Nuprl Lemma : cut-of-property
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[s:fset(E(X))].
(s ⊆ cut(X;f;s) ∧ (∀[c':Cut(X;f)]. cut(X;f;s) ⊆ c' supposing s ⊆ c'))
Proof
Definitions occuring in Statement :
cut-of: cut(X;f;s),
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,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
pi1: fst(t),
exists: ∃x:A. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
so_apply: x[s],
uimplies: b supposing a,
es-cut: Cut(X;f),
and: P ∧ Q,
prop: ℙ,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
cut-of: cut(X;f;s),
f-subset: xs ⊆ ys
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[s:fset(E(X))].
(s \msubseteq{} cut(X;f;s) \mwedge{} (\mforall{}[c':Cut(X;f)]. cut(X;f;s) \msubseteq{} c' supposing s \msubseteq{} c'))
Date html generated:
2016_05_17-AM-07_31_58
Last ObjectModification:
2015_12_28-PM-11_46_24
Theory : event-ordering
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