{ 
[P:Pi_term]. [choice:{c:pi_prefix() 
Pi_term| (c 
pi-choices(P))} ].
(pi-rank(snd(choice)) < pi-rank(P)) }
{ Proof }
Definitions occuring in Statement :
pi-choices: pi-choices(t),
pi-rank: pi-rank(p),
pi_term: Pi_term,
pi_prefix: pi_prefix(),
uall: [x:A]. B[x],
pi2: snd(t),
less_than: a < b,
set: {x:A| B[x]} ,
product: x:A B[x],
l_member: (x l)
Definitions :
proper-iseg: L1 < L2,
iseg: l1 
l2,
gt: i > j,
union: left + right,
or: P 
Q,
pi2: snd(t),
length: ||as||,
strong-subtype: strong-subtype(A;B),
exists: 
x:A. B[x],
le: A B,
ge: i 
j ,
natural_number: $n,
not: 
A,
uimplies: b supposing a,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
pi-rank: pi-rank(p),
axiom: Ax,
less_than: a < b,
pi-choices: pi-choices(t),
universe: Type,
prop: 
,
isect: 
x:A. B[x],
all: x:A. B[x],
function: x:A 
B[x],
uall: [x:A]. B[x],
l_member: (x l),
pi_prefix: pi_prefix(),
rec: rec(x.A[x]),
set: {x:A| B[x]} ,
equal: s = t,
pi_term: Pi_term,
product: x:A B[x],
member: t T,
name: Name,
pi_term_ind_pinew: pi_term_ind_pinew_compseq_tag_def,
pi_term_ind_pirep: pi_term_ind_pirep_compseq_tag_def,
pi_term_ind_pipar: pi_term_ind_pipar_compseq_tag_def,
cand: A c B,
pi_term_ind_pioption: pi_term_ind_pioption_compseq_tag_def,
IdLnk: IdLnk,
Id: Id,
append: as @ bs,
locl: locl(a),
Knd: Knd,
sq_stable: SqStable(P),
pair: <a, b>,
cons: [car / cdr],
tl: tl(l),
hd: hd(l),
add: n + m,
pi_term_ind_picomm: pi_term_ind_picomm_compseq_tag_def,
void: Void,
apply: f a,
so_apply: x[s],
false: False,
iff: P 
Q,
assert: 
b,
list: type List,
nil: [],
pi_term_ind_pizero: pi_term_ind_pizero_compseq_tag_def,
real: 
,
grp_car: |g|,
subtype: S T,
int: 
,
nat: 
,
so_lambda: 
x.t[x],
implies: P Q,
guard: {T},
lambda: x.A[x],
D: Error :D,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
Try: Error :Try,
Unfolds: Error :Unfolds,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
tactic: Error :tactic,
atom: Atom,
sq_type: SQType(T),
THENM: Error :THENM,
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
Complete: Error :Complete,
AllHyps: Error :AllHyps
Lemmas :
subtype_rel_wf,
member_wf,
member_append,
subtype_base_sq,
union_subtype_base,
product_subtype_base,
list_subtype_base,
atom_subtype_base,
nil_member,
nat_wf,
pi2_wf,
pi_term-induction,
uiff_inversion,
member_singleton,
append_wf,
name_wf,
l_member_wf,
pi_prefix_wf,
pi_term_wf,
pi-choices_wf,
pi-rank_wf
\mforall{}[P:Pi\_term]. \mforall{}[choice:\{c:pi\_prefix() \mtimes{} Pi\_term| (c \mmember{} pi-choices(P))\} ].
(pi-rank(snd(choice)) < pi-rank(P))
Date html generated:
2011_08_17-PM-06_52_31
Last ObjectModification:
2011_06_18-PM-12_26_35
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