Nuprl Lemma : imax-class-val
∀[Info,T:Type]. ∀[f:T ⟶ ℤ]. ∀[es:EO+(Info)]. ∀[lb:ℤ]. ∀[X:EClass(T)]. ∀[e:E(X)].
((maximum f[v] ≥ lb with v from X)(e) = imax-list([lb / map(λv.f[v];X(≤(X)(e)))]) ∈ ℤ)
Proof
Definitions occuring in Statement :
imax-class: (maximum f[v] ≥ lb with v from X),
es-interface-predecessors: ≤(X)(e),
eclass-vals: X(L),
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
imax-list: imax-list(L),
map: map(f;as),
cons: [a / b],
uall: ∀[x:A]. B[x],
so_apply: x[s],
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
imax-class: (maximum f[v] ≥ lb with v from X),
subtype_rel: A ⊆r B,
top: Top,
es-E-interface: E(X),
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
eclass-vals: X(L),
imax-list: imax-list(L),
compose: f o g,
combine-list: combine-list(x,y.f[x; y];L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_apply: x[s],
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True
Latex:
\mforall{}[Info,T:Type]. \mforall{}[f:T {}\mrightarrow{} \mBbbZ{}]. \mforall{}[es:EO+(Info)]. \mforall{}[lb:\mBbbZ{}]. \mforall{}[X:EClass(T)]. \mforall{}[e:E(X)].
((maximum f[v] \mgeq{} lb with v from X)(e) = imax-list([lb / map(\mlambda{}v.f[v];X(\mleq{}(X)(e)))]))
Date html generated:
2016_05_16-PM-11_08_36
Last ObjectModification:
2015_12_29-AM-10_35_57
Theory : event-ordering
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