{ 
st1,st2:SimpleType.
((U:Atom 
SimpleType. st-unifies(U;st1;st2) = ff)
(
L:({st:SimpleType| 
st_var?(st)} 
SimpleType) List
U:Atom SimpleType. st-unifies(U;st1;st2) = st-unifies-all(U;L))) }
{ Proof }
Definitions occuring in Statement :
st-unifies-all: st-unifies-all(U;L),
st-unifies: st-unifies(U;st1;st2),
st_var?: st_var?(x),
simple_type: SimpleType,
assert: b,
bfalse: ff,
bool: 
,
all: x:A. B[x],
exists: x:A. B[x],
or: P Q,
set: {x:A| B[x]} ,
function: x:A B[x],
product: x:A B[x],
list: type List,
atom: Atom,
equal: s = t
Definitions :
so_lambda: 
x.t[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_lambda: x y.t[x; y],
fpf-dom: x 
dom(f),
bnot: 
b,
st_class: st_class(kind),
simple_type_ind_st_class: simple_type_ind_st_class_compseq_tag_def,
st_class-kind: st_class-kind(x),
st_list: st_list(kind),
simple_type_ind_st_list: simple_type_ind_st_list_compseq_tag_def,
st_list-kind: st_list-kind(x),
st_union: st_union(left;right),
st_union-left: st_union-left(x),
simple_type_ind_st_union: simple_type_ind_st_union_compseq_tag_def,
st_union-right: st_union-right(x),
st_prod: st_prod(fst;snd),
st_prod-fst: st_prod-fst(x),
simple_type_ind_st_prod: simple_type_ind_st_prod_compseq_tag_def,
st_prod-snd: st_prod-snd(x),
st_arrow: st_arrow(domain;range),
st_arrow-domain: st_arrow-domain(x),
simple_type_ind_st_arrow: simple_type_ind_st_arrow_compseq_tag_def,
st_arrow-range: st_arrow-range(x),
void: Void,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
simple_type_ind: simple_type_ind,
st-similar: st-similar(st1;st2),
st-subst: st-subst(subst;st),
simple_type_ind_st_const: simple_type_ind_st_const_compseq_tag_def,
st_const-ty: st_const-ty(x),
inr: inr x ,
decision: Decision,
apply: f a,
inl: inl x ,
btrue: tt,
sq_type: SQType(T),
tag-by: zT,
ldag: LabeledDAG(T),
labeled-graph: LabeledGraph(T),
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 
T2,
b-union: A 
B,
bag: bag(T),
top: Top,
fpf-cap: f(x)?z,
filter: filter(P;l),
l_member: (x l),
es-E-interface: E(X),
st_const: st_const(ty),
subtype: S 
T,
rev_implies: P 
Q,
implies: P 
Q,
iff: P Q,
band: p 
q,
lambda: x.A[x],
bl-all: (xL.P[x])_b,
eclass: EClass(A[eo; e]),
st-unifies-all: st-unifies-all(U;L),
fpf: a:A fp-> B[a],
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),
simple_type_ind_st_var: simple_type_ind_st_var_compseq_tag_def,
st_var-name: st_var-name(x),
true: True,
prop: 
,
false: False,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
st_var?: st_var?(x),
bfalse: ff,
st-unifies: st-unifies(U;st1;st2),
guard: {T},
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: A,
less_than: a < b,
uimplies: b supposing a,
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
isect: x:A. B[x],
uall: [x:A]. B[x],
universe: Type,
rec: rec(x.A[x]),
member: t T,
list: type List,
product: x:A B[x],
set: {x:A| B[x]} ,
assert: b,
or: P Q,
union: left + right,
all: x:A. B[x],
equal: s = t,
bool: ,
function: x:A B[x],
simple_type: SimpleType,
atom: Atom,
exists: x:A. B[x],
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
nil: [],
pair: <a, b>,
cons: [car / cdr],
Complete: Error :Complete,
Try: Error :Try,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
st_var: st_var(name),
tactic: Error :tactic,
RepUR: Error :RepUR,
RepeatFor: Error :RepeatFor,
ParallelOp: Error :ParallelOp,
THENM: Error :THENM,
suptype: suptype(S; T),
st-vars: st-vars(st),
append: as @ bs,
ExRepD: Error :ExRepD
Lemmas :
st-unifies-all-append,
append_wf,
st-subst_wf,
st-vars_wf,
st-similar_wf,
band_ff_simp,
false_wf,
assert_wf,
true_wf,
st_var?_wf,
ifthenelse_wf,
simple_type_wf,
st_var_wf,
bool_wf,
bfalse_wf,
st-unifies_wf,
st-unifies-all_wf,
iff_wf,
rev_implies_wf,
band_tt_simp,
member_wf,
st_const_wf,
subtype_rel_wf,
list-subtype,
l_member_wf,
subtype_base_sq,
bool_subtype_base,
btrue_wf,
st_const?_wf,
st-unifies_inversion,
band_wf,
st_arrow_wf,
st_prod_wf,
st_union_wf,
st_list_wf,
st_class_wf
\mforall{}st1,st2:SimpleType.
((\mforall{}U:Atom {}\mrightarrow{} SimpleType. st-unifies(U;st1;st2) = ff)
\mvee{} (\mexists{}L:(\{st:SimpleType| \muparrow{}st\_var?(st)\} \mtimes{} SimpleType) List
\mforall{}U:Atom {}\mrightarrow{} SimpleType. st-unifies(U;st1;st2) = st-unifies-all(U;L)))
Date html generated:
2011_08_17-PM-05_00_31
Last ObjectModification:
2011_02_08-AM-00_50_24
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