{ 
[st1,st2:SimpleType]. (
st-similar(st1;st2) 
st-similar(st2;st1)) }
{ Proof }
Definitions occuring in Statement :
st-similar: st-similar(st1;st2),
simple_type: SimpleType,
assert: b,
uall: [x:A]. B[x],
iff: P Q
Definitions :
st_class: st_class(kind),
st_list: st_list(kind),
st_union: st_union(left;right),
st_prod: st_prod(fst;snd),
eq_bool: p =b q,
lt_int: i <z j,
le_int: i 
z j,
eq_int: (i =
j),
st_arrow: st_arrow(domain;range),
st_const: st_const(ty),
limited-type: LimitedType,
st_class-kind: st_class-kind(x),
st_class?: st_class?(x),
simple_type_ind_st_class: simple_type_ind_st_class_compseq_tag_def,
st_list-kind: st_list-kind(x),
st_list?: st_list?(x),
simple_type_ind_st_list: simple_type_ind_st_list_compseq_tag_def,
st_union-right: st_union-right(x),
st_union-left: st_union-left(x),
st_union?: st_union?(x),
simple_type_ind_st_union: simple_type_ind_st_union_compseq_tag_def,
st_prod-snd: st_prod-snd(x),
st_prod-fst: st_prod-fst(x),
st_prod?: st_prod?(x),
simple_type_ind_st_prod: simple_type_ind_st_prod_compseq_tag_def,
st_arrow-range: st_arrow-range(x),
st_arrow-domain: st_arrow-domain(x),
st_arrow?: st_arrow?(x),
simple_type_ind_st_arrow: simple_type_ind_st_arrow_compseq_tag_def,
st_const?: st_const?(x),
simple_type_ind_st_const: simple_type_ind_st_const_compseq_tag_def,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
apply: f a,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (x
L.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bnot: 
b,
bimplies: p q,
band: p 
q,
bor: p 
q,
guard: {T},
sq_type: SQType(T),
btrue: tt,
bool: 
,
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: A,
less_than: a < b,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
st_var-name: st_var-name(x),
st_var?: st_var?(x),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
simple_type_ind_st_var: simple_type_ind_st_var_compseq_tag_def,
simple_type_ind: simple_type_ind,
st_var: st_var(name),
set: {x:A| B[x]} ,
atom: Atom,
union: left + right,
rec: rec(x.A[x]),
universe: Type,
prop: 
,
all: x:A. B[x],
st-similar: st-similar(st1;st2),
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
true: True,
false: False,
void: Void,
simple_type: SimpleType,
iff: P Q,
and: P Q,
product: x:A 
B[x],
pair: <a, b>,
lambda: 
x.A[x],
assert: b,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
implies: P Q,
function: x:A 
B[x],
member: t T,
equal: s = t,
rev_implies: P Q,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
Complete: Error :Complete,
RepUR: Error :RepUR,
CollapseTHENA: Error :CollapseTHENA
Lemmas :
eqtt_to_assert,
eq_atom_wf,
assert_elim,
bool_wf,
assert_of_eq_atom,
bool_subtype_base,
subtype_base_sq,
true_wf,
ifthenelse_wf,
false_wf,
assert_wf,
simple_type_wf,
iff_wf,
st-similar_wf,
assert_witness,
iff_functionality_wrt_iff,
iff_weakening_uiff,
band_wf,
assert_of_band
\mforall{}[st1,st2:SimpleType]. (\muparrow{}st-similar(st1;st2) \mLeftarrow{}{}\mRightarrow{} \muparrow{}st-similar(st2;st1))
Date html generated:
2011_08_17-PM-04_55_50
Last ObjectModification:
2011_02_07-PM-09_12_45
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