
es-E: E,
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
es-le_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
event-ordering+_subtype,
es-E_wf,
event-ordering+_wf,
es-closed-open-interval-decomp-last,
es-locl_transitivity1,
append_assoc,
list_wf,
append_wf,
es-closed-open-interval_wf,
es-pred_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
es-pred-causl,
es-le-pred,
cons_wf,
nil_wf,
squash_wf,
true_wf,
iff_weakening_equal,
append-nil,
subtype_rel_list,
top_wf,
es-closed-open-interval-nil
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e1,e2,e:E].
([e1;e2) = ([e1;e) @ [e;e2))) supposing (e1 \mleq{}loc e and e \mleq{}loc e2 )
Date html generated:
2015_07_17-PM-00_06_31
Last ObjectModification:
2015_02_04-PM-05_38_34
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