Nuprl Lemma : es-cut-le-closed
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[c:Cut(X;f)]. ∀[a,e:E(X)].
(e ∈ c) supposing (e ≤loc a and a ∈ c)
Proof
Definitions occuring in Statement :
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-le: e ≤loc e' ,
es-eq: es-eq(es),
fset-member: a ∈ s,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-cut: Cut(X;f),
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
es-E-interface: E(X),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-le: e ≤loc e' ,
or: P ∨ Q,
squash: ↓T,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[c:Cut(X;f)].
\mforall{}[a,e:E(X)].
(e \mmember{} c) supposing (e \mleq{}loc a and a \mmember{} c)
Date html generated:
2016_05_17-AM-07_28_45
Last ObjectModification:
2016_01_17-PM-02_55_54
Theory : event-ordering
Home
Index