{ 
st1,st2:SimpleType.
(st1 
st2
st2 st1
(
rename:Atom 
Atom
(Inj({a:Atom| (a 
st-vars(st2))} ;Atom;rename)
(st1 = st-subst(
a.st_var(rename a);st2))))) }
{ Proof }
Definitions occuring in Statement :
st-instance: st1 st2,
st-subst: st-subst(subst;st),
st-vars: st-vars(st),
st_var: st_var(name),
simple_type: SimpleType,
inject: Inj(A;B;f),
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
and: P Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
atom: Atom,
equal: s = t,
l_member: (x l)
Definitions :
lambda: x.A[x],
st_var: st_var(name),
apply: f a,
eq_st: eq_st(st1;st2),
subtype: S 
T,
suptype: suptype(S; T),
st-vars: st-vars(st),
st-subst: st-subst(subst;st),
sqequal: s ~ t,
member: t T,
assert: 
b,
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,
uiff: uiff(P;Q),
subtype_rel: A r B,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
st-instance: st1 st2,
exists: x:A. B[x],
and: P Q,
product: x:A 
B[x],
equal: s = t,
simple_type: SimpleType,
inject: Inj(A;B;f),
set: {x:A| B[x]} ,
l_member: (x l),
prop: 
,
universe: Type,
function: x:A B[x],
atom: Atom,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
ExRepD: Error :ExRepD,
st_var?: st_var?(x),
st_class-kind: st_class-kind(x),
st_class: st_class(kind),
simple_type_ind_st_class: simple_type_ind_st_class_compseq_tag_def,
st_list-kind: st_list-kind(x),
st_list: st_list(kind),
simple_type_ind_st_list: simple_type_ind_st_list_compseq_tag_def,
st_union-left: st_union-left(x),
st_union-right: st_union-right(x),
st_union: st_union(left;right),
simple_type_ind_st_union: simple_type_ind_st_union_compseq_tag_def,
st_prod-fst: st_prod-fst(x),
st_prod-snd: st_prod-snd(x),
st_prod: st_prod(fst;snd),
simple_type_ind_st_prod: simple_type_ind_st_prod_compseq_tag_def,
st_arrow-domain: st_arrow-domain(x),
st_arrow-range: st_arrow-range(x),
atom-deq: AtomDeq,
so_lambda: 
x.t[x],
rev_implies: P 
Q,
st_arrow: st_arrow(domain;range),
simple_type_ind_st_arrow: simple_type_ind_st_arrow_compseq_tag_def,
void: Void,
st_const-ty: st_const-ty(x),
st_const: st_const(ty),
simple_type_ind_st_const: simple_type_ind_st_const_compseq_tag_def,
pair: <a, b>,
iff: P Q,
bool: 
,
IdLnk: IdLnk,
Id: Id,
rationals: 
,
so_apply: x[s],
or: P 
Q,
append: as @ bs,
guard: {T},
locl: locl(a),
Knd: Knd,
limited-type: LimitedType,
list: type List,
tl: tl(l),
hd: hd(l),
st_const?: st_const?(x),
st_arrow?: st_arrow?(x),
st_prod?: st_prod?(x),
st_union?: st_union?(x),
st_list?: st_list?(x),
st_class?: st_class?(x),
st_var-name: st_var-name(x),
true: True,
false: False,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
nil: [],
cons: [car / cdr],
l-union: as 
bs,
simple_type_ind_st_var: simple_type_ind_st_var_compseq_tag_def,
union: left + right,
sq_type: SQType(T),
squash: 
T,
base: Base,
bfalse: ff,
btrue: tt,
fpf-dom: x dom(f),
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
cand: A c B,
lt_int: i <z j,
le_int: i z j,
nat: 
,
deq: EqDecider(T),
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',
bimplies: p 
q,
band: p q,
bor: p q,
bnot: b,
int: 
,
unit: Unit,
MaAuto: Error :MaAuto,
deq-member: deq-member(eq;x;L),
intensional-universe: IType,
natural_number: $n,
real: 
,
grp_car: |g|,
select: l[i],
length: ||as||,
fpf-cap: f(x)?z,
es-E-interface: E(X),
int_seg: {i..j
},
quotient: x,y:A//B[x; y],
divides: b | a,
assoced: a ~ b,
set_car: |p|,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
rng_car: |r|,
nat_plus: 
,
atom: Atom$n,
dstype: dstype(TypeNames; d; a),
fset: FSet{T},
MaName: MaName,
consensus-state3: consensus-state3(T),
consensus-rcv: consensus-rcv(V;A),
es-E: E,
runEvents: runEvents(r),
l_contains: A B,
cmp-le: cmp-le(cmp;x;y),
reducible: reducible(a),
prime: prime(a),
l_exists: (xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
sq_exists: x:{A| B[x]},
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
es-causl: (e < e'),
es-locl: (e <loc e'),
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
cut-order: a (X;f) b,
path-goes-thru: x-f*-y thru i,
lg-edge: lg-edge(g;a;b),
infix_ap: x f y,
decidable: Dec(P),
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
value-type: value-type(T),
valueall-type: valueall-type(T),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
sq_stable: SqStable(P),
RepeatFor: Error :RepeatFor,
it: 
,
last: last(L),
remove-repeats: remove-repeats(eq;L)
Lemmas :
l_member-set,
set_subtype_base,
sq_stable_from_decidable,
decidable__l_member,
decidable__atom_equal,
deq_wf,
nat_wf,
strong-subtype-deq-subtype,
strong-subtype_wf,
strong-subtype-set3,
strong-subtype-self,
list-subtype,
length_wf1,
select_wf,
intensional-universe_wf,
not_wf,
bnot_wf,
bool_wf,
assert-deq-member,
not_functionality_wrt_iff,
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
eqff_to_assert,
eqtt_to_assert,
st_var-name_wf,
deq-member_wf,
st_const?_wf,
bfalse_wf,
btrue_wf,
btrue_neq_bfalse,
st_class?_wf,
st_class-kind_wf,
st_list?_wf,
st_list-kind_wf,
st_union-right_wf,
st_union?_wf,
st_union-left_wf,
st_prod-snd_wf,
st_prod?_wf,
st_prod-fst_wf,
st_arrow-range_wf,
subtype_base_sq,
rec_subtype_base,
base_wf,
subtype_rel_wf,
atom_subtype_base,
product_subtype_base,
union_subtype_base,
squash_wf,
st_arrow?_wf,
st_arrow-domain_wf,
false_wf,
assert_wf,
true_wf,
st_var?_wf,
ifthenelse_wf,
st_var_wf,
member_singleton,
st_const_wf,
nil_member,
implies_functionality_wrt_iff,
iff_wf,
rev_implies_wf,
all_functionality_wrt_iff,
member-union,
st_arrow_wf,
l-union_wf,
atom-deq_wf,
st_prod_wf,
st_union_wf,
st_list_wf,
st_class_wf,
inject_wf,
st-instance_wf,
assert-eq_st,
st-subst_wf,
member_wf,
st-vars_wf,
l_member_wf,
simple_type_wf
\mforall{}st1,st2:SimpleType.
(st1 \mleq{} st2
{}\mRightarrow{} st2 \mleq{} st1
{}\mRightarrow{} (\mexists{}rename:Atom {}\mrightarrow{} Atom. (Inj(\{a:Atom| (a \mmember{} st-vars(st2))\} ;Atom;rename) \mwedge{} (st1 = st-subst(\mlambda{}a.st\_\000Cvar(rename a);st2)))))
Date html generated:
2011_08_17-PM-04_57_38
Last ObjectModification:
2011_02_07-PM-01_00_47
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