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]),
select: L[n],
length: ||as||,
concat: concat(ll),
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: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
cand: A c∧ B,
and: P ∧ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
uiff: uiff(P;Q),
so_apply: x[s],
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
subtract: n - m,
guard: {T},
concat: concat(ll),
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
l_all: (∀x∈L.P[x]),
es-locl: (e <loc e'),
es-causl: (e < e'),
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
list: T List,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
existse-between3: ∃e∈(e1,e2].P[e],
bool: 𝔹,
unit: Unit,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
eq_int: (i =z j),
label: ...$L... t,
sq_type: SQType(T),
cons: [a / b],
ge: i ≥ j
Latex:
\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:
2016_05_16-PM-01_20_57
Last ObjectModification:
2016_01_17-PM-08_02_07
Theory : event-ordering
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