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
Lemmas :
uall_wf,
all_wf,
event-ordering+_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_subtype,
sys-antecedent_wf,
fset_wf,
es-E-interface_wf,
exists_wf,
es-cut_wf,
f-subset_wf,
es-eq_wf-interface,
isect_wf,
equal_wf,
cut-of_wf,
fset-member_wf,
fset-member_wf-cut
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:
2015_07_21-PM-03_57_56
Last ObjectModification:
2015_01_27-PM-05_54_00
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