Nuprl Lemma : eo-forward-pred?
∀[Info:Type]. ∀[eo:EO+(Info)]. ∀[e:E].
∀e1:E. (es-pred?(eo.e;e1) = if es-eq(eo) e1 e then inr ⋅ else es-pred?(eo;e1) fi ∈ (E?))
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-pred?: es-pred?(es;e),
es-eq: es-eq(es),
es-E: E,
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,
subtype_rel: A ⊆r B,
es-pred?: es-pred?(es;e),
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
es-eq-E: e = e',
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q),
top: Top,
es-le: e ≤loc e'
Latex:
\mforall{}[Info:Type]. \mforall{}[eo:EO+(Info)]. \mforall{}[e:E].
\mforall{}e1:E. (es-pred?(eo.e;e1) = if es-eq(eo) e1 e then inr \mcdot{} else es-pred?(eo;e1) fi )
Date html generated:
2016_05_16-PM-01_08_25
Last ObjectModification:
2015_12_29-PM-01_50_53
Theory : event-ordering
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