Nuprl Lemma : es-cut-closed-prior
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[c:Cut(X;f)]. ∀[a:E(X)].
(prior(X)(a) ∈ c) supposing ((↑a ∈b prior(X)) and a ∈ c)
Proof
Definitions occuring in Statement :
es-cut: Cut(X;f),
es-prior-interface: prior(X),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-eq: es-eq(es),
fset-member: a ∈ s,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type
Lemmas :
fset-member_witness,
es-E-interface_wf,
es-eq_wf-interface,
eclass-val_wf2,
es-prior-interface_wf,
assert_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
fset-member_wf-cut,
es-cut_wf,
sys-antecedent_wf,
eclass_wf,
bool_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
sq_stable_from_decidable,
fset-member_wf,
es-interface-pred_wf2,
decidable__fset-member,
l_all_iff,
cons_wf,
es-interface-pred_wf,
nil_wf,
l_member_wf,
all_wf,
isect_wf,
cons_member,
equal_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[c:Cut(X;f)].
\mforall{}[a:E(X)].
(prior(X)(a) \mmember{} c) supposing ((\muparrow{}a \mmember{}\msubb{} prior(X)) and a \mmember{} c)
Date html generated:
2015_07_21-PM-03_55_26
Last ObjectModification:
2015_01_27-PM-05_55_50
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