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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
es-hist: es-hist(es;e1;e2),
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
existse-between3: ∃e∈(e1,e2].P[e],
cand: A c∧ B,
guard: {T}
Latex:
\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:
2016_05_16-PM-01_20_04
Last ObjectModification:
2016_01_17-PM-07_58_41
Theory : event-ordering
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