Nuprl Lemma : es-hist-is-concat
∀[Info:Type]
∀es:EO+(Info). ∀LL:Info List List. ∀e1,e2:E.
∀L:Info List
(∃f:ℕ||LL|| + 1 ─→ E
((((f 0) = e1 ∈ E) ∧ f ||LL|| ≤loc e2 )
c∧ (∀i:ℕ||LL||. (f i <loc f (i + 1)))
c∧ ((∀i:ℕ||LL||. (es-hist(es;f i;pred(f (i + 1))) = LL[i] ∈ (Info List)))
∧ (es-hist(es;f ||LL||;e2) = L ∈ (Info List))))) supposing
((es-hist(es;e1;e2) = (concat(LL) @ L) ∈ (Info List)) and
(¬(L = [] ∈ (Info List))) and
(∀L∈LL.¬(L = [] ∈ (Info List))))
supposing loc(e1) = loc(e2) ∈ Id
Proof
Definitions occuring in Statement :
es-hist: es-hist(es;e1;e2),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
Id: Id,
l_all: (∀x∈L.P[x]),
concat: concat(ll),
select: L[n],
length: ||as||,
append: as @ bs,
nil: [],
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
add: n + m,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Lemmas :
list_induction,
all_wf,
isect_wf,
exists_wf,
es-le_wf,
es-locl_wf,
equal_wf,
es-hist_wf,
es-pred_wf,
es-locl-first,
decidable__lt,
false_wf,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-associates,
le-add-cancel,
lelt_wf,
decidable__le,
not-le-2,
zero-add,
sq_stable__le,
add-zero,
le-add-cancel2,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
select_wf,
list_wf,
event-ordering+_wf,
reduce_nil_lemma,
length_of_nil_lemma,
stuck-spread,
base_wf,
list_ind_nil_lemma,
length_nil,
non_neg_length,
nil_wf,
length_wf_nil,
int_seg_wf,
length_wf,
equal-wf-T-base,
less_than_transitivity1,
less_than_irreflexivity,
not_wf,
l_all_wf2,
l_member_wf,
Id_wf,
es-loc_wf,
event-ordering+_subtype,
es-E_wf,
decidable__es-locl,
null-es-hist,
null_wf3,
subtype_rel_list,
top_wf,
assert_of_null,
es-le-not-locl,
cons_wf,
append_wf,
concat_wf,
concat-cons,
append_assoc_sq,
es-hist-is-append,
append_is_nil,
l_all_cons,
length_of_cons_lemma,
eq_int_wf,
bool_wf,
bnot_wf,
subtract_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
length_wf_nat,
subtype_base_sq,
int_subtype_base,
and_wf,
es-causl_wf,
general_arith_equation1,
not-equal-2,
minus-zero,
minus-minus,
squash_wf,
true_wf,
event_ordering_wf,
iff_weakening_equal,
select_cons_tl_sq,
trivial-int-eq1,
length_cons
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}LL:Info List List. \mforall{}e1,e2:E.
\mforall{}L:Info List
(\mexists{}f:\mBbbN{}||LL|| + 1 {}\mrightarrow{} E
((((f 0) = e1) \mwedge{} f ||LL|| \mleq{}loc e2 )
c\mwedge{} (\mforall{}i:\mBbbN{}||LL||. (f i <loc f (i + 1)))
c\mwedge{} ((\mforall{}i:\mBbbN{}||LL||. (es-hist(es;f i;pred(f (i + 1))) = LL[i]))
\mwedge{} (es-hist(es;f ||LL||;e2) = L)))) supposing
((es-hist(es;e1;e2) = (concat(LL) @ L)) and
(\mneg{}(L = [])) and
(\mforall{}L\mmember{}LL.\mneg{}(L = [])))
supposing loc(e1) = loc(e2)
Date html generated:
2015_07_17-PM-00_10_57
Last ObjectModification:
2015_02_04-PM-05_39_40
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