Nuprl Lemma : primed-class-pred
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
Prior(X) es e ~ if 0 <z #(X es pred(e)) then X es pred(e) else Prior(X) es pred(e) fi supposing ¬↑first(e)
Proof
Definitions occuring in Statement :
primed-class: Prior(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 ,
lt_int: i <z j,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
apply: f a,
natural_number: $n,
universe: Type,
sqequal: s ~ t,
bag-size: #(bs)
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].
Prior(X) es e \msim{} if 0 <z \#(X es pred(e)) then X es pred(e) else Prior(X) es pred(e) fi
supposing \mneg{}\muparrow{}first(e)
Date html generated:
2016_05_17-AM-06_34_18
Last ObjectModification:
2015_12_29-AM-00_31_29
Theory : event-ordering
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