begin
definition
let X,
Y,
Z be ( ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ;
let f be ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
Y : ( ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) : ( ( ) ( non
empty )
Element of
K6( the
carrier of
(R_VectorSpace_of_LinearOperators (X : ( ( non empty V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,Y : ( ( non empty V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) )) : ( ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118() ) ( non
empty V87()
strict V112()
V113()
V114()
V115()
V116()
V117()
V118() )
L12()) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ) ) ;
let g be ( ( ) ( )
Element of
BoundedLinearOperators (
Y : ( ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
Z : ( ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) : ( ( ) ( non
empty )
Element of
K6( the
carrier of
(R_VectorSpace_of_LinearOperators (Y : ( ( non empty V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,Z : ( ( non empty V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) )) : ( ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118() ) ( non
empty V87()
strict V112()
V113()
V114()
V115()
V116()
V117()
V118() )
L12()) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ) ) ;
func g * f -> ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
NORMSTR ) ,
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
K6( the
carrier of
(R_VectorSpace_of_LinearOperators (X : ( ( ) ( ) NORMSTR ) ,Z : ( ( Function-like quasi_total ) ( V16() V19(K7(X : ( ( ) ( ) NORMSTR ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(X : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(X : ( ( ) ( ) NORMSTR ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) )) : ( ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118() ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118() )
L12()) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ) )
equals
(modetrans (g : ( ( Function-like quasi_total ) ( V16() V19(X : ( ( ) ( ) NORMSTR ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued ) Element of K6(K7(X : ( ( ) ( ) NORMSTR ) ,REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( complex-valued ext-real-valued real-valued ) set ) ) : ( ( ) ( ) set ) ) ,Y : ( ( ) ( ) Element of X : ( ( ) ( ) NORMSTR ) ) ,Z : ( ( Function-like quasi_total ) ( V16() V19(K7(X : ( ( ) ( ) NORMSTR ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(X : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(X : ( ( ) ( ) NORMSTR ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) )) : ( (
Function-like quasi_total V153(
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) ,
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
V154(
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) ,
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20( the
carrier of
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
Function-like total quasi_total V153(
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) ,
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
V154(
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) ,
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
Lipschitzian )
Element of
K6(
K7( the
carrier of
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) , the
carrier of
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
* (modetrans (f : ( ( Function-like quasi_total ) ( V16() V19(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(X : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ,X : ( ( ) ( ) NORMSTR ) ,Y : ( ( ) ( ) Element of X : ( ( ) ( ) NORMSTR ) ) )) : ( (
Function-like quasi_total V153(
X : ( ( ) ( )
NORMSTR ) ,
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) )
V154(
X : ( ( ) ( )
NORMSTR ) ,
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
X : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) )
V20( the
carrier of
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
Function-like total quasi_total V153(
X : ( ( ) ( )
NORMSTR ) ,
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) )
V154(
X : ( ( ) ( )
NORMSTR ) ,
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) )
Lipschitzian )
Element of
K6(
K7( the
carrier of
X : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) , the
carrier of
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
X : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) )
V20( the
carrier of
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
X : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) , the
carrier of
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ;
end;
definition
let X,
Y,
Z be ( ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ;
let f be ( ( ) (
V16()
Function-like )
Point of ( ( ) ( non
empty )
set ) ) ;
let g be ( ( ) (
V16()
Function-like )
Point of ( ( ) ( non
empty )
set ) ) ;
func g * f -> ( ( ) (
V16()
Function-like )
Point of ( ( ) ( non
empty )
set ) )
equals
(modetrans (g : ( ( Function-like quasi_total ) ( V16() V19(X : ( ( ) ( ) NORMSTR ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued ) Element of K6(K7(X : ( ( ) ( ) NORMSTR ) ,REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( complex-valued ext-real-valued real-valued ) set ) ) : ( ( ) ( ) set ) ) ,Y : ( ( ) ( ) Element of X : ( ( ) ( ) NORMSTR ) ) ,Z : ( ( Function-like quasi_total ) ( V16() V19(K7(X : ( ( ) ( ) NORMSTR ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(X : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(X : ( ( ) ( ) NORMSTR ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) )) : ( (
Function-like quasi_total V153(
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) ,
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
V154(
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) ,
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20( the
carrier of
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
Function-like total quasi_total V153(
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) ,
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
V154(
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) ,
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
Lipschitzian )
Element of
K6(
K7( the
carrier of
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) , the
carrier of
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
* (modetrans (f : ( ( Function-like quasi_total ) ( V16() V19(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(X : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ,X : ( ( ) ( ) NORMSTR ) ,Y : ( ( ) ( ) Element of X : ( ( ) ( ) NORMSTR ) ) )) : ( (
Function-like quasi_total V153(
X : ( ( ) ( )
NORMSTR ) ,
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) )
V154(
X : ( ( ) ( )
NORMSTR ) ,
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
X : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) )
V20( the
carrier of
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
Function-like total quasi_total V153(
X : ( ( ) ( )
NORMSTR ) ,
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) )
V154(
X : ( ( ) ( )
NORMSTR ) ,
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) )
Lipschitzian )
Element of
K6(
K7( the
carrier of
X : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) , the
carrier of
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
X : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) )
V20( the
carrier of
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
X : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) , the
carrier of
Z : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
X : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
X : ( ( ) ( )
NORMSTR ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
X : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ;
end;
theorem
for
T,
S being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
f being ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
for
x0 being ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) st
f : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
is_differentiable_in x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) holds
ex
N being ( ( ) ( )
Neighbourhood of
x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) st
(
N : ( ( ) ( )
Neighbourhood of
b4 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) )
c= dom f : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) : ( ( ) ( )
Element of
K6( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) & ( for
z being ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) )
for
h being ( (
non-zero Function-like quasi_total 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
-convergent ) ( non
empty V16()
non-zero V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
-convergent convergent )
Real_Sequence)
for
c being ( (
Function-like constant quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like constant total quasi_total )
sequence of ( ( ) ( non
empty non
trivial )
set ) ) st
rng c : ( (
Function-like constant quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like constant total quasi_total )
sequence of ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of
K6( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) )
= {x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) } : ( ( ) ( non
empty )
set ) &
rng ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
K6( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) )
c= N : ( ( ) ( )
Neighbourhood of
b4 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) holds
(
(h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) ") : ( (
Function-like ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
Function-like total quasi_total complex-valued ext-real-valued real-valued )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) (
complex-valued ext-real-valued real-valued )
set ) ) : ( ( ) ( )
set ) )
(#) ((f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) - (f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) is
convergent &
(diff (f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) ,x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) )) : ( ( ) (
V16()
Function-like )
Element of the
carrier of
(R_NormSpace_of_BoundedLinearOperators (b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) )) : ( ( non
empty ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
NORMSTR ) : ( ( ) ( non
empty )
set ) )
. z : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
= lim ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) ") : ( ( Function-like ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( complex-valued ext-real-valued real-valued ) set ) ) : ( ( ) ( ) set ) ) (#) ((f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) - (f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) ) ) ) ;
theorem
for
T,
S being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
f being ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
for
x0 being ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) st
f : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
is_differentiable_in x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) holds
for
z being ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) )
for
h being ( (
non-zero Function-like quasi_total 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
-convergent ) ( non
empty V16()
non-zero V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
-convergent convergent )
Real_Sequence)
for
c being ( (
Function-like constant quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like constant total quasi_total )
sequence of ( ( ) ( non
empty non
trivial )
set ) ) st
rng c : ( (
Function-like constant quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like constant total quasi_total )
sequence of ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of
K6( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) )
= {x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) } : ( ( ) ( non
empty )
set ) &
rng ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
K6( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) )
c= dom f : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) : ( ( ) ( )
Element of
K6( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) holds
(
(h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) ") : ( (
Function-like ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
Function-like total quasi_total complex-valued ext-real-valued real-valued )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) (
complex-valued ext-real-valued real-valued )
set ) ) : ( ( ) ( )
set ) )
(#) ((f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) - (f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) is
convergent &
(diff (f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) ,x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) )) : ( ( ) (
V16()
Function-like )
Element of the
carrier of
(R_NormSpace_of_BoundedLinearOperators (b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) )) : ( ( non
empty ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
NORMSTR ) : ( ( ) ( non
empty )
set ) )
. z : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
= lim ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) ") : ( ( Function-like ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( complex-valued ext-real-valued real-valued ) set ) ) : ( ( ) ( ) set ) ) (#) ((f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) - (f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) ) ;
theorem
for
S,
T being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
f being ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
for
x0 being ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) )
for
N being ( ( ) ( )
Neighbourhood of
x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) st
N : ( ( ) ( )
Neighbourhood of
b4 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) )
c= dom f : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) : ( ( ) ( )
Element of
K6( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) holds
for
z being ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) )
for
dv being ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) holds
( ( for
h being ( (
non-zero Function-like quasi_total 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
-convergent ) ( non
empty V16()
non-zero V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
-convergent convergent )
Real_Sequence)
for
c being ( (
Function-like constant quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like constant total quasi_total )
sequence of ( ( ) ( non
empty non
trivial )
set ) ) st
rng c : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
Element of
K6( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) )
= {x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) } : ( ( ) ( non
empty )
set ) &
rng ((h : ( ( ) ( V11() real ext-real ) Real) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( ) ( V11() real ext-real ) Real) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
K6( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) )
c= N : ( ( ) ( )
Neighbourhood of
b4 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) holds
(
(h : ( ( ) ( V11() real ext-real ) Real) ") : ( (
Function-like ) (
V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
Function-like complex-valued ext-real-valued real-valued )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) (
complex-valued ext-real-valued real-valued )
set ) ) : ( ( ) ( )
set ) )
(#) ((f : ( ( Function-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* ((h : ( ( ) ( V11() real ext-real ) Real) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( ) ( V11() real ext-real ) Real) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) - (f : ( ( Function-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* c : ( ( ) ( V11() real ext-real ) Real) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) is
convergent &
dv : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) )
= lim ((h : ( ( ) ( V11() real ext-real ) Real) ") : ( ( Function-like ) ( V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like complex-valued ext-real-valued real-valued ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( complex-valued ext-real-valued real-valued ) set ) ) : ( ( ) ( ) set ) ) (#) ((f : ( ( Function-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* ((h : ( ( ) ( V11() real ext-real ) Real) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( ) ( V11() real ext-real ) Real) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) - (f : ( ( Function-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* c : ( ( ) ( V11() real ext-real ) Real) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) ) ) iff for
e being ( ( ) (
V11()
real ext-real )
Real) st
e : ( ( ) (
V11()
real ext-real )
Real)
> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ) holds
ex
d being ( ( ) (
V11()
real ext-real )
Real) st
(
d : ( ( ) (
V11()
real ext-real )
Real)
> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ) & ( for
h being ( ( ) (
V11()
real ext-real )
Real) st
abs h : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
< d : ( ( ) (
V11()
real ext-real )
Real) &
h : ( ( ) (
V11()
real ext-real )
Real)
<> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ) &
(h : ( ( ) ( V11() real ext-real ) Real) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
+ x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
in N : ( ( ) ( )
Neighbourhood of
b4 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) holds
||.(((h : ( ( ) ( V11() real ext-real ) Real) ") : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) * ((f : ( ( Function-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /. ((h : ( ( ) ( V11() real ext-real ) Real) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( ) ( ) Element of the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) + x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( ) ( ) Element of the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) ) : ( ( ) ( ) Element of the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) - (f : ( ( Function-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /. x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( ) ( ) Element of the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) ) : ( ( ) ( ) Element of the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) ) : ( ( ) ( ) Element of the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) - dv : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( ) ( ) Element of the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) .|| : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
< e : ( ( ) (
V11()
real ext-real )
Real) ) ) ) ;
definition
let S,
T be ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ;
let f be ( (
Function-like ) (
V16()
V19( the
carrier of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) ;
let x0,
z be ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ;
pred f is_Gateaux_differentiable_in x0,
z means
ex
N being ( ( ) ( )
Neighbourhood of
x0 : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
S : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) st
(
N : ( ( ) ( )
Neighbourhood of
x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) )
c= dom f : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
S : ( ( ) ( )
NORMSTR ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
S : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
S : ( ( ) ( )
NORMSTR ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
V16() )
Element of
K6( the
carrier of
S : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) & ex
dv being ( ( ) ( )
Point of ( ( ) ( )
set ) ) st
for
e being ( ( ) (
V11()
real ext-real )
Real) st
e : ( ( ) (
V11()
real ext-real )
Real)
> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ) holds
ex
d being ( ( ) (
V11()
real ext-real )
Real) st
(
d : ( ( ) (
V11()
real ext-real )
Real)
> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ) & ( for
h being ( ( ) (
V11()
real ext-real )
Real) st
abs h : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
< d : ( ( ) (
V11()
real ext-real )
Real) &
h : ( ( ) (
V11()
real ext-real )
Real)
<> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ) &
(h : ( ( ) ( V11() real ext-real ) Real) * z : ( ( Function-like quasi_total ) ( V16() V19(S : ( ( ) ( ) NORMSTR ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued ) Element of K6(K7(S : ( ( ) ( ) NORMSTR ) ,REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( complex-valued ext-real-valued real-valued ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
S : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) )
+ x0 : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
S : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of the
carrier of
S : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) )
in N : ( ( ) ( )
Neighbourhood of
x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) holds
||.(((h : ( ( ) ( V11() real ext-real ) Real) ") : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) * ((f : ( ( Function-like quasi_total ) ( V16() V19(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) /. ((h : ( ( ) ( V11() real ext-real ) Real) * z : ( ( Function-like quasi_total ) ( V16() V19(S : ( ( ) ( ) NORMSTR ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued ) Element of K6(K7(S : ( ( ) ( ) NORMSTR ) ,REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( complex-valued ext-real-valued real-valued ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of S : ( ( ) ( ) NORMSTR ) : ( ( ) ( ) set ) ) + x0 : ( ( Function-like quasi_total ) ( V16() V19(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of S : ( ( ) ( ) NORMSTR ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of T : ( ( ) ( ) Element of S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) - (f : ( ( Function-like quasi_total ) ( V16() V19(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) /. x0 : ( ( Function-like quasi_total ) ( V16() V19(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of T : ( ( ) ( ) Element of S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of T : ( ( ) ( ) Element of S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of T : ( ( ) ( ) Element of S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) - dv : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( ) ( ) Element of the carrier of T : ( ( ) ( ) Element of S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) .|| : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
< e : ( ( ) (
V11()
real ext-real )
Real) ) ) );
end;
definition
let S,
T be ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ;
let f be ( (
Function-like ) (
V16()
V19( the
carrier of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) ;
let x0,
z be ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ;
assume
f : ( (
Function-like ) (
V16()
V19( the
carrier of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
is_Gateaux_differentiable_in x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ,
z : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) )
;
func Gateaux_diff (
f,
x0,
z)
-> ( ( ) ( )
Point of ( ( ) ( )
set ) )
means
ex
N being ( ( ) ( )
Neighbourhood of
x0 : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
S : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) st
(
N : ( ( ) ( )
Neighbourhood of
x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) )
c= dom f : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
S : ( ( ) ( )
NORMSTR ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
S : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
S : ( ( ) ( )
NORMSTR ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
V16() )
Element of
K6( the
carrier of
S : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) & ( for
e being ( ( ) (
V11()
real ext-real )
Real) st
e : ( ( ) (
V11()
real ext-real )
Real)
> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ) holds
ex
d being ( ( ) (
V11()
real ext-real )
Real) st
(
d : ( ( ) (
V11()
real ext-real )
Real)
> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ) & ( for
h being ( ( ) (
V11()
real ext-real )
Real) st
abs h : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
< d : ( ( ) (
V11()
real ext-real )
Real) &
h : ( ( ) (
V11()
real ext-real )
Real)
<> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ) &
(h : ( ( ) ( V11() real ext-real ) Real) * z : ( ( Function-like quasi_total ) ( V16() V19(S : ( ( ) ( ) NORMSTR ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued ) Element of K6(K7(S : ( ( ) ( ) NORMSTR ) ,REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( complex-valued ext-real-valued real-valued ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
S : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) )
+ x0 : ( (
Function-like quasi_total ) (
V16()
V19(
K7(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) )
V20(
S : ( ( ) ( )
NORMSTR ) )
Function-like quasi_total )
Element of
K6(
K7(
K7(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ,
S : ( ( ) ( )
NORMSTR ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of the
carrier of
S : ( ( ) ( )
NORMSTR ) : ( ( ) ( )
set ) )
in N : ( ( ) ( )
Neighbourhood of
x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) holds
||.(((h : ( ( ) ( V11() real ext-real ) Real) ") : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) * ((f : ( ( Function-like quasi_total ) ( V16() V19(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) /. ((h : ( ( ) ( V11() real ext-real ) Real) * z : ( ( Function-like quasi_total ) ( V16() V19(S : ( ( ) ( ) NORMSTR ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued ) Element of K6(K7(S : ( ( ) ( ) NORMSTR ) ,REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( complex-valued ext-real-valued real-valued ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of S : ( ( ) ( ) NORMSTR ) : ( ( ) ( ) set ) ) + x0 : ( ( Function-like quasi_total ) ( V16() V19(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of S : ( ( ) ( ) NORMSTR ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of T : ( ( ) ( ) Element of S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) - (f : ( ( Function-like quasi_total ) ( V16() V19(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) /. x0 : ( ( Function-like quasi_total ) ( V16() V19(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of T : ( ( ) ( ) Element of S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of T : ( ( ) ( ) Element of S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of T : ( ( ) ( ) Element of S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) - it : ( ( Function-like ) ( V16() V19(f : ( ( Function-like quasi_total ) ( V16() V19(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) V20(x0 : ( ( Function-like quasi_total ) ( V16() V19(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) Function-like ) Element of K6(K7(f : ( ( Function-like quasi_total ) ( V16() V19(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(S : ( ( ) ( ) NORMSTR ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ,x0 : ( ( Function-like quasi_total ) ( V16() V19(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) V20(S : ( ( ) ( ) NORMSTR ) ) Function-like quasi_total ) Element of K6(K7(K7(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ,S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the carrier of T : ( ( ) ( ) Element of S : ( ( ) ( ) NORMSTR ) ) : ( ( ) ( ) set ) ) .|| : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
< e : ( ( ) (
V11()
real ext-real )
Real) ) ) ) );
end;
theorem
for
T,
S being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
f being ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
for
x0 being ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) st
f : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
is_differentiable_in x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) holds
for
z being ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) holds
(
f : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
is_Gateaux_differentiable_in x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ,
z : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) &
Gateaux_diff (
f : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) ,
x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ,
z : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) )
= (diff (f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) ,x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) )) : ( ( ) (
V16()
Function-like )
Element of the
carrier of
(R_NormSpace_of_BoundedLinearOperators (b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) )) : ( ( non
empty ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
NORMSTR ) : ( ( ) ( non
empty )
set ) )
. z : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) & ex
N being ( ( ) ( )
Neighbourhood of
x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) st
(
N : ( ( ) ( )
Neighbourhood of
b4 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) )
c= dom f : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) : ( ( ) ( )
Element of
K6( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) & ( for
h being ( (
non-zero Function-like quasi_total 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
-convergent ) ( non
empty V16()
non-zero V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative V132()
V159()
V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
-convergent convergent )
Real_Sequence)
for
c being ( (
Function-like constant quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like constant total quasi_total )
sequence of ( ( ) ( non
empty non
trivial )
set ) ) st
rng c : ( (
Function-like constant quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like constant total quasi_total )
sequence of ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of
K6( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) )
= {x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) } : ( ( ) ( non
empty )
set ) &
rng ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
K6( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) )
c= N : ( ( ) ( )
Neighbourhood of
b4 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) holds
(
(h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) ") : ( (
Function-like ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) )
Function-like total quasi_total complex-valued ext-real-valued real-valued )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) (
complex-valued ext-real-valued real-valued )
set ) ) : ( ( ) ( )
set ) )
(#) ((f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) - (f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) is
convergent &
Gateaux_diff (
f : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) ,
x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ,
z : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) )
= lim ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) ") : ( ( Function-like ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( complex-valued ext-real-valued real-valued ) set ) ) : ( ( ) ( ) set ) ) (#) ((f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* ((h : ( ( non-zero Function-like quasi_total 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent ) ( non empty V16() non-zero V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 : ( ( ) ( empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative V132() V159() V160() V161() V162() V163() V164() V165() V166() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) -convergent convergent ) Real_Sequence) * z : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) + c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) - (f : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /* c : ( ( Function-like constant quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like constant total quasi_total ) sequence of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty V16() V19( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) ) V20( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total ) Element of K6(K7(NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() ) Element of K6(REAL : ( ( ) ( non empty V49() V160() V161() V162() V166() ) set ) ) : ( ( ) ( ) set ) ) , the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Function-like quasi_total ) ( non
empty V16()
V19(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total )
Element of
K6(
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V160()
V161()
V162()
V163()
V164()
V165()
V166() )
Element of
K6(
REAL : ( ( ) ( non
empty V49()
V160()
V161()
V162()
V166() )
set ) ) : ( ( ) ( )
set ) ) , the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) ) ) ) ) ;
theorem
for
T,
S,
U being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
R being ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) st
R : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
/. (0. T : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) : ( ( ) (
V68(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
= 0. U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) (
V68(
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) holds
for
L being ( (
Function-like quasi_total V153(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total V153(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian )
LinearOperator of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) holds
R : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
* L : ( (
Function-like quasi_total V153(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total V153(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian )
LinearOperator of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) is ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) ;
theorem
for
S,
T,
U being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
R being ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
for
L being ( (
Function-like quasi_total V153(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total V153(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian )
LinearOperator of
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) holds
L : ( (
Function-like quasi_total V153(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total V153(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian )
LinearOperator of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
* R : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) is ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) ;
theorem
for
S,
T,
U being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
R1 being ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) st
R1 : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
/. (0. S : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) : ( ( ) (
V68(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
= 0. T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) (
V68(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) holds
for
R2 being ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) st
R2 : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
/. (0. T : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) : ( ( ) (
V68(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
= 0. U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) (
V68(
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) holds
R2 : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
* R1 : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) is ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) ;
theorem
for
S,
T,
U being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
R1 being ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) st
R1 : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
/. (0. S : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) : ( ( ) (
V68(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
= 0. T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) (
V68(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) holds
for
R2 being ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) st
R2 : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
/. (0. T : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) : ( ( ) (
V68(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
= 0. U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) (
V68(
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) holds
for
L being ( (
Function-like quasi_total V153(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total V153(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian )
LinearOperator of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) holds
R2 : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
* (L : ( ( Function-like quasi_total V153(b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) V154(b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) Lipschitzian ) ( non empty V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total V153(b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) V154(b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) + R1 : ( ( Function-like RestFunc-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like RestFunc-like ) RestFunc of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) is ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) ;
theorem
for
S,
T,
U being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
R1 being ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) st
R1 : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
/. (0. S : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) : ( ( ) (
V68(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
= 0. T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) (
V68(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) holds
for
R2 being ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) st
R2 : ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
/. (0. T : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) : ( ( ) (
V68(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
= 0. U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) (
V68(
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) )
Element of the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) holds
for
L1 being ( (
Function-like quasi_total V153(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total V153(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian )
LinearOperator of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
for
L2 being ( (
Function-like quasi_total V153(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian ) ( non
empty V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like total quasi_total V153(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
V154(
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) )
Lipschitzian )
LinearOperator of
T : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) holds
(L2 : ( ( Function-like quasi_total V153(b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b3 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) V154(b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b3 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) Lipschitzian ) ( non empty V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b3 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total V153(b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b3 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) V154(b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b3 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) Lipschitzian ) LinearOperator of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b3 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) * R1 : ( ( Function-like RestFunc-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like RestFunc-like ) RestFunc of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
+ (R2 : ( ( Function-like RestFunc-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b3 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like RestFunc-like ) RestFunc of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b3 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) * (L1 : ( ( Function-like quasi_total V153(b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) V154(b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) Lipschitzian ) ( non empty V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like total quasi_total V153(b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) V154(b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) + R1 : ( ( Function-like RestFunc-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like RestFunc-like ) RestFunc of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ) ) : ( ( Function-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) Element of K6(K7( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) , the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) is ( (
Function-like RestFunc-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b3 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like RestFunc-like )
RestFunc of
S : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ,
U : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) ) ;
theorem
for
S,
T being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
x0 being ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) )
for
U being ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace)
for
f1 being ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) st
f1 : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
is_differentiable_in x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) holds
for
f2 being ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b4 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) st
f2 : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b4 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
is_differentiable_in f1 : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
/. x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
Element of the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) holds
(
f2 : ( (
Function-like ) (
V16()
V19( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b4 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,)
* f1 : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b2 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
PartFunc of ,) : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b4 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b4 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
is_differentiable_in x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) &
diff (
(f2 : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b4 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) * f1 : ( ( Function-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) ) : ( (
Function-like ) (
V16()
V19( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V20( the
carrier of
b4 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like )
Element of
K6(
K7( the
carrier of
b1 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b4 : ( ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like ) ( non
empty non
trivial V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
RealNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ,
x0 : ( ( ) ( )
Point of ( ( ) ( non
empty non
trivial )
set ) ) ) : ( ( ) (
V16()
Function-like )
Element of the
carrier of
(R_NormSpace_of_BoundedLinearOperators (b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b4 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) )) : ( ( non
empty ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
NORMSTR ) : ( ( ) ( non
empty )
set ) )
= (diff (f2 : ( ( Function-like ) ( V16() V19( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b4 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) ,(f1 : ( ( Function-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) /. x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) ) : ( ( ) ( ) Element of the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) )) : ( ( ) (
V16()
Function-like )
Element of the
carrier of
(R_NormSpace_of_BoundedLinearOperators (b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b4 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) )) : ( ( non
empty ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
NORMSTR ) : ( ( ) ( non
empty )
set ) )
* (diff (f1 : ( ( Function-like ) ( V16() V19( the carrier of b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) V20( the carrier of b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) : ( ( ) ( non empty non trivial ) set ) ) Function-like ) PartFunc of ,) ,x0 : ( ( ) ( ) Point of ( ( ) ( non empty non trivial ) set ) ) )) : ( ( ) (
V16()
Function-like )
Element of the
carrier of
(R_NormSpace_of_BoundedLinearOperators (b1 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) ,b2 : ( ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) ( non empty non trivial V87() V112() V113() V114() V115() V116() V117() V118() V122() V123() RealNormSpace-like ) RealNormSpace) )) : ( ( non
empty ) ( non
empty V87()
V112()
V113()
V114()
V115()
V116()
V117()
V118()
V122()
V123()
RealNormSpace-like )
NORMSTR ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V16()
Function-like )
Point of ( ( ) ( non
empty )
set ) ) ) ;