{ 
[ste:st_exp{i:l}()]. [nu1,nu2:Atom 
SimpleType].
(ste-type(ste) nu1) = (ste-type(ste) nu2)
supposing (x
ste-freevars(ste).(nu1 x) = (nu2 x)) }
{ Proof }
Definitions occuring in Statement :
ste-type: ste-type(ste),
ste-freevars: ste-freevars(ste),
st_exp: st_exp{i:l}(),
simple_type: SimpleType,
uimplies: b supposing a,
uall: [x:A]. B[x],
apply: f a,
function: x:A B[x],
atom: Atom,
equal: s = t,
l_all: (xL.P[x])
Definitions :
st_var?: Error :st_var?,
st_const?: Error :st_const?,
st_arrow?: Error :st_arrow?,
st_arrow-domain: Error :st_arrow-domain,
simple_type_ind_st_arrow: Error :simple_type_ind_st_arrow_compseq_tag_def,
st_arrow-range: Error :st_arrow-range,
ifthenelse: if b then t else f fi ,
st_arrow: Error :st_arrow,
list-diff: list-diff(eq;as;bs),
st_exp_ind_ste_lambda: st_exp_ind_ste_lambda_compseq_tag_def,
st-ap: st-ap(st1;st2),
atom-deq: AtomDeq,
l-union: as 
bs,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
st_exp_ind_ste_ap: st_exp_ind_ste_ap_compseq_tag_def,
void: Void,
st-meaning: [[st]],
top: Top,
pi1: fst(t),
st_exp_ind_ste_const: st_exp_ind_ste_const_compseq_tag_def,
list: type List,
nil: [],
cons: [car / cdr],
eclass: EClass(A[eo; e]),
pair: <a, b>,
fpf: a:A fp-> B[a],
tl: tl(l),
hd: hd(l),
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
st_exp_ind_ste_var: st_exp_ind_ste_var_compseq_tag_def,
st_exp_ind: st_exp_ind,
product: x:A 
B[x],
st-constant: st-constant{i:l}(Info),
union: left + right,
rec: rec(x.A[x]),
limited-type: LimitedType,
ste-freevars: ste-freevars(ste),
universe: Type,
l_member: (x l),
set: {x:A| B[x]} ,
lambda: 
x.A[x],
all: x:A. B[x],
axiom: Ax,
ste-type: ste-type(ste),
apply: f a,
prop: 
,
l_all: (xL.P[x]),
so_lambda: 
x.t[x],
function: x:A B[x],
simple_type: Error :simple_type,
atom: Atom,
st_exp: st_exp{i:l}(),
uimplies: b supposing a,
equal: s = t,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
Auto: Error :Auto,
Try: Error :Try,
CollapseTHEN: Error :CollapseTHEN,
RepUR: Error :RepUR,
CollapseTHENA: Error :CollapseTHENA,
tactic: Error :tactic,
rev_implies: P 
Q,
or: P 
Q,
iff: P 
Q,
es-causle: e c e',
implies: P Q,
nat: 
,
exists: 
x:A. B[x],
cand: A c B,
guard: {T},
deq: EqDecider(T),
bool: 
,
squash: 
T,
true: True,
MaAuto: Error :MaAuto,
ParallelOp: Error :ParallelOp,
RepeatFor: Error :RepeatFor,
BHyp: Error :BHyp,
false: False,
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
btrue: tt,
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'),
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,
assert: 
b,
bnot: b,
int: 
,
unit: Unit,
D: Error :D
Lemmas :
not_functionality_wrt_iff,
member_singleton,
member-list-diff,
false_wf,
assert_of_eq_atom,
not_functionality_wrt_uiff,
assert_wf,
assert_of_bnot,
uiff_transitivity,
not_wf,
eqff_to_assert,
bool_wf,
eqtt_to_assert,
ifthenelse_wf,
eq_atom_wf,
bnot_wf,
squash_wf,
true_wf,
member-union,
nat_wf,
cons_member,
top_wf,
member_wf,
Error :simple_type_wf,
pi1_wf_top,
l_all_wf,
l_member_wf,
l_all_wf2,
st_exp_wf,
ste-freevars_wf,
uall_wf,
st-constant_wf,
subtype_rel_wf,
ste-type_wf,
st-ap_wf,
l-union_wf,
atom-deq_wf,
Error :st_arrow_wf,
list-diff_wf
\mforall{}[ste:st\_exp\{i:l\}()]. \mforall{}[nu1,nu2:Atom {}\mrightarrow{} SimpleType].
(ste-type(ste) nu1) = (ste-type(ste) nu2) supposing (\mforall{}x\mmember{}ste-freevars(ste).(nu1 x) = (nu2 x))
Date html generated:
2011_08_17-PM-05_09_50
Last ObjectModification:
2011_02_04-PM-11_03_19
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