{ 
[U:Atom 
SimpleType]. [x:Atom]. [st:SimpleType].
st-unifies(U;st_var(x);st) ~ ff
supposing (x 
st-vars(st)) 
(
st_var?(st)) }
{ Proof }
Definitions occuring in Statement :
st-unifies: st-unifies(U;st1;st2),
st-vars: st-vars(st),
st_var?: st_var?(x),
st_var: st_var(name),
simple_type: SimpleType,
assert: b,
bfalse: ff,
uimplies: b supposing a,
uall: [x:A]. B[x],
not: A,
and: P Q,
function: x:A B[x],
atom: Atom,
sqequal: s ~ t,
l_member: (x l)
Definitions :
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
subtype: S 
T,
suptype: suptype(S; T),
set: {x:A| B[x]} ,
rev_uimplies: rev_uimplies(P;Q),
st_var: st_var(name),
st-subst: st-subst(subst;st),
eq_bool: p =b q,
lt_int: i <z j,
le_int: i 
z j,
eq_int: (i =
j),
eq_atom: x =a y,
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: (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',
st-similar: st-similar(st1;st2),
bimplies: p 
q,
band: p q,
bnot: b,
bor: p 
q,
st-vars: st-vars(st),
eclass: EClass(A[eo; e]),
bfalse: ff,
pair: <a, b>,
fpf: a:A fp-> B[a],
void: Void,
false: False,
st_var?: st_var?(x),
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),
simple_type_ind_st_var: simple_type_ind_st_var_compseq_tag_def,
st_var-name: st_var-name(x),
exists: x:A. B[x],
rec: rec(x.A[x]),
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
less_than: a < b,
uiff: uiff(P;Q),
guard: {T},
implies: P Q,
universe: Type,
equal: s = t,
sq_type: SQType(T),
bool: 
,
st-unifies: st-unifies(U;st1;st2),
subtype_rel: A r B,
all: x:A. B[x],
function: x:A B[x],
product: x:A 
B[x],
not: A,
assert: b,
l_member: (x l),
prop: 
,
and: P Q,
atom: Atom,
uimplies: b supposing a,
sqequal: s ~ t,
uall: [x:A]. B[x],
member: t T,
simple_type: SimpleType,
isect: 
x:A. B[x],
Auto: Error :Auto,
D: Error :D,
THENM: Error :THENM,
CollapseTHEN: Error :CollapseTHEN,
RepUR: Error :RepUR,
tactic: Error :tactic,
st-rank: st-rank(st),
natural_number: $n,
RepeatFor: Error :RepeatFor,
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,
add: n + m,
limited-type: LimitedType,
btrue: tt,
unit: Unit,
imax: imax(a;b),
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|,
nat: 
,
int: 
,
true: True,
IdLnk: IdLnk,
Id: Id,
rationals: 
,
so_apply: x[s],
or: P Q,
append: as @ bs,
locl: locl(a),
Knd: Knd,
iff: P 
Q,
l-union: as 
bs,
list: type List,
nil: [],
cons: [car / cdr],
union: left + right,
Unfold: Error :Unfold,
Try: Error :Try,
ORELSE: Error :ORELSE,
CollapseTHENA: Error :CollapseTHENA,
base: Base,
so_lambda: 
x.t[x]
Lemmas :
rec_subtype_base,
base_wf,
subtype_rel_wf,
product_subtype_base,
union_subtype_base,
st-subst-rank,
nat_wf,
st-rank_wf,
le_wf,
assert_of_le_int,
eqtt_to_assert,
uiff_transitivity,
member-union,
atom-deq_wf,
l-union_wf,
nil_member,
true_wf,
atom_subtype_base,
member_singleton,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
lt_int_wf,
bnot_wf,
le_int_wf,
st-similar-rank,
l_member_wf,
st-vars_wf,
st_var_wf,
simple_type_wf,
member_wf,
st-subst_wf,
st-similar_wf,
assert_wf,
false_wf,
not_wf,
assert_of_bnot,
eqff_to_assert,
st_var?_wf,
bfalse_wf,
st-unifies_wf,
bool_wf,
bool_subtype_base,
subtype_base_sq
\mforall{}[U:Atom {}\mrightarrow{} SimpleType]. \mforall{}[x:Atom]. \mforall{}[st:SimpleType].
st-unifies(U;st\_var(x);st) \msim{} ff supposing (x \mmember{} st-vars(st)) \mwedge{} (\mneg{}\muparrow{}st\_var?(st))
Date html generated:
2011_08_17-PM-04_58_38
Last ObjectModification:
2011_02_08-PM-12_17_15
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