Nuprl Lemma : eo-strict-forward-pred?
∀[Info:Type]. ∀[eo:EO+(Info)]. ∀[e:E].
∀e1:E. (es-pred?(eo>e;e1) = if loc(e) = loc(e1) ∧b (es-eq(eo) pred(e1) e) then inr ⋅ else es-pred?(eo;e1) fi ∈ (E?))
Proof
Definitions occuring in Statement :
eo-strict-forward: eo>e,
event-ordering+: EO+(Info),
es-pred?: es-pred?(es;e),
es-pred: pred(e),
es-eq: es-eq(es),
es-loc: loc(e),
es-E: E,
eq_id: a = b,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
it: ⋅,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
unit: Unit,
apply: f a,
inr: inr x ,
union: left + right,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
top: Top,
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
false: False,
so_lambda: λ2x.t[x],
or: P ∨ Q,
so_apply: x[s],
decidable: Dec(P),
guard: {T},
es-locl: (e <loc e'),
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
band: p ∧b q,
ifthenelse: if b then t else f fi ,
deq: EqDecider(T),
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
label: ...$L... t,
exists: ∃x:A. B[x],
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
es-eq-E: e = e'
Latex:
\mforall{}[Info:Type]. \mforall{}[eo:EO+(Info)]. \mforall{}[e:E].
\mforall{}e1:E
(es-pred?(eo>e;e1)
= if loc(e) = loc(e1) \mwedge{}\msubb{} (es-eq(eo) pred(e1) e) then inr \mcdot{} else es-pred?(eo;e1) fi )
Date html generated:
2016_05_16-PM-01_17_41
Last ObjectModification:
2015_12_29-PM-02_05_01
Theory : event-ordering
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