Nuprl Lemma : es-cut-at-property
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X). ∀c:Cut(X;f). ∀i:Id.
((∀e:E(X). ((e ∈ c(i)) ⇐⇒ (loc(e) = i ∈ Id) ∧ e ∈ c))
∧ (∀e,e':E(X). (e before e' ∈ c(i) ⇐⇒ (e <loc e') ∧ (e' ∈ c(i)))))
Proof
Definitions occuring in Statement :
es-cut-at: c(i),
es-cut: Cut(X;f),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-eq: es-eq(es),
es-loc: loc(e),
fset-member: a ∈ s,
Id: Id,
l_before: x before y ∈ l,
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
es-cut: Cut(X;f),
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
es-E-interface: E(X),
es-cut-at: c(i),
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
es-locl: (e <loc e'),
es-causl: (e < e'),
squash: ↓T,
uiff: uiff(P;Q),
es-le: e ≤loc e' ,
label: ...$L... t
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X). \mforall{}c:Cut(X;f). \mforall{}i:Id.
((\mforall{}e:E(X). ((e \mmember{} c(i)) \mLeftarrow{}{}\mRightarrow{} (loc(e) = i) \mwedge{} e \mmember{} c))
\mwedge{} (\mforall{}e,e':E(X). (e before e' \mmember{} c(i) \mLeftarrow{}{}\mRightarrow{} (e <loc e') \mwedge{} (e' \mmember{} c(i)))))
Date html generated:
2016_05_17-AM-07_30_43
Last ObjectModification:
2016_01_17-PM-02_57_14
Theory : event-ordering
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