Nuprl Lemma : es-local-pred-property2
∀[Info:Type]
∀es:EO+(Info). ∀e:E. ∀P:{e':E| (e' <loc e)} ⟶ 𝔹.
((↑can-apply(last(P);e) ⇐⇒ ∃a:E. ((a <loc e) ∧ (↑(P a))))
∧ (do-apply(last(P);e) <loc e)
∧ (↑(P do-apply(last(P);e)))
∧ (∀e'':E. ((e'' <loc e) ⇒ (do-apply(last(P);e) <loc e'') ⇒ (¬↑(P e''))))
supposing ↑can-apply(last(P);e))
Proof
Definitions occuring in Statement :
es-local-pred: last(P),
event-ordering+: EO+(Info),
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,
function: x:A ⟶ B[x],
universe: Type,
do-apply: do-apply(f;x),
can-apply: can-apply(f;x)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
implies: P ⇒ Q,
so_apply: x[s],
or: P ∨ Q,
isl: isl(x),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True,
uimplies: b supposing a,
sq_exists: ∃x:{A| B[x]},
sq_type: SQType(T),
guard: {T},
not: ¬A,
false: False,
es-locl: (e <loc e'),
es-causl: (e < e'),
squash: ↓T,
bfalse: ff,
exists: ∃x:A. B[x],
sq_stable: SqStable(P)
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}P:\{e':E| (e' <loc e)\} {}\mrightarrow{} \mBbbB{}.
((\muparrow{}can-apply(last(P);e) \mLeftarrow{}{}\mRightarrow{} \mexists{}a:E. ((a <loc e) \mwedge{} (\muparrow{}(P a))))
\mwedge{} (do-apply(last(P);e) <loc e)
\mwedge{} (\muparrow{}(P do-apply(last(P);e)))
\mwedge{} (\mforall{}e'':E. ((e'' <loc e) {}\mRightarrow{} (do-apply(last(P);e) <loc e'') {}\mRightarrow{} (\mneg{}\muparrow{}(P e''))))
supposing \muparrow{}can-apply(last(P);e))
Date html generated:
2016_05_16-PM-11_27_23
Last ObjectModification:
2016_01_17-PM-07_10_57
Theory : event-ordering
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