{ 
[ste:st_exp{i:l}()]. [rho:Atom 
Type]. [nu:Atom SimpleType].
[sigma1,sigma2:x:Atom st-meaning-aux(nu x; rho)].
(ste-val(ste) sigma1) = (ste-val(ste) sigma2)
supposing (x
ste-freevars(ste).(sigma1 x) = (sigma2 x)) }
{ Proof }
Definitions occuring in Statement :
ste-val: ste-val(ste),
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,
universe: Type,
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,
pi2: snd(t),
pi1: fst(t),
st_exp_ind_ste_const: st_exp_ind_ste_const_compseq_tag_def,
rev_implies: P 
Q,
or: P 
Q,
iff: P 
Q,
es-causle: e c
e',
nat: 
,
cand: A c
B,
exists: 
x:A. B[x],
implies: P Q,
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: st_exp_ind,
st_exp_ind_ste_var: st_exp_ind_ste_var_compseq_tag_def,
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),
l_member: (x l),
set: {x:A| B[x]} ,
lambda: 
x.A[x],
all: x:A. B[x],
axiom: Ax,
ste-val: ste-val(ste),
prop: 
,
member: t T,
simple_type: Error :simple_type,
function: x:A B[x],
universe: Type,
atom: Atom,
st_exp: st_exp{i:l}(),
uall: [x:A]. B[x],
uimplies: b supposing a,
isect: 
x:A. B[x],
st-meaning-aux: st-meaning-aux{i:l}(Info;st;rho),
apply: f a,
ste-type: ste-type(ste),
l_all: (xL.P[x]),
so_lambda: 
x.t[x],
equal: s = t,
Try: Error :Try,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
Unfolds: Error :Unfolds,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
tactic: Error :tactic,
st-meaning: [[st]],
RepUR: Error :RepUR,
eq_st: eq_st(st1;st2),
fpf-dom: x dom(f),
void: Void,
simple_type_ind_st_const: Error :simple_type_ind_st_const_compseq_tag_def,
st_const-ty: Error :st_const-ty,
top: Top,
st_const: Error :st_const,
false: False,
bfalse: ff,
btrue: tt,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
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: 
,
bool: 
,
unit: Unit,
MaAuto: Error :MaAuto,
guard: {T},
deq: EqDecider(T),
ParallelOp: Error :ParallelOp,
RepeatFor: Error :RepeatFor,
ORELSE: Error :ORELSE,
AllHyps: Error :AllHyps,
simple_type_ind: Error :simple_type_ind,
true: True,
it: 
,
st_var: Error :st_var,
simple_type_ind_st_var: Error :simple_type_ind_st_var_compseq_tag_def,
sqequal: s ~ t,
AssertBY: Error :AssertBY,
sq_type: SQType(T),
ycomb: Y
Lemmas :
member-list-diff,
not_functionality_wrt_iff,
member_singleton,
not_functionality_wrt_uiff,
assert_of_eq_atom,
eq_atom_wf,
subtype_base_sq,
assert-eq_st,
true_wf,
false_wf,
Error :st_var_wf,
member-union,
ifthenelse_wf,
Error :st_const_wf,
top_wf,
bool_wf,
Error :st_arrow?_wf,
assert_wf,
not_wf,
bnot_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
eqtt_to_assert,
Error :st_arrow-domain_wf,
eq_st_wf,
Error :st_arrow-range_wf,
equal-top,
l_member_wf,
cons_member,
nat_wf,
Error :simple_type_wf,
st-meaning-aux_wf,
l_all_wf2,
l_all_wf,
st_exp_wf,
ste-freevars_wf,
uall_wf,
ste-type_wf,
member_wf,
st-ap_wf,
l-union_wf,
atom-deq_wf,
Error :st_arrow_wf,
list-diff_wf
\mforall{}[ste:st\_exp\{i:l\}()]. \mforall{}[rho:Atom {}\mrightarrow{} Type]. \mforall{}[nu:Atom {}\mrightarrow{} SimpleType].
\mforall{}[sigma1,sigma2:x:Atom {}\mrightarrow{} st-meaning-aux(nu x; rho)].
(ste-val(ste) sigma1) = (ste-val(ste) sigma2)
supposing (\mforall{}x\mmember{}ste-freevars(ste).(sigma1 x) = (sigma2 x))
Date html generated:
2011_08_17-PM-05_10_38
Last ObjectModification:
2011_02_05-AM-00_02_07
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