Nuprl Lemma : global-eo-before
∀[L:(Id × Top) List]. ∀[e:E]. (before(e) ~ filter(λn.loc(n) = loc(e);upto(e)))
Proof
Definitions occuring in Statement :
global-eo: global-eo(L),
es-before: before(e),
es-loc: loc(e),
es-E: E,
eq_id: a = b,
Id: Id,
upto: upto(n),
filter: filter(P;l),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
lambda: λx.A[x],
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
uimplies: b supposing a,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
guard: {T},
lelt: i ≤ j < k,
sq_type: SQType(T),
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
es-before: before(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
squash: ↓T,
l_all: (∀x∈L.P[x]),
cand: A c∧ B,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
Id: Id,
inject: Inj(A;B;f),
sq_stable: SqStable(P),
l_member: (x ∈ l),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[L:(Id \mtimes{} Top) List]. \mforall{}[e:E]. (before(e) \msim{} filter(\mlambda{}n.loc(n) = loc(e);upto(e)))
Date html generated:
2016_05_17-AM-08_30_11
Last ObjectModification:
2016_01_17-PM-02_50_22
Theory : event-ordering
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