Nuprl Lemma : max-f-class-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[f:A ⟶ ℤ]. ∀[X:EClass(A)]. ∀[e:E].
(v from X with maximum f[v])(e) ~ accum_list(v,e.if f[v] <z f[X(e)] then X(e) else v fi ;e.X(e);≤(X)(e))
supposing ↑e ∈b (v from X with maximum f[v])
Proof
Definitions occuring in Statement :
max-f-class: (v from X with maximum f[v]),
es-interface-predecessors: ≤(X)(e),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
accum_list: accum_list(a,x.f[a; x];x.base[x];L),
assert: ↑b,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
int: ℤ,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
max-f-class: (v from X with maximum f[v]),
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} \mBbbZ{}]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
(v from X with maximum f[v])(e) \msim{} accum\_list(v,e.if f[v] <z f[X(e)]
then X(e)
else v
fi ;e.X(e);\mleq{}(X)(e))
supposing \muparrow{}e \mmember{}\msubb{} (v from X with maximum f[v])
Date html generated:
2016_05_16-PM-11_10_48
Last ObjectModification:
2015_12_29-AM-10_32_06
Theory : event-ordering
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