{ 
[Info,T:Type]. [X:EClass(T)]. Prior(X) = (X)' supposing Singlevalued(X) }
{ Proof }
Definitions occuring in Statement :
es-prior-val: (X)',
primed-class: Prior(X),
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
uall: [x:A]. B[x],
universe: Type,
equal: s = t
Definitions :
record-select: r.x,
set: {x:A| B[x]} ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: 
b,
apply: f a,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
dep-isect: Error :dep-isect,
record+: record+,
bag: bag(T),
subtype: S 
T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: 
x.A[x],
top: Top,
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
void: Void,
false: False,
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
function: x:A 
B[x],
all: x:A. B[x],
uall: [x:A]. B[x],
uimplies: b supposing a,
so_lambda: 
x y.t[x; y],
prop: 
,
isect: 
x:A. B[x],
axiom: Ax,
primed-class: Prior(X),
es-prior-val: (X)',
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
universe: Type,
member: t 
T,
equal: s = t,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
Try: Error :Try,
RepeatFor: Error :RepeatFor,
Unfold: Error :Unfold,
tactic: Error :tactic,
es-local-pred: last(P),
eclass-val: X(e),
in-eclass: e 
X,
local-pred-class: local-pred-class(P),
es-prior-interface: prior(X),
RepUR: Error :RepUR,
empty-bag: {},
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
bag-only: only(bs),
single-bag: {x},
bag_only_single: bag_only_single{bag_only_single_compseq_tag_def:o}(x),
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
eq_int: (i =
j),
cand: A c B,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
infix_ap: x f y,
es-causl: (e < e'),
bool: 
,
real: 
,
grp_car: |g|,
int: 
,
nat: 
,
bag-size: bag-size(bs),
natural_number: $n,
lt_int: i <z j,
or: P 
Q,
union: left + right,
sq_exists: 
x:{A| B[x]},
implies: P 
Q,
es-locl: (e <loc e'),
D: Error :D,
MaAuto: Error :MaAuto,
CollapseTHENA: Error :CollapseTHENA,
record: record(x.T[x]),
so_lambda: x.t[x],
sq_type: SQType(T),
Subst': Error :Subst',
ExRepD: Error :ExRepD,
es-loc: loc(e),
Id: Id,
rev_uimplies: rev_uimplies(P;Q),
le_int: i z j,
bor: p q,
band: p q,
bimplies: p q,
bnot: b,
es-ble: e loc e',
es-bless: e <loc e',
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_type: eq_type(T;T'),
b-exists: (i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
grp_blt: a < b,
set_blt: a < b,
null: null(as),
Complete: Error :Complete,
THENM: Error :THENM,
it: 
,
true: True,
bfalse: ff,
limited-type: LimitedType,
btrue: tt,
unit: Unit,
squash: 
T,
guard: {T},
rev_implies: P 
Q,
iff: P Q,
sqequal: s ~ t,
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
exists: x:A. B[x],
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
decidable: Dec(P),
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
inject: Inj(A;B;f),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
value-type: value-type(T),
valueall-type: valueall-type(T),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
sq_stable: SqStable(P),
nequal: a 
b T
Lemmas :
nequal_wf,
neg_assert_of_eq_int,
rev_implies_wf,
iff_wf,
all_functionality_wrt_iff,
eq_int_eq_true,
sq_stable__not,
sq_stable__all,
sq_stable__assert,
sq_stable__and,
decidable__es-locl,
sq_stable_from_decidable,
sq_stable_wf,
bag-size-one,
bool_subtype_base,
not_functionality_wrt_uiff,
assert_of_bnot,
uiff_transitivity,
eqff_to_assert,
eqtt_to_assert,
squash_wf,
assert_functionality_wrt_uiff,
iff_weakening_uiff,
implies_functionality_wrt_iff,
sv-class-iff,
bnot_wf,
assert_elim,
false_wf,
ifthenelse_wf,
true_wf,
assert_of_eq_int,
assert_of_lt_int,
es-loc_wf,
es-locl-total,
Id_wf,
subtype_base_sq,
set_subtype_base,
assert_wf,
not_wf,
es-locl_wf,
lt_int_wf,
nat_wf,
bag-size_wf,
es-local-pred_wf,
bool_wf,
es-base-E_wf,
subtype_rel_self,
eq_int_wf,
bag-only_wf,
single-bag_wf,
empty-bag_wf,
es-E_wf,
bag_wf,
eclass_wf,
es-prior-val_wf,
primed-class_wf,
es-interface-top,
subtype_rel_wf,
event-ordering+_wf,
member_wf,
event-ordering+_inc,
sv-class_wf
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. Prior(X) = (X)' supposing Singlevalued(X)
Date html generated:
2011_08_16-PM-04_50_46
Last ObjectModification:
2011_06_20-AM-01_08_42
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