Nuprl Lemma : es-is-interface-co-restrict
∀[Info,A:Type]. ∀[I:EClass(A)]. ∀[P:es:EO+(Info) ─→ E ─→ ℙ]. ∀[p:∀es:EO+(Info). ∀e:E. Dec(P[es;e])]. ∀[es:EO+(Info)].
∀[e:E].
uiff(↑e ∈b (I|¬p);(↑e ∈b I) ∧ (¬P[es;e]))
Proof
Definitions occuring in Statement :
es-interface-co-restrict: (I|¬p),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
decidable: Dec(P),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
not: ¬A,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
all_wf,
es-E_wf,
event-ordering+_subtype,
decidable_wf,
bag_size_empty_lemma,
assert_witness,
false_wf,
assert_wf,
eq_int_wf,
bag-size_wf,
nat_wf,
not_wf,
equal_wf,
in-eclass_wf,
es-interface-subtype_rel2,
event-ordering+_wf,
top_wf,
es-interface-co-restrict_wf,
eclass_wf
Latex:
\mforall{}[Info,A:Type]. \mforall{}[I:EClass(A)]. \mforall{}[P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
\mforall{}[p:\mforall{}es:EO+(Info). \mforall{}e:E. Dec(P[es;e])]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} (I|\mneg{}p);(\muparrow{}e \mmember{}\msubb{} I) \mwedge{} (\mneg{}P[es;e]))
Date html generated:
2015_07_20-PM-03_29_24
Last ObjectModification:
2015_01_27-PM-10_17_46
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