{ 
[P:SimpleType 
']
((name:Atom. P[st_var(name)])
(ty:Type. P[st_const(ty)])
(domain,range:SimpleType.
(P[domain] P[range] P[st_arrow(domain;range)]))
(fst,snd:SimpleType. (P[fst] P[snd] P[st_prod(fst;snd)]))
(left,right:SimpleType.
(P[left] P[right] P[st_union(left;right)]))
(kind:SimpleType. (P[kind] P[st_list(kind)]))
(kind:SimpleType. (P[kind] P[st_class(kind)]))
{x:SimpleType. P[x]}) }
{ Proof }
Definitions occuring in Statement :
st_class: st_class(kind),
st_list: st_list(kind),
st_union: st_union(left;right),
st_prod: st_prod(fst;snd),
st_arrow: st_arrow(domain;range),
st_const: st_const(ty),
st_var: st_var(name),
simple_type: SimpleType,
uall: [x:A]. B[x],
prop: ,
guard: {T},
so_apply: x[s],
all: x:A. B[x],
implies: P Q,
function: x:A B[x],
atom: Atom,
universe: Type
Definitions :
inr: inr x ,
fpf: a:A fp-> B[a],
decision: Decision,
inl: inl x ,
tag-by: z
T,
ldag: LabeledDAG(T),
labeled-graph: LabeledGraph(T),
record+: record+,
record: record(x.T[x]),
eclass: EClass(A[eo; e]),
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 
T2,
b-union: A 
B,
rev_implies: P 
Q,
or: P 
Q,
iff: P Q,
bag: bag(T),
list: type List,
set: {x:A| B[x]} ,
top: Top,
true: True,
so_lambda: 
x.t[x],
type-monotone: Monotone(T.F[T]),
union: left + right,
st_var: st_var(name),
st_const: st_const(ty),
st_arrow: st_arrow(domain;range),
st_prod: st_prod(fst;snd),
st_union: st_union(left;right),
st_list: st_list(kind),
st_class: st_class(kind),
equal: s = t,
member: t 
T,
rec: rec(x.A[x]),
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
product: x:A B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
guard: {T},
uall: [x:A]. B[x],
isect: x:A. B[x],
simple_type: SimpleType,
atom: Atom,
universe: Type,
prop: ,
all: x:A. B[x],
implies: P Q,
function: x:A B[x],
apply: f a,
so_apply: x[s]
Lemmas :
subtype_rel_simple_product,
subtype_rel_sum,
subtype_rel_wf,
uall_wf,
type-monotone_wf,
simple_type_wf,
st_var_wf,
st_const_wf,
st_arrow_wf,
st_prod_wf,
st_union_wf,
st_list_wf,
st_class_wf,
member_wf
\mforall{}[P:SimpleType {}\mrightarrow{} \mBbbP{}']
((\mforall{}name:Atom. P[st\_var(name)])
{}\mRightarrow{} (\mforall{}ty:Type. P[st\_const(ty)])
{}\mRightarrow{} (\mforall{}domain,range:SimpleType. (P[domain] {}\mRightarrow{} P[range] {}\mRightarrow{} P[st\_arrow(domain;range)]))
{}\mRightarrow{} (\mforall{}fst,snd:SimpleType. (P[fst] {}\mRightarrow{} P[snd] {}\mRightarrow{} P[st\_prod(fst;snd)]))
{}\mRightarrow{} (\mforall{}left,right:SimpleType. (P[left] {}\mRightarrow{} P[right] {}\mRightarrow{} P[st\_union(left;right)]))
{}\mRightarrow{} (\mforall{}kind:SimpleType. (P[kind] {}\mRightarrow{} P[st\_list(kind)]))
{}\mRightarrow{} (\mforall{}kind:SimpleType. (P[kind] {}\mRightarrow{} P[st\_class(kind)]))
{}\mRightarrow{} \{\mforall{}x:SimpleType. P[x]\})
Date html generated:
2011_08_17-PM-04_42_34
Last ObjectModification:
2011_02_06-PM-04_03_47
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