{ 
[Info,A,B,C,D:Type]. [X:EClass(A)]. [Y:EClass(B)]. [f:A 
B 
C].
[g:A D C]. [h:B D].
(f[p] where p from X;Y) = (g[p] where p from X;(h[y] where y from Y))
supposing a:A. b:B. (f[<a, b>] = g[<a, h[b]>]) }
{ Proof }
Definitions occuring in Statement :
es-interface-pair-prior: X;Y,
map-class: (f[v] where v from X),
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
function: x:A B[x],
pair: <a, b>,
product: x:A B[x],
universe: Type,
equal: s = t
Definitions :
fpf-dom: x 
dom(f),
guard: {T},
cand: A c
B,
rev_uimplies: rev_uimplies(P;Q),
es-prior-val: (X)',
sqequal: s ~ t,
es-prior-interface: prior(X),
exists: 
x:A. B[x],
es-interface-at: X@i,
intensional-universe: IType,
tag-by: zT,
or: P 
Q,
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 
T2,
b-union: A 
B,
list: type List,
fpf-cap: f(x)?z,
record: record(x.T[x]),
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,
squash: 
T,
sq_stable: SqStable(P),
es-local-pred: last(P),
eclass-val: X(e),
true: True,
rev_implies: P 
Q,
iff: P 
Q,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
es-E-interface: E(X),
bag: bag(T),
natural_number: $n,
void: Void,
record-select: r.x,
set: {x:A| B[x]} ,
dep-isect: Error :dep-isect,
record+: record+,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
false: False,
bfalse: ff,
btrue: tt,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
eq_atom: x =a y,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$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_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,
in-eclass: e X,
assert: 
b,
bnot: 
b,
int: 
,
unit: Unit,
union: left + right,
implies: P Q,
bool: 
,
eclass-compose1: f o X,
es-filter-image: f[X],
sv-class: Singlevalued(X),
subtype: S T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: 
x.A[x],
limited-type: LimitedType,
top: Top,
so_lambda: 
x.t[x],
pair: <a, b>,
fpf: a:A fp-> B[a],
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,
axiom: Ax,
es-interface-pair-prior: X;Y,
apply: f a,
so_apply: x[s],
map-class: (f[v] where v from X),
prop: 
,
all: x:A. B[x],
product: x:A B[x],
function: x:A B[x],
uimplies: b supposing a,
equal: s = t,
universe: Type,
uall: [x:A]. B[x],
member: t T,
eclass: EClass(A[eo; e]),
so_lambda: x y.t[x; y],
isect: x:A. B[x],
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
Complete: Error :Complete,
Try: Error :Try,
Auto: Error :Auto
Lemmas :
es-E_wf,
le_wf,
event-ordering+_wf,
sv-class_wf,
map-class_wf,
es-interface-pair-prior_wf,
es-interface-extensionality,
event-ordering+_inc,
eclass_wf,
bool_wf,
eqtt_to_assert,
assert_wf,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
in-eclass_wf,
member_wf,
subtype_rel_wf,
es-interface-top,
es-interface-subtype_rel2,
es-base-E_wf,
subtype_rel_self,
top_wf,
false_wf,
ifthenelse_wf,
true_wf,
sq_stable__assert,
intensional-universe_wf,
is-map-class,
is-pair-prior,
eclass-val_wf,
map-class-val,
pair-prior-val,
es-prior-val_wf
\mforall{}[Info,A,B,C,D:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[f:A \mtimes{} B {}\mrightarrow{} C]. \mforall{}[g:A \mtimes{} D {}\mrightarrow{} C]. \mforall{}[h:B {}\mrightarrow{} D].
(f[p] where p from X;Y) = (g[p] where p from X;(h[y] where y from Y))
supposing \mforall{}a:A. \mforall{}b:B. (f[<a, b>] = g[<a, h[b]>])
Date html generated:
2011_08_16-PM-05_39_16
Last ObjectModification:
2011_06_20-AM-01_29_23
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