Nuprl Lemma : es-closed-interval-vals-decomp
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A)]. ∀[e1,e2:E].
X[e1;e2]
= (if e1 <loc e2 ∧b e1 ∈b X then [X(e1)] else [] fi @ X(e1, e2) @ if e2 ∈b X then [X(e2)] else [] fi )
∈ (A List)
supposing e1 ≤loc e2
Proof
Definitions occuring in Statement :
es-closed-interval-vals: X[e1;e2],
es-prior-interval-vals: X(e1, e2),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-bless: e <loc e',
es-le: e ≤loc e' ,
es-E: E,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
es-interval-open-interval,
es-bless_wf,
bool_wf,
iff_transitivity,
equal-wf-T-base,
assert_wf,
es-locl_wf,
iff_weakening_uiff,
eqtt_to_assert,
assert-es-bless,
list_ind_cons_lemma,
list_ind_nil_lemma,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
es-le_wf,
event-ordering+_subtype,
es-E_wf,
eclass_wf,
event-ordering+_wf,
append_wf,
cons_wf,
iff_weakening_equal,
squash_wf,
true_wf,
list_wf,
ite_rw_true,
equal_wf,
es-interval_wf,
es-open-interval_wf,
nil_wf,
in-eclass_wf,
es-interface-subtype_rel2,
top_wf,
length_wf_nat,
nat_wf,
mapfilter_wf,
eclass-val_wf,
es-E-interface-property,
es-prior-interval-vals_wf,
uiff_transitivity,
filter_cons_lemma,
filter_nil_lemma,
map_cons_lemma,
map_nil_lemma,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
mapfilter-append,
mapfilter-nil,
l_member_wf,
l_all_cons,
l_all_nil
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[e1,e2:E].
X[e1;e2]
= (if e1 <loc e2 \mwedge{}\msubb{} e1 \mmember{}\msubb{} X then [X(e1)] else [] fi
@ X(e1, e2)
@ if e2 \mmember{}\msubb{} X then [X(e2)] else [] fi )
supposing e1 \mleq{}loc e2
Date html generated:
2015_07_17-PM-01_05_37
Last ObjectModification:
2015_02_04-PM-05_31_07
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