Nuprl Lemma : class-output-support-no-repeats
∀[Info: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. (e1 ↓∈ bg ⇒ e2 ↓∈ 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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
squash: ↓T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
bag-no-repeats: bag-no-repeats(T;bs),
and: P ∧ Q,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
class-output-support: class-output-support(es;bg),
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),
rev_uimplies: rev_uimplies(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,
rev_implies: P ⇐ Q,
no_repeats: no_repeats(T;l),
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
ge: i ≥ j
Latex:
\mforall{}[Info: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. (e1 \mdownarrow{}\mmember{} bg {}\mRightarrow{} e2 \mdownarrow{}\mmember{} bg {}\mRightarrow{} (\mneg{}(e1 <loc e2)))))
Date html generated:
2016_05_16-PM-01_34_53
Last ObjectModification:
2016_01_17-PM-08_00_45
Theory : event-ordering
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