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
Lemmas :
sys-antecedent-closure,
cons_wf,
es-interface-pred_wf,
nil_wf,
fset-closed_wf,
es-eq_wf-interface,
es-interface-pred_wf2,
fset-member_witness,
fset-member_wf,
f-subset_wf,
es-cut_wf,
uall_wf,
isect_wf,
fset_wf,
es-E-interface_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
sq_stable_from_decidable,
decidable__fset-closed
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:
2015_07_21-PM-03_55_14
Last ObjectModification:
2015_01_27-PM-05_56_53
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