Nuprl Lemma : interface-predecessors-split
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀e:E(X). ∀A,B:E(X) List.
(∃p:E(X)
(p ≤loc e
∧ (≤(X)(p) = A ∈ (E(X) List))
∧ (filter(λa.p <loc a;≤(X)(e)) = B ∈ (E(X) List))
∧ (p <loc e) supposing ¬↑null(B)
∧ (p = last(A) ∈ E))) supposing
((¬↑null(A)) and
(≤(X)(e) = (A @ B) ∈ (E(X) List)))
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-bless: e <loc e',
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
last: last(L),
filter: filter(P;l),
append: as @ bs,
null: null(as),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
lambda: λx.A[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
iseg-remainder-as-filter,
es-E-interface_wf,
es-locl_wf,
event-ordering+_subtype,
es-locl-antireflexive,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
es-locl_transitivity2,
es-le_weakening,
es-locl_irreflexivity,
assert_wf,
es-interface-predecessors-sorted-by-locl,
es-bless_wf,
assert-es-bless,
equal_wf,
list_wf,
filter_wf5,
l_member_wf,
length_wf,
length-append,
es-interface-predecessors_wf,
squash_wf,
true_wf,
es-E_wf,
eclass_wf,
top_wf,
event-ordering+_wf,
subtype_rel_list,
Id_wf,
es-loc_wf,
list-cases,
length_of_nil_lemma,
null_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
null_cons_lemma,
non_neg_length,
length_wf_nat
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E(X). \mforall{}A,B:E(X) List.
(\mexists{}p:E(X)
(p \mleq{}loc e
\mwedge{} (\mleq{}(X)(p) = A)
\mwedge{} (filter(\mlambda{}a.p <loc a;\mleq{}(X)(e)) = B)
\mwedge{} (p <loc e) supposing \mneg{}\muparrow{}null(B)
\mwedge{} (p = last(A)))) supposing
((\mneg{}\muparrow{}null(A)) and
(\mleq{}(X)(e) = (A @ B)))
Date html generated:
2015_07_21-PM-03_39_13
Last ObjectModification:
2015_01_27-PM-06_31_02
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