{ 
U:Atom 
SimpleType. st:SimpleType. x:Atom.
((x 
st-vars(st))
((st-rank(st-subst(U;st_var(x))) 
st-rank(st-subst(U;st)))
((
st_var?(st))
(st-rank(st-subst(U;st_var(x))) < st-rank(st-subst(U;st)))))) }
{ Proof }
Definitions occuring in Statement :
st-subst: st-subst(subst;st),
st-vars: st-vars(st),
st-rank: st-rank(st),
st_var?: st_var?(x),
st_var: st_var(name),
simple_type: SimpleType,
assert: b,
le: A B,
all: x:A. B[x],
not: A,
implies: P Q,
and: P Q,
less_than: a < b,
function: x:A B[x],
atom: Atom,
l_member: (x l)
Definitions :
simple_type_ind_st_class: simple_type_ind_st_class_compseq_tag_def,
simple_type_ind_st_list: simple_type_ind_st_list_compseq_tag_def,
simple_type_ind_st_union: simple_type_ind_st_union_compseq_tag_def,
simple_type_ind_st_prod: simple_type_ind_st_prod_compseq_tag_def,
natural_number: $n,
add: n + m,
lt_int: i <z j,
bfalse: ff,
suptype: suptype(S; T),
limited-type: LimitedType,
btrue: tt,
eq_int: (i =
j),
eq_atom: x =a y,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
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',
bimplies: p q,
band: p q,
bor: p 
q,
le_int: i z j,
bnot: b,
unit: Unit,
bool: 
,
imax: imax(a;b),
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
uiff: uiff(P;Q),
cand: A c B,
atom-deq: AtomDeq,
simple_type_ind_st_arrow: simple_type_ind_st_arrow_compseq_tag_def,
simple_type_ind_st_const: simple_type_ind_st_const_compseq_tag_def,
real: 
,
grp_car: |g|,
subtype: S 
T,
nat: 
,
int: 
,
void: Void,
false: False,
true: True,
subtype_rel: A r B,
sq_type: SQType(T),
IdLnk: IdLnk,
Id: Id,
rationals: 
,
apply: f a,
so_apply: x[s],
or: P Q,
append: as @ bs,
guard: {T},
locl: locl(a),
Knd: Knd,
uimplies: b supposing a,
exists: x:A. B[x],
iff: P 
Q,
l-union: as 
bs,
list: type List,
nil: [],
cons: [car / cdr],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
prop: 
,
st_var?: st_var?(x),
st-rank: st-rank(st),
st-vars: st-vars(st),
set: {x:A| B[x]} ,
union: left + right,
rec: rec(x.A[x]),
simple_type_ind_st_var: simple_type_ind_st_var_compseq_tag_def,
st-subst: st-subst(subst;st),
universe: Type,
equal: s = t,
member: t T,
all: x:A. B[x],
and: P Q,
product: x:A 
B[x],
implies: P Q,
less_than: a < b,
not: A,
assert: b,
le: A B,
l_member: (x l),
atom: Atom,
simple_type: SimpleType,
function: x:A B[x],
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
Unfold: Error :Unfold,
Try: Error :Try,
ORELSE: Error :ORELSE,
CollapseTHENA: Error :CollapseTHENA,
RepUR: Error :RepUR,
D: Error :D,
RepeatFor: Error :RepeatFor
Lemmas :
member_wf,
l_member_wf,
simple_type_wf,
st-subst_wf,
nat_wf,
st-rank_wf,
le_wf,
assert_wf,
bool_wf,
assert_of_le_int,
eqtt_to_assert,
uiff_transitivity,
member-union,
st-vars_wf,
atom-deq_wf,
l-union_wf,
nil_member,
true_wf,
not_wf,
false_wf,
atom_subtype_base,
subtype_base_sq,
member_singleton,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
lt_int_wf,
bnot_wf,
le_int_wf
\mforall{}U:Atom {}\mrightarrow{} SimpleType. \mforall{}st:SimpleType. \mforall{}x:Atom.
((x \mmember{} st-vars(st))
{}\mRightarrow{} ((st-rank(st-subst(U;st\_var(x))) \mleq{} st-rank(st-subst(U;st)))
\mwedge{} ((\mneg{}\muparrow{}st\_var?(st)) {}\mRightarrow{} (st-rank(st-subst(U;st\_var(x))) < st-rank(st-subst(U;st))))))
Date html generated:
2011_08_17-PM-04_54_31
Last ObjectModification:
2011_02_08-PM-12_16_09
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