Nuprl Lemma : eq-sm-command_wf
[Op:Type]. [eq:EqDecider(Op)]. (eq-sm-command(eq) 
EqDecider(sm-command(Op)))
Proof not projected
Definitions occuring in Statement :
eq-sm-command: eq-sm-command(eq),
sm-command: sm-command(Op),
uall: [x:A]. B[x],
member: t T,
universe: Type,
deq: EqDecider(T)
Definitions :
intensional-universe: IType,
so_lambda: 
x.t[x],
in-eclass: e 
X,
eq_knd: a = b,
fpf-dom: x dom(f),
eqof: eqof(d),
IdLnk: IdLnk,
rationals: 
,
append: as @ bs,
locl: locl(a),
Knd: Knd,
list: type List,
limited-type: LimitedType,
false: False,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
prop: 
,
rev_implies: P 
Q,
pair: <a, b>,
spread: spread def,
apply: f a,
so_apply: x[s],
implies: P 
Q,
or: P 
Q,
guard: {T},
l_member: (x 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),
fpf: a:A fp-> B[a],
subtype: S 
T,
uimplies: b supposing a,
subtype_rel: A r B,
eclass: EClass(A[eo; e]),
int: 
,
atom: Atom$n,
Id: Id,
product: x:A 
B[x],
union: left + right,
iff: P Q,
spreadn: spread3,
band: p q,
eq_int: (i =
j),
eq_id: a = b,
lambda: x.A[x],
set: {x:A| B[x]} ,
assert: 
b,
bool: 
,
function: x:A 
B[x],
all: x:A. B[x],
sm-command: sm-command(Op),
eq-sm-command: eq-sm-command(eq),
axiom: Ax,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
deq: EqDecider(T),
member: t T,
equal: s = t,
universe: Type,
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),
true: True,
pi2: snd(t),
void: Void,
top: Top,
pi1: fst(t),
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
cand: A c B,
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_exists: (
xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
sq_exists: x:{A| B[x]},
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
es-causl: (e < e'),
es-locl: (e <loc e'),
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'),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
cut-order: a (X;f) b,
path-goes-thru: x-f*-y thru i,
lg-edge: lg-edge(g;a;b),
ses-action: Action(e),
ses-legal-sequence: Legal(pas) given prvt,
decidable: Dec(P),
rev_uimplies: rev_uimplies(P;Q),
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
set_eq: =,
set_le: ,
grp_eq: =,
rng_eq: =,
eq_atom: x =a y,
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'),
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_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bnot: b,
bimplies: p q,
bor: p q,
atom: Atom,
sq_type: SQType(T),
sqequal: s ~ t,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
RepeatFor: Error :RepeatFor,
Unfold: Error :Unfold,
MaAuto: Error :MaAuto
Lemmas :
pi2_wf,
atom2_subtype_base,
int_subtype_base,
subtype_base_sq,
pi1_wf_top,
squash_wf,
Id_wf,
uiff_transitivity,
assert_of_band,
and_functionality_wrt_uiff,
assert-eq-id,
and_functionality_wrt_uiff2,
assert_of_eq_int,
decidable_wf,
decidable__assert,
top_wf,
pi1_wf,
true_wf,
sq_stable__assert,
assert_wf,
ifthenelse_wf,
false_wf,
sm-command_wf,
eq_int_wf,
band_wf,
eq_id_wf,
member_wf,
bool_wf,
iff_wf,
deq_wf,
rev_implies_wf,
intensional-universe_wf,
subtype_rel_wf
\mforall{}[Op:Type]. \mforall{}[eq:EqDecider(Op)]. (eq-sm-command(eq) \mmember{} EqDecider(sm-command(Op)))
Date html generated:
2011_10_20-PM-04_07_33
Last ObjectModification:
2011_01_25-PM-01_08_04
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