{ 
[st1,st2:SimpleType]. ((
eq_st(st1;st2)) 
(st1 ~ st2)) }
{ Proof }
Definitions occuring in Statement :
eq_st: eq_st(st1;st2),
simple_type: SimpleType,
assert: b,
uall: [x:A]. B[x],
implies: P Q,
sqequal: s ~ t
Definitions :
eq_st: eq_st(st1;st2),
equal: s = t,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
rec: rec(x.A[x]),
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
and: P 
Q,
uiff: uiff(P;Q),
atom: Atom,
product: x:A 
B[x],
union: left + right,
base: Base,
universe: Type,
so_lambda: 
x.t[x],
sq_type: SQType(T),
uimplies: b supposing a,
subtype_rel: A 
r B,
all: x:A. B[x],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
lambda: x.A[x],
member: t 
T,
implies: P Q,
function: x:A 
B[x],
prop: 
,
assert: b,
simple_type: Error :simple_type,
sqequal: s ~ t,
valueall-type: valueall-type(T),
atom: Atom$n,
int: 
,
quotient: x,y:A//B[x; y],
set: {x:A| B[x]} ,
tunion: 
x:A.B[x],
b-union: A B,
list: type List,
eq_term: a == b
Lemmas :
simple_type-valueall-type,
assert-eq_term,
valueall-type_wf,
subtype_base_sq,
rec_subtype_base,
base_wf,
subtype_rel_wf,
atom_subtype_base,
union_subtype_base,
product_subtype_base,
eq_st_wf,
assert_wf,
Error :simple_type_wf
\mforall{}[st1,st2:SimpleType]. ((\muparrow{}eq\_st(st1;st2)) {}\mRightarrow{} (st1 \msim{} st2))
Date html generated:
2011_08_17-PM-04_50_36
Last ObjectModification:
2011_02_04-AM-11_34_58
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