Nuprl Lemma : es-cut-union
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[c1,c2:Cut(X;f)]. (c1 ⋃ c2 ∈ Cut(X;f))
Proof
Definitions occuring in Statement :
es-cut: Cut(X;f),
sys-antecedent: sys-antecedent(es;Sys),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-eq: es-eq(es),
fset-union: x ⋃ y,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
prop: ℙ,
uimplies: b supposing a,
sys-antecedent: sys-antecedent(es;Sys),
es-cut: Cut(X;f),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[c1,c2:Cut(X;f)].
(c1 \mcup{} c2 \mmember{} Cut(X;f))
Date html generated:
2016_05_17-AM-07_31_01
Last ObjectModification:
2015_12_28-PM-11_45_59
Theory : event-ordering
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