Nuprl Lemma : es-is-interface-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. (↑e ∈b (I|p) ⇐⇒ (↑e ∈b I) ∧ P[es;e])
Proof
Definitions occuring in Statement :
es-interface-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),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
all_wf,
es-E_wf,
event-ordering+_subtype,
decidable_wf,
assert_wf,
eq_int_wf,
bag-size_wf,
nat_wf,
assert_witness,
bag_size_empty_lemma,
false_wf,
equal_wf,
event-ordering+_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.
(\muparrow{}e \mmember{}\msubb{} (I|p) \mLeftarrow{}{}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} I) \mwedge{} P[es;e])
Date html generated:
2015_07_20-PM-03_28_35
Last ObjectModification:
2015_01_27-PM-10_19_19
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