Nuprl Lemma : es-cut-exists
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X). ∀s:fset(E(X)).
∃c:Cut(X;f). (s ⊆ c ∧ (∀[c':Cut(X;f)]. c ⊆ c' supposing s ⊆ 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-eq: es-eq(es),
f-subset: xs ⊆ ys,
fset: fset(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
es-cut: Cut(X;f),
sys-antecedent: sys-antecedent(es;Sys),
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a,
f-subset: xs ⊆ ys,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
fset-closure: (c = fs closure of s),
sq_stable: SqStable(P),
squash: ↓T
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X). \mforall{}s:fset(E(X)).
\mexists{}c:Cut(X;f). (s \msubseteq{} c \mwedge{} (\mforall{}[c':Cut(X;f)]. c \msubseteq{} c' supposing s \msubseteq{} c'))
Date html generated:
2016_05_17-AM-07_27_43
Last ObjectModification:
2016_01_17-PM-02_58_04
Theory : event-ordering
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