{ 
[P:ClassDerivation 
']
((args:BaseDef. P[cdvbase(args)])
(fst,snd:ClassDerivation. (P[fst] P[snd] P[cdvpair(fst;snd)]))
(X:ClassDerivation. dummy:Unit. (P[X] P[cdvdelay(X;dummy)]))
([typ,argtype:Type].
arg:ClassDerivation. fun:argtype bag(typ).
(P[arg] P[cdvcomb(typ;argtype;arg;fun)]))
([typ,argtype:Type].
arg:ClassDerivation. fun:argtype bag(typ) bag(typ).
(P[arg] P[cdvreccomb(typ;argtype;arg;fun)]))
{x:ClassDerivation. P[x]}) }
{ Proof }
Definitions occuring in Statement :
cdvreccomb: cdvreccomb(typ;argtype;arg;fun),
cdvcomb: cdvcomb(typ;argtype;arg;fun),
cdvdelay: cdvdelay(X;dummy),
cdvpair: cdvpair(fst;snd),
cdvbase: cdvbase(args),
classderiv: ClassDerivation,
base-deriv: BaseDef,
uall: [x:A]. B[x],
prop: ,
guard: {T},
so_apply: x[s],
all: x:A. B[x],
implies: P Q,
unit: Unit,
function: x:A B[x],
universe: Type,
bag: bag(T)
Definitions :
natural_number: $n,
it: 
,
pair: <a, b>,
inr: inr x ,
fpf: a:A fp-> B[a],
name: Name,
decision: Decision,
inl: inl x ,
int: 
,
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,
list: type List,
set: {x:A| B[x]} ,
top: Top,
true: True,
type-monotone: Monotone(T.F[T]),
union: left + right,
cdvbase: cdvbase(args),
cdvpair: cdvpair(fst;snd),
cdvdelay: cdvdelay(X;dummy),
cdvcomb: cdvcomb(typ;argtype;arg;fun),
cdvreccomb: cdvreccomb(typ;argtype;arg;fun),
lambda: 
x.A[x],
equal: s = t,
member: t 
T,
strong-subtype: strong-subtype(A;B),
rec: rec(x.A[x]),
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,
bag: bag(T),
so_lambda: 
x.t[x],
unit: Unit,
guard: {T},
uall: [x:A]. B[x],
isect: x:A. B[x],
universe: Type,
base-deriv: BaseDef,
so_apply: x[s],
apply: f a,
classderiv: ClassDerivation,
prop: ,
implies: P Q,
all: x:A. B[x],
function: x:A B[x]
Lemmas :
cdvpair_wf,
classderiv_wf,
cdvdelay_wf,
unit_wf,
cdvcomb_wf,
bag_wf,
uall_wf,
cdvreccomb_wf,
base-deriv_wf,
cdvbase_wf,
type-monotone_wf,
subtype_rel_wf,
subtype_rel_sum,
subtype_rel_simple_product,
subtype_rel_product,
member_wf,
it_wf
\mforall{}[P:ClassDerivation {}\mrightarrow{} \mBbbP{}']
((\mforall{}args:BaseDef. P[cdvbase(args)])
{}\mRightarrow{} (\mforall{}fst,snd:ClassDerivation. (P[fst] {}\mRightarrow{} P[snd] {}\mRightarrow{} P[cdvpair(fst;snd)]))
{}\mRightarrow{} (\mforall{}X:ClassDerivation. \mforall{}dummy:Unit. (P[X] {}\mRightarrow{} P[cdvdelay(X;dummy)]))
{}\mRightarrow{} (\mforall{}[typ,argtype:Type].
\mforall{}arg:ClassDerivation. \mforall{}fun:argtype {}\mrightarrow{} bag(typ).
(P[arg] {}\mRightarrow{} P[cdvcomb(typ;argtype;arg;fun)]))
{}\mRightarrow{} (\mforall{}[typ,argtype:Type].
\mforall{}arg:ClassDerivation. \mforall{}fun:argtype {}\mrightarrow{} bag(typ) {}\mrightarrow{} bag(typ).
(P[arg] {}\mRightarrow{} P[cdvreccomb(typ;argtype;arg;fun)]))
{}\mRightarrow{} \{\mforall{}x:ClassDerivation. P[x]\})
Date html generated:
2011_08_17-PM-04_23_39
Last ObjectModification:
2011_06_18-AM-11_35_26
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