Nuprl Lemma : class-output-support-no_repeats
∀[Info,T:Type]. ∀[es:EO+(Info)]. ∀[bg:bag(E)].
  (bag-no-repeats(E;class-output-support(es;bg))) supposing 
     (bag-no-repeats(E;bg) and 
     (∀e1,e2:E.  (e2 ↓∈ bg 
⇒ e1 ↓∈ bg 
⇒ (¬(e1 <loc e2)))))
Proof
Definitions occuring in Statement : 
class-output-support: class-output-support(es;bg)
, 
event-ordering+: EO+(Info)
, 
es-locl: (e <loc e')
, 
es-E: E
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
universe: Type
, 
bag-member: x ↓∈ bs
, 
bag-no-repeats: bag-no-repeats(T;bs)
, 
bag: bag(T)
Definitions unfolded in proof : 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
bag-no-repeats: bag-no-repeats(T;bs)
, 
squash: ↓T
, 
class-output-support: class-output-support(es;bg)
, 
sq_stable: SqStable(P)
, 
exists: ∃x:A. B[x]
, 
and: P ∧ Q
, 
true: True
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
bag-combine: ⋃x∈bs.f[x]
, 
bag-map: bag-map(f;bs)
, 
bag-union: bag-union(bbs)
, 
cand: A c∧ B
, 
uiff: uiff(P;Q)
, 
all: ∀x:A. B[x]
, 
top: Top
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
false: False
, 
not: ¬A
, 
less_than: a < b
, 
Id: Id
, 
sq_type: SQType(T)
, 
no_repeats: no_repeats(T;l)
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
nat: ℕ
, 
ge: i ≥ j 
, 
es-locl: (e <loc e')
Latex:
\mforall{}[Info,T:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[bg:bag(E)].
    (bag-no-repeats(E;class-output-support(es;bg)))  supposing 
          (bag-no-repeats(E;bg)  and 
          (\mforall{}e1,e2:E.    (e2  \mdownarrow{}\mmember{}  bg  {}\mRightarrow{}  e1  \mdownarrow{}\mmember{}  bg  {}\mRightarrow{}  (\mneg{}(e1  <loc  e2)))))
Date html generated:
2016_05_16-PM-01_59_23
Last ObjectModification:
2016_01_17-PM-07_50_41
Theory : event-ordering
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