Nuprl Lemma : es-hist-is-append
∀[Info:Type]
∀es:EO+(Info). ∀e1,e2:E. ∀L1,L2:Info List.
(∃e∈(e1,e2].(es-hist(es;e1;pred(e)) = L1 ∈ (Info List)) ∧ (es-hist(es;e;e2) = L2 ∈ (Info List))) supposing
((es-hist(es;e1;e2) = (L1 @ L2) ∈ (Info List)) and
(¬(L2 = [] ∈ (Info List))) and
(¬(L1 = [] ∈ (Info List))))
Proof
Definitions occuring in Statement :
es-hist: es-hist(es;e1;e2),
event-ordering+: EO+(Info),
existse-between3: ∃e∈(e1,e2].P[e],
es-pred: pred(e),
es-E: E,
append: as @ bs,
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
equal-wf-T-base,
list_wf,
length-append,
length_wf,
equal_wf,
length-map,
es-interval_wf,
pos_length,
es-subinterval,
es-interval-non-zero,
length_wf_nat,
es-hist_wf,
append_wf,
not_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
es-pred_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
es-interval-partition,
map_wf,
es-info_wf,
map_append_sq,
general-append-cancellation,
decidable__equal_int,
false_wf,
not-equal-2,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-commutes,
le-add-cancel,
add-swap,
or_wf
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}e1,e2:E. \mforall{}L1,L2:Info List.
(\mexists{}e\mmember{}(e1,e2].(es-hist(es;e1;pred(e)) = L1) \mwedge{} (es-hist(es;e;e2) = L2)) supposing
((es-hist(es;e1;e2) = (L1 @ L2)) and
(\mneg{}(L2 = [])) and
(\mneg{}(L1 = [])))
Date html generated:
2015_07_17-PM-00_10_20
Last ObjectModification:
2015_01_28-AM-00_13_14
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