Nuprl Lemma : prior-val-pred
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
(X)' es e ~ if pred(e) ∈b X then {X(pred(e))} else (X)' es pred(e) fi supposing ¬↑first(e)
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
apply: f a,
universe: Type,
sqequal: s ~ t,
single-bag: {x}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
not: ¬A,
false: False,
bfalse: ff,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(X)' es e \msim{} if pred(e) \mmember{}\msubb{} X then \{X(pred(e))\} else (X)' es pred(e) fi supposing \mneg{}\muparrow{}first(e)
Date html generated:
2016_05_17-AM-06_34_02
Last ObjectModification:
2015_12_29-AM-00_32_05
Theory : event-ordering
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