Nuprl Lemma : es-local-pred-cases
∀[Info:Type]
∀es:EO+(Info). ∀e:E. ∀P:{e':E| (e' <loc e)} ⟶ 𝔹.
(¬↑first(e))
∧ (((↑(P pred(e))) ∧ (do-apply(last(P);e) = pred(e) ∈ E))
∨ ((¬↑(P pred(e))) ∧ (↑can-apply(last(P);pred(e))) ∧ (do-apply(last(P);e) = do-apply(last(P);pred(e)) ∈ 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-first: first(e),
es-pred: pred(e),
es-E: E,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
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],
uimplies: b supposing a,
implies: P ⇒ Q,
and: P ∧ Q,
or: P ∨ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
prop: ℙ,
not: ¬A,
false: False,
guard: {T},
can-apply: can-apply(f;x),
so_lambda: λ2x.t[x],
so_apply: x[s],
isl: isl(x),
sq_exists: ∃x:{A| B[x]},
do-apply: do-apply(f;x),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
bool: 𝔹
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}P:\{e':E| (e' <loc e)\} {}\mrightarrow{} \mBbbB{}.
(\mneg{}\muparrow{}first(e))
\mwedge{} (((\muparrow{}(P pred(e))) \mwedge{} (do-apply(last(P);e) = pred(e)))
\mvee{} ((\mneg{}\muparrow{}(P pred(e)))
\mwedge{} (\muparrow{}can-apply(last(P);pred(e)))
\mwedge{} (do-apply(last(P);e) = do-apply(last(P);pred(e)))))
supposing \muparrow{}can-apply(last(P);e)
Date html generated:
2016_05_16-PM-11_28_03
Last ObjectModification:
2015_12_29-AM-10_21_59
Theory : event-ordering
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