{ 
[A:Type]. [B,C:A 
Type]. [eq:EqDecider(A)]. [f:a:A fp-> B[a]].
[g:a:A fp-> C[a]].
g 
f 
g
supposing x:A
(((
x 
dom(f)) 
(x dom(g)))
((B[x] r C[x]) c (f(x) = g(x)))) }
{ Proof }
Definitions occuring in Statement :
fpf-join: f g,
fpf-sub: f g,
fpf-ap: f(x),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
subtype_rel: A r B,
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
cand: A c B,
so_apply: x[s],
all: x:A. B[x],
implies: P Q,
and: P Q,
function: x:A B[x],
universe: Type,
equal: s = t,
deq: EqDecider(T)
Definitions :
eqof: eqof(d),
union: left + right,
or: P 
Q,
eq_knd: a = b,
fpf-join: f g,
axiom: Ax,
void: Void,
false: False,
limited-type: LimitedType,
intensional-universe: IType,
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
true: True,
guard: {T},
btrue: tt,
sq_type: SQType(T),
bool: 
,
list_ind: list_ind def,
reduce: reduce(f;k;as),
deq-member: deq-member(eq;x;L),
fpf-ap: f(x),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
subtype: S T,
l_member: (x l),
pair: <a, b>,
list: type List,
top: Top,
fpf-dom: x dom(f),
prop: 
,
and: P Q,
subtype_rel: A r B,
cand: A c B,
implies: P Q,
uimplies: b supposing a,
product: x:A 
B[x],
lambda: 
x.A[x],
set: {x:A| B[x]} ,
assert: b,
apply: f a,
so_apply: x[s],
so_lambda: 
x.t[x],
fpf: a:A fp-> B[a],
isect: 
x:A. B[x],
all: x:A. B[x],
deq: EqDecider(T),
fpf-sub: f g,
uall: [x:A]. B[x],
function: x:A B[x],
universe: Type,
member: t T,
equal: s = t,
CollapseTHEN: Error :CollapseTHEN,
Unfold: Error :Unfold,
tactic: Error :tactic,
rev_implies: P 
Q,
iff: P Q,
unit: Unit,
pi2: snd(t),
fpf-cap: f(x)?z,
int: 
,
bnot: 
b,
bor: p q,
band: p q,
bimplies: p q,
eq_lnk: a = b,
eq_id: a = b,
eq_str: Error :eq_str,
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_atom: eq_atom$n(x;y),
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],
infix_ap: x f y,
grp_blt: a < b,
set_blt: a < b,
null: null(as),
eq_atom: x =a y,
eq_int: (i =
j),
le_int: i z j,
lt_int: i <z j,
eq_bool: p =b q,
bfalse: ff
Lemmas :
bnot_wf,
not_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
iff_weakening_uiff,
eqtt_to_assert,
fpf-join-dom2,
fpf-sub_wf,
top_wf,
member_wf,
fpf_wf,
fpf-ap_wf,
fpf-dom_wf,
assert_wf,
subtype_rel_wf,
subtype_base_sq,
fpf-trivial-subtype-top,
l_member_wf,
assert_elim,
bool_wf,
bool_subtype_base,
deq_wf,
intensional-universe_wf,
pair_wf,
assert_witness,
false_wf,
ifthenelse_wf,
true_wf,
fpf-join_wf
\mforall{}[A:Type]. \mforall{}[B,C:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[g:a:A fp-> C[a]].
g \msubseteq{} f \moplus{} g supposing \mforall{}x:A. (((\muparrow{}x \mmember{} dom(f)) \mwedge{} (\muparrow{}x \mmember{} dom(g))) {}\mRightarrow{} ((B[x] \msubseteq{}r C[x]) c\mwedge{} (f(x) = g(x))))
Date html generated:
2011_08_10-AM-08_00_32
Last ObjectModification:
2011_06_18-AM-08_19_30
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