Nuprl Lemma : cp-test_wf
∀[T:Type]. ∀[cp:ClassProgram(T)]. ∀[i:{i:Id| (i ∈ cp-domain(cp))} ].
(cp-test(cp;i) ∈ k:{k:Knd| (k ∈ cp-kinds(cp) i)} ⟶ cp-ktype(cp;i;k) ⟶ cp-state-type(cp;i) ⟶ (T + Top))
Proof
Definitions occuring in Statement :
cp-test: cp-test(cp;i),
cp-state-type: cp-state-type(cp;i),
cp-ktype: cp-ktype(cp;i;k),
cp-kinds: cp-kinds(cp),
cp-domain: cp-domain(cp),
class-program: ClassProgram(T),
Knd: Knd,
Id: Id,
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
cp-test: cp-test(cp;i),
cp-state-type: cp-state-type(cp;i),
cp-ktype: cp-ktype(cp;i;k),
cp-kinds: cp-kinds(cp),
cp-domain: cp-domain(cp),
class-program: ClassProgram(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
fpf-domain: fpf-domain(f),
spreadn: spread6,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
sq_type: SQType(T),
guard: {T},
top: Top
Latex:
\mforall{}[T:Type]. \mforall{}[cp:ClassProgram(T)]. \mforall{}[i:\{i:Id| (i \mmember{} cp-domain(cp))\} ].
(cp-test(cp;i) \mmember{} k:\{k:Knd| (k \mmember{} cp-kinds(cp) i)\}
{}\mrightarrow{} cp-ktype(cp;i;k)
{}\mrightarrow{} cp-state-type(cp;i)
{}\mrightarrow{} (T + Top))
Date html generated:
2016_05_16-PM-00_58_16
Last ObjectModification:
2015_12_29-PM-01_43_37
Theory : event-ordering
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