Nuprl Lemma : global-eo-first
∀[L:(Id × Top) List]. ∀[e:E]. (first(e) ~ (∀x∈upto(e).¬bloc(x) = loc(e))_b)
Proof
Definitions occuring in Statement :
global-eo: global-eo(L),
es-first: first(e),
es-loc: loc(e),
es-E: E,
eq_id: a = b,
Id: Id,
bl-all: (∀x∈L.P[x])_b,
upto: upto(n),
list: T List,
bnot: ¬bb,
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
top: Top,
uimplies: b supposing a,
int_seg: {i..j-},
es-base-E: es-base-E(es),
record-select: r.x,
global-eo: global-eo(L),
mk-extended-eo: mk-extended-eo,
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
mk-eo: mk-eo(E;dom;l;R;locless;pred;rank),
mk-eo-record: mk-eo-record(E;dom;l;R;locless;pred;rank),
btrue: tt,
lelt: i ≤ j < k,
and: P ∧ Q,
prop: ℙ,
true: True,
es-first: first(e),
bnot: ¬bb,
es-pred: pred(e),
es-eq-E: e = e',
es-base-pred: pred1(e),
let: let,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
less_than: a < b,
squash: ↓T,
has-value: (a)↓,
Id: Id,
so_lambda: λ2x.t[x],
so_apply: x[s],
int_iseg: {i...j},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
pi1: fst(t),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
sq_type: SQType(T),
assert: ↑b,
bor: p ∨bq,
nequal: a ≠ b ∈ T ,
rev_uimplies: rev_uimplies(P;Q),
l_all: (∀x∈L.P[x]),
le: A ≤ B,
less_than': less_than'(a;b),
ge: i ≥ j ,
nat: ℕ,
cand: A c∧ B,
l_exists: (∃x∈L. P[x]),
sq_stable: SqStable(P)
Latex:
\mforall{}[L:(Id \mtimes{} Top) List]. \mforall{}[e:E]. (first(e) \msim{} (\mforall{}x\mmember{}upto(e).\mneg{}\msubb{}loc(x) = loc(e))\_b)
Date html generated:
2016_05_17-AM-08_29_29
Last ObjectModification:
2016_01_17-PM-02_56_22
Theory : event-ordering
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