Nuprl Lemma : es-interface-local-pred-bool
∀[Info:Type]
∀P:es:EO+(Info) ⟶ E ⟶ 𝔹
∃X:EClass({e':E| (e' <loc e) ∧ (↑(P es e')) ∧ (∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑(P es e''))))} )
∀es:EO+(Info). ∀e:E.
((↑e ∈b X ⇐⇒ ∃a:E. ((a <loc e) ∧ (↑(P es a)))) ∧ es-p-local-pred(es;λe.(↑(P es e))) e X(e) supposing ↑e ∈b X)
Proof
Definitions occuring in Statement :
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-p-local-pred: es-p-local-pred(es;P),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
uimplies: b supposing a,
local-pred-class: local-pred-class(P),
eclass-val: X(e),
es-p-local-pred: es-p-local-pred(es;P),
in-eclass: e ∈b X,
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
isl: isl(x),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
top: Top,
eq_int: (i =z j),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_exists: ∃x:{A| B[x]},
bfalse: ff,
cand: A c∧ B,
false: False,
es-locl: (e <loc e'),
es-causl: (e < e'),
squash: ↓T,
not: ¬A,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]
\mforall{}P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbB{}
\mexists{}X:EClass(\{e':E|
(e' <loc e)
\mwedge{} (\muparrow{}(P es e'))
\mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}(P es e''))))\} )
\mforall{}es:EO+(Info). \mforall{}e:E.
((\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \mexists{}a:E. ((a <loc e) \mwedge{} (\muparrow{}(P es a))))
\mwedge{} es-p-local-pred(es;\mlambda{}e.(\muparrow{}(P es e))) e X(e) supposing \muparrow{}e \mmember{}\msubb{} X)
Date html generated:
2016_05_16-PM-11_28_44
Last ObjectModification:
2016_01_17-PM-07_10_27
Theory : event-ordering
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