REAL is non empty V35() set
NAT is non empty V17() V18() V19() Element of K32(REAL)
K32(REAL) is non empty set
NAT is non empty V17() V18() V19() set
K32(NAT) is non empty set
K32(NAT) is non empty set
COMPLEX is non empty V35() set
RAT is non empty V35() set
INT is non empty V35() set
K33(COMPLEX,COMPLEX) is non empty set
K32(K33(COMPLEX,COMPLEX)) is non empty set
K33(K33(COMPLEX,COMPLEX),COMPLEX) is non empty set
K32(K33(K33(COMPLEX,COMPLEX),COMPLEX)) is non empty set
K33(REAL,REAL) is non empty set
K32(K33(REAL,REAL)) is non empty set
K33(K33(REAL,REAL),REAL) is non empty set
K32(K33(K33(REAL,REAL),REAL)) is non empty set
K33(RAT,RAT) is non empty set
K32(K33(RAT,RAT)) is non empty set
K33(K33(RAT,RAT),RAT) is non empty set
K32(K33(K33(RAT,RAT),RAT)) is non empty set
K33(INT,INT) is non empty set
K32(K33(INT,INT)) is non empty set
K33(K33(INT,INT),INT) is non empty set
K32(K33(K33(INT,INT),INT)) is non empty set
K33(NAT,NAT) is non empty set
K33(K33(NAT,NAT),NAT) is non empty set
K32(K33(K33(NAT,NAT),NAT)) is non empty set
{} is empty V17() V18() V19() V21() V22() V23() V24() V25() set
1 is non empty V17() V18() V19() V23() V24() V25() Element of NAT
0 is empty V17() V18() V19() V21() V22() V23() V24() V25() Element of NAT
- 1 is V24() V25() Element of REAL
K107(0) is V24() V25() set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
(0. CS) + (0. CS) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(0. CS),(0. CS)) is Element of the U1 of CS
K4((0. CS),(0. CS)) is set
the U5 of CS . K4((0. CS),(0. CS)) is set
((0. CS) + (0. CS)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (0. CS)),(0. CS)) is Element of the U1 of CS
K4(((0. CS) + (0. CS)),(0. CS)) is set
the U5 of CS . K4(((0. CS) + (0. CS)),(0. CS)) is set
1 * p1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,1,p1) is set
K4(1,p1) is set
the Mult of CS . K4(1,p1) is set
(0. CS) + (1 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(1 * p1)) is Element of the U1 of CS
K4((0. CS),(1 * p1)) is set
the U5 of CS . K4((0. CS),(1 * p1)) is set
((0. CS) + (1 * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (1 * p1)),(0. CS)) is Element of the U1 of CS
K4(((0. CS) + (1 * p1)),(0. CS)) is set
the U5 of CS . K4(((0. CS) + (1 * p1)),(0. CS)) is set
0 * p is Element of the U1 of CS
K138( the Mult of CS,0,p) is set
K4(0,p) is set
the Mult of CS . K4(0,p) is set
(0 * p) + (1 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p),(1 * p1)) is Element of the U1 of CS
K4((0 * p),(1 * p1)) is set
the U5 of CS . K4((0 * p),(1 * p1)) is set
((0 * p) + (1 * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * p) + (1 * p1)),(0. CS)) is Element of the U1 of CS
K4(((0 * p) + (1 * p1)),(0. CS)) is set
the U5 of CS . K4(((0 * p) + (1 * p1)),(0. CS)) is set
0 * p2 is Element of the U1 of CS
K138( the Mult of CS,0,p2) is set
K4(0,p2) is set
the Mult of CS . K4(0,p2) is set
((0 * p) + (1 * p1)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * p) + (1 * p1)),(0 * p2)) is Element of the U1 of CS
K4(((0 * p) + (1 * p1)),(0 * p2)) is set
the U5 of CS . K4(((0 * p) + (1 * p1)),(0 * p2)) is set
1 * p2 is Element of the U1 of CS
K138( the Mult of CS,1,p2) is set
K4(1,p2) is set
the Mult of CS . K4(1,p2) is set
((0. CS) + (0. CS)) + (1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (0. CS)),(1 * p2)) is Element of the U1 of CS
K4(((0. CS) + (0. CS)),(1 * p2)) is set
the U5 of CS . K4(((0. CS) + (0. CS)),(1 * p2)) is set
(0 * p) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p),(0. CS)) is Element of the U1 of CS
K4((0 * p),(0. CS)) is set
the U5 of CS . K4((0 * p),(0. CS)) is set
((0 * p) + (0. CS)) + (1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * p) + (0. CS)),(1 * p2)) is Element of the U1 of CS
K4(((0 * p) + (0. CS)),(1 * p2)) is set
the U5 of CS . K4(((0 * p) + (0. CS)),(1 * p2)) is set
0 * p1 is Element of the U1 of CS
K138( the Mult of CS,0,p1) is set
K4(0,p1) is set
the Mult of CS . K4(0,p1) is set
(0 * p) + (0 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p),(0 * p1)) is Element of the U1 of CS
K4((0 * p),(0 * p1)) is set
the U5 of CS . K4((0 * p),(0 * p1)) is set
((0 * p) + (0 * p1)) + (1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * p) + (0 * p1)),(1 * p2)) is Element of the U1 of CS
K4(((0 * p) + (0 * p1)),(1 * p2)) is set
the U5 of CS . K4(((0 * p) + (0 * p1)),(1 * p2)) is set
1 * p is Element of the U1 of CS
K138( the Mult of CS,1,p) is set
K4(1,p) is set
the Mult of CS . K4(1,p) is set
(1 * p) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * p),(0. CS)) is Element of the U1 of CS
K4((1 * p),(0. CS)) is set
the U5 of CS . K4((1 * p),(0. CS)) is set
((1 * p) + (0. CS)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((1 * p) + (0. CS)),(0. CS)) is Element of the U1 of CS
K4(((1 * p) + (0. CS)),(0. CS)) is set
the U5 of CS . K4(((1 * p) + (0. CS)),(0. CS)) is set
(1 * p) + (0 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * p),(0 * p1)) is Element of the U1 of CS
K4((1 * p),(0 * p1)) is set
the U5 of CS . K4((1 * p),(0 * p1)) is set
((1 * p) + (0 * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((1 * p) + (0 * p1)),(0. CS)) is Element of the U1 of CS
K4(((1 * p) + (0 * p1)),(0. CS)) is set
the U5 of CS . K4(((1 * p) + (0 * p1)),(0. CS)) is set
((1 * p) + (0 * p1)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((1 * p) + (0 * p1)),(0 * p2)) is Element of the U1 of CS
K4(((1 * p) + (0 * p1)),(0 * p2)) is set
the U5 of CS . K4(((1 * p) + (0 * p1)),(0 * p2)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
(0. CS) + (0. CS) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(0. CS),(0. CS)) is Element of the U1 of CS
K4((0. CS),(0. CS)) is set
the U5 of CS . K4((0. CS),(0. CS)) is set
1 * p1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,1,p1) is set
K4(1,p1) is set
the Mult of CS . K4(1,p1) is set
(0. CS) + (1 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(1 * p1)) is Element of the U1 of CS
K4((0. CS),(1 * p1)) is set
the U5 of CS . K4((0. CS),(1 * p1)) is set
0 * p is Element of the U1 of CS
K138( the Mult of CS,0,p) is set
K4(0,p) is set
the Mult of CS . K4(0,p) is set
(0 * p) + (1 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p),(1 * p1)) is Element of the U1 of CS
K4((0 * p),(1 * p1)) is set
the U5 of CS . K4((0 * p),(1 * p1)) is set
1 * p is Element of the U1 of CS
K138( the Mult of CS,1,p) is set
K4(1,p) is set
the Mult of CS . K4(1,p) is set
(1 * p) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * p),(0. CS)) is Element of the U1 of CS
K4((1 * p),(0. CS)) is set
the U5 of CS . K4((1 * p),(0. CS)) is set
0 * p1 is Element of the U1 of CS
K138( the Mult of CS,0,p1) is set
K4(0,p1) is set
the Mult of CS . K4(0,p1) is set
(1 * p) + (0 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * p),(0 * p1)) is Element of the U1 of CS
K4((1 * p),(0 * p1)) is set
the U5 of CS . K4((1 * p),(0 * p1)) is set
p2 is V24() V25() Element of REAL
p2 * p is Element of the U1 of CS
K138( the Mult of CS,p2,p) is set
K4(p2,p) is set
the Mult of CS . K4(p2,p) is set
r is V24() V25() Element of REAL
r * p1 is Element of the U1 of CS
K138( the Mult of CS,r,p1) is set
K4(r,p1) is set
the Mult of CS . K4(r,p1) is set
(p2 * p) - (r * p1) is Element of the U1 of CS
- (r * p1) is Element of the U1 of CS
K176(CS,(p2 * p),(- (r * p1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p2 * p),(- (r * p1))) is Element of the U1 of CS
K4((p2 * p),(- (r * p1))) is set
the U5 of CS . K4((p2 * p),(- (r * p1))) is set
- p1 is Element of the U1 of CS
r * (- p1) is Element of the U1 of CS
K138( the Mult of CS,r,(- p1)) is set
K4(r,(- p1)) is set
the Mult of CS . K4(r,(- p1)) is set
(p2 * p) + (r * (- p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p2 * p),(r * (- p1))) is Element of the U1 of CS
K4((p2 * p),(r * (- p1))) is set
the U5 of CS . K4((p2 * p),(r * (- p1))) is set
- r is V24() V25() Element of REAL
(- r) * p1 is Element of the U1 of CS
K138( the Mult of CS,(- r),p1) is set
K4((- r),p1) is set
the Mult of CS . K4((- r),p1) is set
(p2 * p) + ((- r) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p2 * p),((- r) * p1)) is Element of the U1 of CS
K4((p2 * p),((- r) * p1)) is set
the U5 of CS . K4((p2 * p),((- r) * p1)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is V24() V25() Element of REAL
r1 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,r1,p) is set
K4(r1,p) is set
the Mult of CS . K4(r1,p) is set
p is V24() V25() Element of REAL
p * p1 is Element of the U1 of CS
K138( the Mult of CS,p,p1) is set
K4(p,p1) is set
the Mult of CS . K4(p,p1) is set
(r1 * p) + (p * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(r1 * p),(p * p1)) is Element of the U1 of CS
K4((r1 * p),(p * p1)) is set
the U5 of CS . K4((r1 * p),(p * p1)) is set
p1 is V24() V25() Element of REAL
p1 * p2 is Element of the U1 of CS
K138( the Mult of CS,p1,p2) is set
K4(p1,p2) is set
the Mult of CS . K4(p1,p2) is set
((r1 * p) + (p * p1)) + (p1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * p) + (p * p1)),(p1 * p2)) is Element of the U1 of CS
K4(((r1 * p) + (p * p1)),(p1 * p2)) is set
the U5 of CS . K4(((r1 * p) + (p * p1)),(p1 * p2)) is set
(((r1 * p) + (p * p1)) + (p1 * p2)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r1 * p) + (p * p1)) + (p1 * p2)),(0. CS)) is Element of the U1 of CS
K4((((r1 * p) + (p * p1)) + (p1 * p2)),(0. CS)) is set
the U5 of CS . K4((((r1 * p) + (p * p1)) + (p1 * p2)),(0. CS)) is set
0 * r is Element of the U1 of CS
K138( the Mult of CS,0,r) is set
K4(0,r) is set
the Mult of CS . K4(0,r) is set
(((r1 * p) + (p * p1)) + (p1 * p2)) + (0 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r1 * p) + (p * p1)) + (p1 * p2)),(0 * r)) is Element of the U1 of CS
K4((((r1 * p) + (p * p1)) + (p1 * p2)),(0 * r)) is set
the U5 of CS . K4((((r1 * p) + (p * p1)) + (p1 * p2)),(0 * r)) is set
r1 is V24() V25() Element of REAL
r1 * p2 is Element of the U1 of CS
K138( the Mult of CS,r1,p2) is set
K4(r1,p2) is set
the Mult of CS . K4(r1,p2) is set
p is V24() V25() Element of REAL
p * r is Element of the U1 of CS
K138( the Mult of CS,p,r) is set
K4(p,r) is set
the Mult of CS . K4(p,r) is set
(r1 * p2) + (p * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * p2),(p * r)) is Element of the U1 of CS
K4((r1 * p2),(p * r)) is set
the U5 of CS . K4((r1 * p2),(p * r)) is set
p1 is V24() V25() Element of REAL
p1 * p is Element of the U1 of CS
K138( the Mult of CS,p1,p) is set
K4(p1,p) is set
the Mult of CS . K4(p1,p) is set
((r1 * p2) + (p * r)) + (p1 * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * p2) + (p * r)),(p1 * p)) is Element of the U1 of CS
K4(((r1 * p2) + (p * r)),(p1 * p)) is set
the U5 of CS . K4(((r1 * p2) + (p * r)),(p1 * p)) is set
(p1 * p) + (r1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p1 * p),(r1 * p2)) is Element of the U1 of CS
K4((p1 * p),(r1 * p2)) is set
the U5 of CS . K4((p1 * p),(r1 * p2)) is set
((p1 * p) + (r1 * p2)) + (p * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p1 * p) + (r1 * p2)),(p * r)) is Element of the U1 of CS
K4(((p1 * p) + (r1 * p2)),(p * r)) is set
the U5 of CS . K4(((p1 * p) + (r1 * p2)),(p * r)) is set
(p1 * p) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p1 * p),(0. CS)) is Element of the U1 of CS
K4((p1 * p),(0. CS)) is set
the U5 of CS . K4((p1 * p),(0. CS)) is set
((p1 * p) + (0. CS)) + (r1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p1 * p) + (0. CS)),(r1 * p2)) is Element of the U1 of CS
K4(((p1 * p) + (0. CS)),(r1 * p2)) is set
the U5 of CS . K4(((p1 * p) + (0. CS)),(r1 * p2)) is set
(((p1 * p) + (0. CS)) + (r1 * p2)) + (p * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p1 * p) + (0. CS)) + (r1 * p2)),(p * r)) is Element of the U1 of CS
K4((((p1 * p) + (0. CS)) + (r1 * p2)),(p * r)) is set
the U5 of CS . K4((((p1 * p) + (0. CS)) + (r1 * p2)),(p * r)) is set
0 * p1 is Element of the U1 of CS
K138( the Mult of CS,0,p1) is set
K4(0,p1) is set
the Mult of CS . K4(0,p1) is set
(p1 * p) + (0 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p1 * p),(0 * p1)) is Element of the U1 of CS
K4((p1 * p),(0 * p1)) is set
the U5 of CS . K4((p1 * p),(0 * p1)) is set
((p1 * p) + (0 * p1)) + (r1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p1 * p) + (0 * p1)),(r1 * p2)) is Element of the U1 of CS
K4(((p1 * p) + (0 * p1)),(r1 * p2)) is set
the U5 of CS . K4(((p1 * p) + (0 * p1)),(r1 * p2)) is set
(((p1 * p) + (0 * p1)) + (r1 * p2)) + (p * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p1 * p) + (0 * p1)) + (r1 * p2)),(p * r)) is Element of the U1 of CS
K4((((p1 * p) + (0 * p1)) + (r1 * p2)),(p * r)) is set
the U5 of CS . K4((((p1 * p) + (0 * p1)) + (r1 * p2)),(p * r)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is V24() V25() Element of REAL
r1 is V24() V25() Element of REAL
r1 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,r1,p) is set
K4(r1,p) is set
the Mult of CS . K4(r1,p) is set
r * r1 is V24() V25() Element of REAL
(r * r1) * p is Element of the U1 of CS
K138( the Mult of CS,(r * r1),p) is set
K4((r * r1),p) is set
the Mult of CS . K4((r * r1),p) is set
p is V24() V25() Element of REAL
p * p1 is Element of the U1 of CS
K138( the Mult of CS,p,p1) is set
K4(p,p1) is set
the Mult of CS . K4(p,p1) is set
(r1 * p) + (p * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(r1 * p),(p * p1)) is Element of the U1 of CS
K4((r1 * p),(p * p1)) is set
the U5 of CS . K4((r1 * p),(p * p1)) is set
r * p is V24() V25() Element of REAL
(r * p) * p1 is Element of the U1 of CS
K138( the Mult of CS,(r * p),p1) is set
K4((r * p),p1) is set
the Mult of CS . K4((r * p),p1) is set
((r * r1) * p) + ((r * p) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * r1) * p),((r * p) * p1)) is Element of the U1 of CS
K4(((r * r1) * p),((r * p) * p1)) is set
the U5 of CS . K4(((r * r1) * p),((r * p) * p1)) is set
p1 is V24() V25() Element of REAL
p1 * p2 is Element of the U1 of CS
K138( the Mult of CS,p1,p2) is set
K4(p1,p2) is set
the Mult of CS . K4(p1,p2) is set
((r1 * p) + (p * p1)) + (p1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * p) + (p * p1)),(p1 * p2)) is Element of the U1 of CS
K4(((r1 * p) + (p * p1)),(p1 * p2)) is set
the U5 of CS . K4(((r1 * p) + (p * p1)),(p1 * p2)) is set
r * (((r1 * p) + (p * p1)) + (p1 * p2)) is Element of the U1 of CS
K138( the Mult of CS,r,(((r1 * p) + (p * p1)) + (p1 * p2))) is set
K4(r,(((r1 * p) + (p * p1)) + (p1 * p2))) is set
the Mult of CS . K4(r,(((r1 * p) + (p * p1)) + (p1 * p2))) is set
r * p1 is V24() V25() Element of REAL
(r * p1) * p2 is Element of the U1 of CS
K138( the Mult of CS,(r * p1),p2) is set
K4((r * p1),p2) is set
the Mult of CS . K4((r * p1),p2) is set
(((r * r1) * p) + ((r * p) * p1)) + ((r * p1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r * r1) * p) + ((r * p) * p1)),((r * p1) * p2)) is Element of the U1 of CS
K4((((r * r1) * p) + ((r * p) * p1)),((r * p1) * p2)) is set
the U5 of CS . K4((((r * r1) * p) + ((r * p) * p1)),((r * p1) * p2)) is set
r * (r1 * p) is Element of the U1 of CS
K138( the Mult of CS,r,(r1 * p)) is set
K4(r,(r1 * p)) is set
the Mult of CS . K4(r,(r1 * p)) is set
(r * (r1 * p)) + ((r * p) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * (r1 * p)),((r * p) * p1)) is Element of the U1 of CS
K4((r * (r1 * p)),((r * p) * p1)) is set
the U5 of CS . K4((r * (r1 * p)),((r * p) * p1)) is set
((r * (r1 * p)) + ((r * p) * p1)) + ((r * p1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * (r1 * p)) + ((r * p) * p1)),((r * p1) * p2)) is Element of the U1 of CS
K4(((r * (r1 * p)) + ((r * p) * p1)),((r * p1) * p2)) is set
the U5 of CS . K4(((r * (r1 * p)) + ((r * p) * p1)),((r * p1) * p2)) is set
r * (p * p1) is Element of the U1 of CS
K138( the Mult of CS,r,(p * p1)) is set
K4(r,(p * p1)) is set
the Mult of CS . K4(r,(p * p1)) is set
(r * (r1 * p)) + (r * (p * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * (r1 * p)),(r * (p * p1))) is Element of the U1 of CS
K4((r * (r1 * p)),(r * (p * p1))) is set
the U5 of CS . K4((r * (r1 * p)),(r * (p * p1))) is set
((r * (r1 * p)) + (r * (p * p1))) + ((r * p1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * (r1 * p)) + (r * (p * p1))),((r * p1) * p2)) is Element of the U1 of CS
K4(((r * (r1 * p)) + (r * (p * p1))),((r * p1) * p2)) is set
the U5 of CS . K4(((r * (r1 * p)) + (r * (p * p1))),((r * p1) * p2)) is set
r * ((r1 * p) + (p * p1)) is Element of the U1 of CS
K138( the Mult of CS,r,((r1 * p) + (p * p1))) is set
K4(r,((r1 * p) + (p * p1))) is set
the Mult of CS . K4(r,((r1 * p) + (p * p1))) is set
(r * ((r1 * p) + (p * p1))) + ((r * p1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * ((r1 * p) + (p * p1))),((r * p1) * p2)) is Element of the U1 of CS
K4((r * ((r1 * p) + (p * p1))),((r * p1) * p2)) is set
the U5 of CS . K4((r * ((r1 * p) + (p * p1))),((r * p1) * p2)) is set
r * (p1 * p2) is Element of the U1 of CS
K138( the Mult of CS,r,(p1 * p2)) is set
K4(r,(p1 * p2)) is set
the Mult of CS . K4(r,(p1 * p2)) is set
(r * ((r1 * p) + (p * p1))) + (r * (p1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * ((r1 * p) + (p * p1))),(r * (p1 * p2))) is Element of the U1 of CS
K4((r * ((r1 * p) + (p * p1))),(r * (p1 * p2))) is set
the U5 of CS . K4((r * ((r1 * p) + (p * p1))),(r * (p1 * p2))) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p + p1 is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,p,p1) is Element of the U1 of CS
K4(p,p1) is set
the U5 of CS . K4(p,p1) is set
p2 is Element of the U1 of CS
(p + p1) + p2 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + p1),p2) is Element of the U1 of CS
K4((p + p1),p2) is set
the U5 of CS . K4((p + p1),p2) is set
r is Element of the U1 of CS
p + r is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,r) is Element of the U1 of CS
K4(p,r) is set
the U5 of CS . K4(p,r) is set
r1 is Element of the U1 of CS
r + r1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,r1) is Element of the U1 of CS
K4(r,r1) is set
the U5 of CS . K4(r,r1) is set
p1 + r1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p1,r1) is Element of the U1 of CS
K4(p1,r1) is set
the U5 of CS . K4(p1,r1) is set
(p + r) + (p1 + r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + r),(p1 + r1)) is Element of the U1 of CS
K4((p + r),(p1 + r1)) is set
the U5 of CS . K4((p + r),(p1 + r1)) is set
p is Element of the U1 of CS
(r + r1) + p is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + r1),p) is Element of the U1 of CS
K4((r + r1),p) is set
the U5 of CS . K4((r + r1),p) is set
((p + p1) + p2) + ((r + r1) + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + p1) + p2),((r + r1) + p)) is Element of the U1 of CS
K4(((p + p1) + p2),((r + r1) + p)) is set
the U5 of CS . K4(((p + p1) + p2),((r + r1) + p)) is set
p2 + p is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p2,p) is Element of the U1 of CS
K4(p2,p) is set
the U5 of CS . K4(p2,p) is set
((p + r) + (p1 + r1)) + (p2 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + r) + (p1 + r1)),(p2 + p)) is Element of the U1 of CS
K4(((p + r) + (p1 + r1)),(p2 + p)) is set
the U5 of CS . K4(((p + r) + (p1 + r1)),(p2 + p)) is set
p + (p1 + r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,(p1 + r1)) is Element of the U1 of CS
K4(p,(p1 + r1)) is set
the U5 of CS . K4(p,(p1 + r1)) is set
r + (p + (p1 + r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,(p + (p1 + r1))) is Element of the U1 of CS
K4(r,(p + (p1 + r1))) is set
the U5 of CS . K4(r,(p + (p1 + r1))) is set
(r + (p + (p1 + r1))) + (p2 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + (p + (p1 + r1))),(p2 + p)) is Element of the U1 of CS
K4((r + (p + (p1 + r1))),(p2 + p)) is set
the U5 of CS . K4((r + (p + (p1 + r1))),(p2 + p)) is set
(p + p1) + r1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + p1),r1) is Element of the U1 of CS
K4((p + p1),r1) is set
the U5 of CS . K4((p + p1),r1) is set
r + ((p + p1) + r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,((p + p1) + r1)) is Element of the U1 of CS
K4(r,((p + p1) + r1)) is set
the U5 of CS . K4(r,((p + p1) + r1)) is set
(r + ((p + p1) + r1)) + (p2 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + ((p + p1) + r1)),(p2 + p)) is Element of the U1 of CS
K4((r + ((p + p1) + r1)),(p2 + p)) is set
the U5 of CS . K4((r + ((p + p1) + r1)),(p2 + p)) is set
(r + r1) + (p + p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + r1),(p + p1)) is Element of the U1 of CS
K4((r + r1),(p + p1)) is set
the U5 of CS . K4((r + r1),(p + p1)) is set
((r + r1) + (p + p1)) + (p2 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r + r1) + (p + p1)),(p2 + p)) is Element of the U1 of CS
K4(((r + r1) + (p + p1)),(p2 + p)) is set
the U5 of CS . K4(((r + r1) + (p + p1)),(p2 + p)) is set
(p + p1) + (p2 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + p1),(p2 + p)) is Element of the U1 of CS
K4((p + p1),(p2 + p)) is set
the U5 of CS . K4((p + p1),(p2 + p)) is set
(r + r1) + ((p + p1) + (p2 + p)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + r1),((p + p1) + (p2 + p))) is Element of the U1 of CS
K4((r + r1),((p + p1) + (p2 + p))) is set
the U5 of CS . K4((r + r1),((p + p1) + (p2 + p))) is set
((p + p1) + p2) + p is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + p1) + p2),p) is Element of the U1 of CS
K4(((p + p1) + p2),p) is set
the U5 of CS . K4(((p + p1) + p2),p) is set
(r + r1) + (((p + p1) + p2) + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + r1),(((p + p1) + p2) + p)) is Element of the U1 of CS
K4((r + r1),(((p + p1) + p2) + p)) is set
the U5 of CS . K4((r + r1),(((p + p1) + p2) + p)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is V24() V25() Element of REAL
p * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p,p) is set
K4(p,p) is set
the Mult of CS . K4(p,p) is set
p1 is V24() V25() Element of REAL
p1 * p1 is Element of the U1 of CS
K138( the Mult of CS,p1,p1) is set
K4(p1,p1) is set
the Mult of CS . K4(p1,p1) is set
(p * p) + (p1 * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(p * p),(p1 * p1)) is Element of the U1 of CS
K4((p * p),(p1 * p1)) is set
the U5 of CS . K4((p * p),(p1 * p1)) is set
q is V24() V25() Element of REAL
q * p2 is Element of the U1 of CS
K138( the Mult of CS,q,p2) is set
K4(q,p2) is set
the Mult of CS . K4(q,p2) is set
((p * p) + (p1 * p1)) + (q * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p * p) + (p1 * p1)),(q * p2)) is Element of the U1 of CS
K4(((p * p) + (p1 * p1)),(q * p2)) is set
the U5 of CS . K4(((p * p) + (p1 * p1)),(q * p2)) is set
q1 is V24() V25() Element of REAL
q1 * p is Element of the U1 of CS
K138( the Mult of CS,q1,p) is set
K4(q1,p) is set
the Mult of CS . K4(q1,p) is set
r is V24() V25() Element of REAL
r * p1 is Element of the U1 of CS
K138( the Mult of CS,r,p1) is set
K4(r,p1) is set
the Mult of CS . K4(r,p1) is set
(q1 * p) + (r * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q1 * p),(r * p1)) is Element of the U1 of CS
K4((q1 * p),(r * p1)) is set
the U5 of CS . K4((q1 * p),(r * p1)) is set
y is V24() V25() Element of REAL
y * p2 is Element of the U1 of CS
K138( the Mult of CS,y,p2) is set
K4(y,p2) is set
the Mult of CS . K4(y,p2) is set
((q1 * p) + (r * p1)) + (y * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * p) + (r * p1)),(y * p2)) is Element of the U1 of CS
K4(((q1 * p) + (r * p1)),(y * p2)) is set
the U5 of CS . K4(((q1 * p) + (r * p1)),(y * p2)) is set
z2 is V24() V25() Element of REAL
z2 * r is Element of the U1 of CS
K138( the Mult of CS,z2,r) is set
K4(z2,r) is set
the Mult of CS . K4(z2,r) is set
z2 * p is V24() V25() Element of REAL
z2 * p1 is V24() V25() Element of REAL
z2 * q is V24() V25() Element of REAL
z1 is V24() V25() Element of REAL
z1 * r1 is Element of the U1 of CS
K138( the Mult of CS,z1,r1) is set
K4(z1,r1) is set
the Mult of CS . K4(z1,r1) is set
(z2 * r) + (z1 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z2 * r),(z1 * r1)) is Element of the U1 of CS
K4((z2 * r),(z1 * r1)) is set
the U5 of CS . K4((z2 * r),(z1 * r1)) is set
z1 * q1 is V24() V25() Element of REAL
(z2 * p) + (z1 * q1) is V24() V25() Element of REAL
((z2 * p) + (z1 * q1)) * p is Element of the U1 of CS
K138( the Mult of CS,((z2 * p) + (z1 * q1)),p) is set
K4(((z2 * p) + (z1 * q1)),p) is set
the Mult of CS . K4(((z2 * p) + (z1 * q1)),p) is set
z1 * r is V24() V25() Element of REAL
(z2 * p1) + (z1 * r) is V24() V25() Element of REAL
((z2 * p1) + (z1 * r)) * p1 is Element of the U1 of CS
K138( the Mult of CS,((z2 * p1) + (z1 * r)),p1) is set
K4(((z2 * p1) + (z1 * r)),p1) is set
the Mult of CS . K4(((z2 * p1) + (z1 * r)),p1) is set
(((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) + (z1 * r)) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z2 * p) + (z1 * q1)) * p),(((z2 * p1) + (z1 * r)) * p1)) is Element of the U1 of CS
K4((((z2 * p) + (z1 * q1)) * p),(((z2 * p1) + (z1 * r)) * p1)) is set
the U5 of CS . K4((((z2 * p) + (z1 * q1)) * p),(((z2 * p1) + (z1 * r)) * p1)) is set
z1 * y is V24() V25() Element of REAL
(z2 * q) + (z1 * y) is V24() V25() Element of REAL
((z2 * q) + (z1 * y)) * p2 is Element of the U1 of CS
K138( the Mult of CS,((z2 * q) + (z1 * y)),p2) is set
K4(((z2 * q) + (z1 * y)),p2) is set
the Mult of CS . K4(((z2 * q) + (z1 * y)),p2) is set
((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) + (z1 * r)) * p1)) + (((z2 * q) + (z1 * y)) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) + (z1 * r)) * p1)),(((z2 * q) + (z1 * y)) * p2)) is Element of the U1 of CS
K4(((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) + (z1 * r)) * p1)),(((z2 * q) + (z1 * y)) * p2)) is set
the U5 of CS . K4(((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) + (z1 * r)) * p1)),(((z2 * q) + (z1 * y)) * p2)) is set
(z2 * p) * p is Element of the U1 of CS
K138( the Mult of CS,(z2 * p),p) is set
K4((z2 * p),p) is set
the Mult of CS . K4((z2 * p),p) is set
(z2 * p1) * p1 is Element of the U1 of CS
K138( the Mult of CS,(z2 * p1),p1) is set
K4((z2 * p1),p1) is set
the Mult of CS . K4((z2 * p1),p1) is set
((z2 * p) * p) + ((z2 * p1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z2 * p) * p),((z2 * p1) * p1)) is Element of the U1 of CS
K4(((z2 * p) * p),((z2 * p1) * p1)) is set
the U5 of CS . K4(((z2 * p) * p),((z2 * p1) * p1)) is set
(z2 * q) * p2 is Element of the U1 of CS
K138( the Mult of CS,(z2 * q),p2) is set
K4((z2 * q),p2) is set
the Mult of CS . K4((z2 * q),p2) is set
(((z2 * p) * p) + ((z2 * p1) * p1)) + ((z2 * q) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z2 * p) * p) + ((z2 * p1) * p1)),((z2 * q) * p2)) is Element of the U1 of CS
K4((((z2 * p) * p) + ((z2 * p1) * p1)),((z2 * q) * p2)) is set
the U5 of CS . K4((((z2 * p) * p) + ((z2 * p1) * p1)),((z2 * q) * p2)) is set
(z1 * q1) * p is Element of the U1 of CS
K138( the Mult of CS,(z1 * q1),p) is set
K4((z1 * q1),p) is set
the Mult of CS . K4((z1 * q1),p) is set
(z1 * r) * p1 is Element of the U1 of CS
K138( the Mult of CS,(z1 * r),p1) is set
K4((z1 * r),p1) is set
the Mult of CS . K4((z1 * r),p1) is set
((z1 * q1) * p) + ((z1 * r) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * q1) * p),((z1 * r) * p1)) is Element of the U1 of CS
K4(((z1 * q1) * p),((z1 * r) * p1)) is set
the U5 of CS . K4(((z1 * q1) * p),((z1 * r) * p1)) is set
(z1 * y) * p2 is Element of the U1 of CS
K138( the Mult of CS,(z1 * y),p2) is set
K4((z1 * y),p2) is set
the Mult of CS . K4((z1 * y),p2) is set
(((z1 * q1) * p) + ((z1 * r) * p1)) + ((z1 * y) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * q1) * p) + ((z1 * r) * p1)),((z1 * y) * p2)) is Element of the U1 of CS
K4((((z1 * q1) * p) + ((z1 * r) * p1)),((z1 * y) * p2)) is set
the U5 of CS . K4((((z1 * q1) * p) + ((z1 * r) * p1)),((z1 * y) * p2)) is set
((((z2 * p) * p) + ((z2 * p1) * p1)) + ((z2 * q) * p2)) + ((((z1 * q1) * p) + ((z1 * r) * p1)) + ((z1 * y) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z2 * p) * p) + ((z2 * p1) * p1)) + ((z2 * q) * p2)),((((z1 * q1) * p) + ((z1 * r) * p1)) + ((z1 * y) * p2))) is Element of the U1 of CS
K4(((((z2 * p) * p) + ((z2 * p1) * p1)) + ((z2 * q) * p2)),((((z1 * q1) * p) + ((z1 * r) * p1)) + ((z1 * y) * p2))) is set
the U5 of CS . K4(((((z2 * p) * p) + ((z2 * p1) * p1)) + ((z2 * q) * p2)),((((z1 * q1) * p) + ((z1 * r) * p1)) + ((z1 * y) * p2))) is set
((z2 * p) * p) + ((z1 * q1) * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z2 * p) * p),((z1 * q1) * p)) is Element of the U1 of CS
K4(((z2 * p) * p),((z1 * q1) * p)) is set
the U5 of CS . K4(((z2 * p) * p),((z1 * q1) * p)) is set
((z2 * p1) * p1) + ((z1 * r) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z2 * p1) * p1),((z1 * r) * p1)) is Element of the U1 of CS
K4(((z2 * p1) * p1),((z1 * r) * p1)) is set
the U5 of CS . K4(((z2 * p1) * p1),((z1 * r) * p1)) is set
(((z2 * p) * p) + ((z1 * q1) * p)) + (((z2 * p1) * p1) + ((z1 * r) * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z2 * p) * p) + ((z1 * q1) * p)),(((z2 * p1) * p1) + ((z1 * r) * p1))) is Element of the U1 of CS
K4((((z2 * p) * p) + ((z1 * q1) * p)),(((z2 * p1) * p1) + ((z1 * r) * p1))) is set
the U5 of CS . K4((((z2 * p) * p) + ((z1 * q1) * p)),(((z2 * p1) * p1) + ((z1 * r) * p1))) is set
((z2 * q) * p2) + ((z1 * y) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z2 * q) * p2),((z1 * y) * p2)) is Element of the U1 of CS
K4(((z2 * q) * p2),((z1 * y) * p2)) is set
the U5 of CS . K4(((z2 * q) * p2),((z1 * y) * p2)) is set
((((z2 * p) * p) + ((z1 * q1) * p)) + (((z2 * p1) * p1) + ((z1 * r) * p1))) + (((z2 * q) * p2) + ((z1 * y) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z2 * p) * p) + ((z1 * q1) * p)) + (((z2 * p1) * p1) + ((z1 * r) * p1))),(((z2 * q) * p2) + ((z1 * y) * p2))) is Element of the U1 of CS
K4(((((z2 * p) * p) + ((z1 * q1) * p)) + (((z2 * p1) * p1) + ((z1 * r) * p1))),(((z2 * q) * p2) + ((z1 * y) * p2))) is set
the U5 of CS . K4(((((z2 * p) * p) + ((z1 * q1) * p)) + (((z2 * p1) * p1) + ((z1 * r) * p1))),(((z2 * q) * p2) + ((z1 * y) * p2))) is set
(((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) * p1) + ((z1 * r) * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z2 * p) + (z1 * q1)) * p),(((z2 * p1) * p1) + ((z1 * r) * p1))) is Element of the U1 of CS
K4((((z2 * p) + (z1 * q1)) * p),(((z2 * p1) * p1) + ((z1 * r) * p1))) is set
the U5 of CS . K4((((z2 * p) + (z1 * q1)) * p),(((z2 * p1) * p1) + ((z1 * r) * p1))) is set
((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) * p1) + ((z1 * r) * p1))) + (((z2 * q) * p2) + ((z1 * y) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) * p1) + ((z1 * r) * p1))),(((z2 * q) * p2) + ((z1 * y) * p2))) is Element of the U1 of CS
K4(((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) * p1) + ((z1 * r) * p1))),(((z2 * q) * p2) + ((z1 * y) * p2))) is set
the U5 of CS . K4(((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) * p1) + ((z1 * r) * p1))),(((z2 * q) * p2) + ((z1 * y) * p2))) is set
((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) + (z1 * r)) * p1)) + (((z2 * q) * p2) + ((z1 * y) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) + (z1 * r)) * p1)),(((z2 * q) * p2) + ((z1 * y) * p2))) is Element of the U1 of CS
K4(((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) + (z1 * r)) * p1)),(((z2 * q) * p2) + ((z1 * y) * p2))) is set
the U5 of CS . K4(((((z2 * p) + (z1 * q1)) * p) + (((z2 * p1) + (z1 * r)) * p1)),(((z2 * q) * p2) + ((z1 * y) * p2))) is set
z2 is Element of the U1 of CS
z1 is Element of the U1 of CS
x2 is Element of the U1 of CS
y " is V24() V25() Element of REAL
q * (y ") is V24() V25() Element of REAL
- (q * (y ")) is V24() V25() Element of REAL
1 * r is Element of the U1 of CS
K138( the Mult of CS,1,r) is set
K4(1,r) is set
the Mult of CS . K4(1,r) is set
(- (q * (y "))) * r1 is Element of the U1 of CS
K138( the Mult of CS,(- (q * (y "))),r1) is set
K4((- (q * (y "))),r1) is set
the Mult of CS . K4((- (q * (y "))),r1) is set
(1 * r) + ((- (q * (y "))) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * r),((- (q * (y "))) * r1)) is Element of the U1 of CS
K4((1 * r),((- (q * (y "))) * r1)) is set
the U5 of CS . K4((1 * r),((- (q * (y "))) * r1)) is set
- r1 is Element of the U1 of CS
(q * (y ")) * (- r1) is Element of the U1 of CS
K138( the Mult of CS,(q * (y ")),(- r1)) is set
K4((q * (y ")),(- r1)) is set
the Mult of CS . K4((q * (y ")),(- r1)) is set
(1 * r) + ((q * (y ")) * (- r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * r),((q * (y ")) * (- r1))) is Element of the U1 of CS
K4((1 * r),((q * (y ")) * (- r1))) is set
the U5 of CS . K4((1 * r),((q * (y ")) * (- r1))) is set
(q * (y ")) * r1 is Element of the U1 of CS
K138( the Mult of CS,(q * (y ")),r1) is set
K4((q * (y ")),r1) is set
the Mult of CS . K4((q * (y ")),r1) is set
- ((q * (y ")) * r1) is Element of the U1 of CS
(1 * r) + (- ((q * (y ")) * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * r),(- ((q * (y ")) * r1))) is Element of the U1 of CS
K4((1 * r),(- ((q * (y ")) * r1))) is set
the U5 of CS . K4((1 * r),(- ((q * (y ")) * r1))) is set
- (1 * r) is Element of the U1 of CS
1 * q is V24() V25() Element of REAL
(- (q * (y "))) * y is V24() V25() Element of REAL
(1 * q) + ((- (q * (y "))) * y) is V24() V25() Element of REAL
- q is V24() V25() Element of REAL
(y ") * y is V24() V25() Element of REAL
(- q) * ((y ") * y) is V24() V25() Element of REAL
q + ((- q) * ((y ") * y)) is V24() V25() Element of REAL
(- q) * 1 is V24() V25() Element of REAL
q + ((- q) * 1) is V24() V25() Element of REAL
1 * p is V24() V25() Element of REAL
(- (q * (y "))) * q1 is V24() V25() Element of REAL
(1 * p) + ((- (q * (y "))) * q1) is V24() V25() Element of REAL
((1 * p) + ((- (q * (y "))) * q1)) * p is Element of the U1 of CS
K138( the Mult of CS,((1 * p) + ((- (q * (y "))) * q1)),p) is set
K4(((1 * p) + ((- (q * (y "))) * q1)),p) is set
the Mult of CS . K4(((1 * p) + ((- (q * (y "))) * q1)),p) is set
1 * p1 is V24() V25() Element of REAL
(- (q * (y "))) * r is V24() V25() Element of REAL
(1 * p1) + ((- (q * (y "))) * r) is V24() V25() Element of REAL
((1 * p1) + ((- (q * (y "))) * r)) * p1 is Element of the U1 of CS
K138( the Mult of CS,((1 * p1) + ((- (q * (y "))) * r)),p1) is set
K4(((1 * p1) + ((- (q * (y "))) * r)),p1) is set
the Mult of CS . K4(((1 * p1) + ((- (q * (y "))) * r)),p1) is set
(((1 * p) + ((- (q * (y "))) * q1)) * p) + (((1 * p1) + ((- (q * (y "))) * r)) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((1 * p) + ((- (q * (y "))) * q1)) * p),(((1 * p1) + ((- (q * (y "))) * r)) * p1)) is Element of the U1 of CS
K4((((1 * p) + ((- (q * (y "))) * q1)) * p),(((1 * p1) + ((- (q * (y "))) * r)) * p1)) is set
the U5 of CS . K4((((1 * p) + ((- (q * (y "))) * q1)) * p),(((1 * p1) + ((- (q * (y "))) * r)) * p1)) is set
0 * p2 is Element of the U1 of CS
K138( the Mult of CS,0,p2) is set
K4(0,p2) is set
the Mult of CS . K4(0,p2) is set
((((1 * p) + ((- (q * (y "))) * q1)) * p) + (((1 * p1) + ((- (q * (y "))) * r)) * p1)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((1 * p) + ((- (q * (y "))) * q1)) * p) + (((1 * p1) + ((- (q * (y "))) * r)) * p1)),(0 * p2)) is Element of the U1 of CS
K4(((((1 * p) + ((- (q * (y "))) * q1)) * p) + (((1 * p1) + ((- (q * (y "))) * r)) * p1)),(0 * p2)) is set
the U5 of CS . K4(((((1 * p) + ((- (q * (y "))) * q1)) * p) + (((1 * p1) + ((- (q * (y "))) * r)) * p1)),(0 * p2)) is set
((((1 * p) + ((- (q * (y "))) * q1)) * p) + (((1 * p1) + ((- (q * (y "))) * r)) * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((1 * p) + ((- (q * (y "))) * q1)) * p) + (((1 * p1) + ((- (q * (y "))) * r)) * p1)),(0. CS)) is Element of the U1 of CS
K4(((((1 * p) + ((- (q * (y "))) * q1)) * p) + (((1 * p1) + ((- (q * (y "))) * r)) * p1)),(0. CS)) is set
the U5 of CS . K4(((((1 * p) + ((- (q * (y "))) * q1)) * p) + (((1 * p1) + ((- (q * (y "))) * r)) * p1)),(0. CS)) is set
0 * r is Element of the U1 of CS
K138( the Mult of CS,0,r) is set
K4(0,r) is set
the Mult of CS . K4(0,r) is set
1 * r1 is Element of the U1 of CS
K138( the Mult of CS,1,r1) is set
K4(1,r1) is set
the Mult of CS . K4(1,r1) is set
(0 * r) + (1 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * r),(1 * r1)) is Element of the U1 of CS
K4((0 * r),(1 * r1)) is set
the U5 of CS . K4((0 * r),(1 * r1)) is set
(0 * r) + r1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * r),r1) is Element of the U1 of CS
K4((0 * r),r1) is set
the U5 of CS . K4((0 * r),r1) is set
(0. CS) + r1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),r1) is Element of the U1 of CS
K4((0. CS),r1) is set
the U5 of CS . K4((0. CS),r1) is set
0 * q is V24() V25() Element of REAL
1 * y is V24() V25() Element of REAL
(0 * q) + (1 * y) is V24() V25() Element of REAL
0 * p is V24() V25() Element of REAL
1 * q1 is V24() V25() Element of REAL
(0 * p) + (1 * q1) is V24() V25() Element of REAL
((0 * p) + (1 * q1)) * p is Element of the U1 of CS
K138( the Mult of CS,((0 * p) + (1 * q1)),p) is set
K4(((0 * p) + (1 * q1)),p) is set
the Mult of CS . K4(((0 * p) + (1 * q1)),p) is set
0 * p1 is V24() V25() Element of REAL
1 * r is V24() V25() Element of REAL
(0 * p1) + (1 * r) is V24() V25() Element of REAL
((0 * p1) + (1 * r)) * p1 is Element of the U1 of CS
K138( the Mult of CS,((0 * p1) + (1 * r)),p1) is set
K4(((0 * p1) + (1 * r)),p1) is set
the Mult of CS . K4(((0 * p1) + (1 * r)),p1) is set
(((0 * p) + (1 * q1)) * p) + (((0 * p1) + (1 * r)) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((0 * p) + (1 * q1)) * p),(((0 * p1) + (1 * r)) * p1)) is Element of the U1 of CS
K4((((0 * p) + (1 * q1)) * p),(((0 * p1) + (1 * r)) * p1)) is set
the U5 of CS . K4((((0 * p) + (1 * q1)) * p),(((0 * p1) + (1 * r)) * p1)) is set
((((0 * p) + (1 * q1)) * p) + (((0 * p1) + (1 * r)) * p1)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((0 * p) + (1 * q1)) * p) + (((0 * p1) + (1 * r)) * p1)),(0 * p2)) is Element of the U1 of CS
K4(((((0 * p) + (1 * q1)) * p) + (((0 * p1) + (1 * r)) * p1)),(0 * p2)) is set
the U5 of CS . K4(((((0 * p) + (1 * q1)) * p) + (((0 * p1) + (1 * r)) * p1)),(0 * p2)) is set
((((0 * p) + (1 * q1)) * p) + (((0 * p1) + (1 * r)) * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((0 * p) + (1 * q1)) * p) + (((0 * p1) + (1 * r)) * p1)),(0. CS)) is Element of the U1 of CS
K4(((((0 * p) + (1 * q1)) * p) + (((0 * p1) + (1 * r)) * p1)),(0. CS)) is set
the U5 of CS . K4(((((0 * p) + (1 * q1)) * p) + (((0 * p1) + (1 * r)) * p1)),(0. CS)) is set
z2 is Element of the U1 of CS
z1 is Element of the U1 of CS
0 * r1 is Element of the U1 of CS
K138( the Mult of CS,0,r1) is set
K4(0,r1) is set
the Mult of CS . K4(0,r1) is set
(1 * r) + (0 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * r),(0 * r1)) is Element of the U1 of CS
K4((1 * r),(0 * r1)) is set
the U5 of CS . K4((1 * r),(0 * r1)) is set
r + (0 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,(0 * r1)) is Element of the U1 of CS
K4(r,(0 * r1)) is set
the U5 of CS . K4(r,(0 * r1)) is set
r + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,(0. CS)) is Element of the U1 of CS
K4(r,(0. CS)) is set
the U5 of CS . K4(r,(0. CS)) is set
0 * y is V24() V25() Element of REAL
(1 * q) + (0 * y) is V24() V25() Element of REAL
0 * q1 is V24() V25() Element of REAL
(1 * p) + (0 * q1) is V24() V25() Element of REAL
((1 * p) + (0 * q1)) * p is Element of the U1 of CS
K138( the Mult of CS,((1 * p) + (0 * q1)),p) is set
K4(((1 * p) + (0 * q1)),p) is set
the Mult of CS . K4(((1 * p) + (0 * q1)),p) is set
0 * r is V24() V25() Element of REAL
(1 * p1) + (0 * r) is V24() V25() Element of REAL
((1 * p1) + (0 * r)) * p1 is Element of the U1 of CS
K138( the Mult of CS,((1 * p1) + (0 * r)),p1) is set
K4(((1 * p1) + (0 * r)),p1) is set
the Mult of CS . K4(((1 * p1) + (0 * r)),p1) is set
(((1 * p) + (0 * q1)) * p) + (((1 * p1) + (0 * r)) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((1 * p) + (0 * q1)) * p),(((1 * p1) + (0 * r)) * p1)) is Element of the U1 of CS
K4((((1 * p) + (0 * q1)) * p),(((1 * p1) + (0 * r)) * p1)) is set
the U5 of CS . K4((((1 * p) + (0 * q1)) * p),(((1 * p1) + (0 * r)) * p1)) is set
((((1 * p) + (0 * q1)) * p) + (((1 * p1) + (0 * r)) * p1)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((1 * p) + (0 * q1)) * p) + (((1 * p1) + (0 * r)) * p1)),(0 * p2)) is Element of the U1 of CS
K4(((((1 * p) + (0 * q1)) * p) + (((1 * p1) + (0 * r)) * p1)),(0 * p2)) is set
the U5 of CS . K4(((((1 * p) + (0 * q1)) * p) + (((1 * p1) + (0 * r)) * p1)),(0 * p2)) is set
((((1 * p) + (0 * q1)) * p) + (((1 * p1) + (0 * r)) * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((1 * p) + (0 * q1)) * p) + (((1 * p1) + (0 * r)) * p1)),(0. CS)) is Element of the U1 of CS
K4(((((1 * p) + (0 * q1)) * p) + (((1 * p1) + (0 * r)) * p1)),(0. CS)) is set
the U5 of CS . K4(((((1 * p) + (0 * q1)) * p) + (((1 * p1) + (0 * r)) * p1)),(0. CS)) is set
z2 is Element of the U1 of CS
z2 is Element of the U1 of CS
z1 is Element of the U1 of CS
x2 is Element of the U1 of CS
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is V24() V25() Element of REAL
p is V24() V25() Element of REAL
p * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p,p) is set
K4(p,p) is set
the Mult of CS . K4(p,p) is set
r1 * p is V24() V25() Element of REAL
(r1 * p) * p is Element of the U1 of CS
K138( the Mult of CS,(r1 * p),p) is set
K4((r1 * p),p) is set
the Mult of CS . K4((r1 * p),p) is set
p1 is V24() V25() Element of REAL
p1 * p1 is Element of the U1 of CS
K138( the Mult of CS,p1,p1) is set
K4(p1,p1) is set
the Mult of CS . K4(p1,p1) is set
(p * p) + (p1 * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(p * p),(p1 * p1)) is Element of the U1 of CS
K4((p * p),(p1 * p1)) is set
the U5 of CS . K4((p * p),(p1 * p1)) is set
r1 * p1 is V24() V25() Element of REAL
(r1 * p1) * p1 is Element of the U1 of CS
K138( the Mult of CS,(r1 * p1),p1) is set
K4((r1 * p1),p1) is set
the Mult of CS . K4((r1 * p1),p1) is set
((r1 * p) * p) + ((r1 * p1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * p) * p),((r1 * p1) * p1)) is Element of the U1 of CS
K4(((r1 * p) * p),((r1 * p1) * p1)) is set
the U5 of CS . K4(((r1 * p) * p),((r1 * p1) * p1)) is set
q is V24() V25() Element of REAL
q * p2 is Element of the U1 of CS
K138( the Mult of CS,q,p2) is set
K4(q,p2) is set
the Mult of CS . K4(q,p2) is set
((p * p) + (p1 * p1)) + (q * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p * p) + (p1 * p1)),(q * p2)) is Element of the U1 of CS
K4(((p * p) + (p1 * p1)),(q * p2)) is set
the U5 of CS . K4(((p * p) + (p1 * p1)),(q * p2)) is set
r1 * q is V24() V25() Element of REAL
(r1 * q) * p2 is Element of the U1 of CS
K138( the Mult of CS,(r1 * q),p2) is set
K4((r1 * q),p2) is set
the Mult of CS . K4((r1 * q),p2) is set
(((r1 * p) * p) + ((r1 * p1) * p1)) + ((r1 * q) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r1 * p) * p) + ((r1 * p1) * p1)),((r1 * q) * p2)) is Element of the U1 of CS
K4((((r1 * p) * p) + ((r1 * p1) * p1)),((r1 * q) * p2)) is set
the U5 of CS . K4((((r1 * p) * p) + ((r1 * p1) * p1)),((r1 * q) * p2)) is set
q1 is V24() V25() Element of REAL
q1 * r is Element of the U1 of CS
K138( the Mult of CS,q1,r) is set
K4(q1,r) is set
the Mult of CS . K4(q1,r) is set
(((p * p) + (p1 * p1)) + (q * p2)) + (q1 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p * p) + (p1 * p1)) + (q * p2)),(q1 * r)) is Element of the U1 of CS
K4((((p * p) + (p1 * p1)) + (q * p2)),(q1 * r)) is set
the U5 of CS . K4((((p * p) + (p1 * p1)) + (q * p2)),(q1 * r)) is set
r1 * ((((p * p) + (p1 * p1)) + (q * p2)) + (q1 * r)) is Element of the U1 of CS
K138( the Mult of CS,r1,((((p * p) + (p1 * p1)) + (q * p2)) + (q1 * r))) is set
K4(r1,((((p * p) + (p1 * p1)) + (q * p2)) + (q1 * r))) is set
the Mult of CS . K4(r1,((((p * p) + (p1 * p1)) + (q * p2)) + (q1 * r))) is set
r1 * q1 is V24() V25() Element of REAL
(r1 * q1) * r is Element of the U1 of CS
K138( the Mult of CS,(r1 * q1),r) is set
K4((r1 * q1),r) is set
the Mult of CS . K4((r1 * q1),r) is set
((((r1 * p) * p) + ((r1 * p1) * p1)) + ((r1 * q) * p2)) + ((r1 * q1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((r1 * p) * p) + ((r1 * p1) * p1)) + ((r1 * q) * p2)),((r1 * q1) * r)) is Element of the U1 of CS
K4(((((r1 * p) * p) + ((r1 * p1) * p1)) + ((r1 * q) * p2)),((r1 * q1) * r)) is set
the U5 of CS . K4(((((r1 * p) * p) + ((r1 * p1) * p1)) + ((r1 * q) * p2)),((r1 * q1) * r)) is set
r1 * (p * p) is Element of the U1 of CS
K138( the Mult of CS,r1,(p * p)) is set
K4(r1,(p * p)) is set
the Mult of CS . K4(r1,(p * p)) is set
(r1 * (p * p)) + ((r1 * p1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * (p * p)),((r1 * p1) * p1)) is Element of the U1 of CS
K4((r1 * (p * p)),((r1 * p1) * p1)) is set
the U5 of CS . K4((r1 * (p * p)),((r1 * p1) * p1)) is set
((r1 * (p * p)) + ((r1 * p1) * p1)) + ((r1 * q) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * (p * p)) + ((r1 * p1) * p1)),((r1 * q) * p2)) is Element of the U1 of CS
K4(((r1 * (p * p)) + ((r1 * p1) * p1)),((r1 * q) * p2)) is set
the U5 of CS . K4(((r1 * (p * p)) + ((r1 * p1) * p1)),((r1 * q) * p2)) is set
(((r1 * (p * p)) + ((r1 * p1) * p1)) + ((r1 * q) * p2)) + ((r1 * q1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r1 * (p * p)) + ((r1 * p1) * p1)) + ((r1 * q) * p2)),((r1 * q1) * r)) is Element of the U1 of CS
K4((((r1 * (p * p)) + ((r1 * p1) * p1)) + ((r1 * q) * p2)),((r1 * q1) * r)) is set
the U5 of CS . K4((((r1 * (p * p)) + ((r1 * p1) * p1)) + ((r1 * q) * p2)),((r1 * q1) * r)) is set
r1 * (p1 * p1) is Element of the U1 of CS
K138( the Mult of CS,r1,(p1 * p1)) is set
K4(r1,(p1 * p1)) is set
the Mult of CS . K4(r1,(p1 * p1)) is set
(r1 * (p * p)) + (r1 * (p1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * (p * p)),(r1 * (p1 * p1))) is Element of the U1 of CS
K4((r1 * (p * p)),(r1 * (p1 * p1))) is set
the U5 of CS . K4((r1 * (p * p)),(r1 * (p1 * p1))) is set
((r1 * (p * p)) + (r1 * (p1 * p1))) + ((r1 * q) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * (p * p)) + (r1 * (p1 * p1))),((r1 * q) * p2)) is Element of the U1 of CS
K4(((r1 * (p * p)) + (r1 * (p1 * p1))),((r1 * q) * p2)) is set
the U5 of CS . K4(((r1 * (p * p)) + (r1 * (p1 * p1))),((r1 * q) * p2)) is set
(((r1 * (p * p)) + (r1 * (p1 * p1))) + ((r1 * q) * p2)) + ((r1 * q1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r1 * (p * p)) + (r1 * (p1 * p1))) + ((r1 * q) * p2)),((r1 * q1) * r)) is Element of the U1 of CS
K4((((r1 * (p * p)) + (r1 * (p1 * p1))) + ((r1 * q) * p2)),((r1 * q1) * r)) is set
the U5 of CS . K4((((r1 * (p * p)) + (r1 * (p1 * p1))) + ((r1 * q) * p2)),((r1 * q1) * r)) is set
r1 * ((p * p) + (p1 * p1)) is Element of the U1 of CS
K138( the Mult of CS,r1,((p * p) + (p1 * p1))) is set
K4(r1,((p * p) + (p1 * p1))) is set
the Mult of CS . K4(r1,((p * p) + (p1 * p1))) is set
(r1 * ((p * p) + (p1 * p1))) + ((r1 * q) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * ((p * p) + (p1 * p1))),((r1 * q) * p2)) is Element of the U1 of CS
K4((r1 * ((p * p) + (p1 * p1))),((r1 * q) * p2)) is set
the U5 of CS . K4((r1 * ((p * p) + (p1 * p1))),((r1 * q) * p2)) is set
((r1 * ((p * p) + (p1 * p1))) + ((r1 * q) * p2)) + ((r1 * q1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * ((p * p) + (p1 * p1))) + ((r1 * q) * p2)),((r1 * q1) * r)) is Element of the U1 of CS
K4(((r1 * ((p * p) + (p1 * p1))) + ((r1 * q) * p2)),((r1 * q1) * r)) is set
the U5 of CS . K4(((r1 * ((p * p) + (p1 * p1))) + ((r1 * q) * p2)),((r1 * q1) * r)) is set
r1 * (q * p2) is Element of the U1 of CS
K138( the Mult of CS,r1,(q * p2)) is set
K4(r1,(q * p2)) is set
the Mult of CS . K4(r1,(q * p2)) is set
(r1 * ((p * p) + (p1 * p1))) + (r1 * (q * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * ((p * p) + (p1 * p1))),(r1 * (q * p2))) is Element of the U1 of CS
K4((r1 * ((p * p) + (p1 * p1))),(r1 * (q * p2))) is set
the U5 of CS . K4((r1 * ((p * p) + (p1 * p1))),(r1 * (q * p2))) is set
((r1 * ((p * p) + (p1 * p1))) + (r1 * (q * p2))) + ((r1 * q1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * ((p * p) + (p1 * p1))) + (r1 * (q * p2))),((r1 * q1) * r)) is Element of the U1 of CS
K4(((r1 * ((p * p) + (p1 * p1))) + (r1 * (q * p2))),((r1 * q1) * r)) is set
the U5 of CS . K4(((r1 * ((p * p) + (p1 * p1))) + (r1 * (q * p2))),((r1 * q1) * r)) is set
r1 * (q1 * r) is Element of the U1 of CS
K138( the Mult of CS,r1,(q1 * r)) is set
K4(r1,(q1 * r)) is set
the Mult of CS . K4(r1,(q1 * r)) is set
((r1 * ((p * p) + (p1 * p1))) + (r1 * (q * p2))) + (r1 * (q1 * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * ((p * p) + (p1 * p1))) + (r1 * (q * p2))),(r1 * (q1 * r))) is Element of the U1 of CS
K4(((r1 * ((p * p) + (p1 * p1))) + (r1 * (q * p2))),(r1 * (q1 * r))) is set
the U5 of CS . K4(((r1 * ((p * p) + (p1 * p1))) + (r1 * (q * p2))),(r1 * (q1 * r))) is set
r1 * (((p * p) + (p1 * p1)) + (q * p2)) is Element of the U1 of CS
K138( the Mult of CS,r1,(((p * p) + (p1 * p1)) + (q * p2))) is set
K4(r1,(((p * p) + (p1 * p1)) + (q * p2))) is set
the Mult of CS . K4(r1,(((p * p) + (p1 * p1)) + (q * p2))) is set
(r1 * (((p * p) + (p1 * p1)) + (q * p2))) + (r1 * (q1 * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * (((p * p) + (p1 * p1)) + (q * p2))),(r1 * (q1 * r))) is Element of the U1 of CS
K4((r1 * (((p * p) + (p1 * p1)) + (q * p2))),(r1 * (q1 * r))) is set
the U5 of CS . K4((r1 * (((p * p) + (p1 * p1)) + (q * p2))),(r1 * (q1 * r))) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p + p1 is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,p,p1) is Element of the U1 of CS
K4(p,p1) is set
the U5 of CS . K4(p,p1) is set
p2 is Element of the U1 of CS
(p + p1) + p2 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + p1),p2) is Element of the U1 of CS
K4((p + p1),p2) is set
the U5 of CS . K4((p + p1),p2) is set
r is Element of the U1 of CS
((p + p1) + p2) + r is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + p1) + p2),r) is Element of the U1 of CS
K4(((p + p1) + p2),r) is set
the U5 of CS . K4(((p + p1) + p2),r) is set
r1 is Element of the U1 of CS
p + r1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,r1) is Element of the U1 of CS
K4(p,r1) is set
the U5 of CS . K4(p,r1) is set
p is Element of the U1 of CS
r1 + p is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r1,p) is Element of the U1 of CS
K4(r1,p) is set
the U5 of CS . K4(r1,p) is set
p1 + p is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p1,p) is Element of the U1 of CS
K4(p1,p) is set
the U5 of CS . K4(p1,p) is set
(p + r1) + (p1 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + r1),(p1 + p)) is Element of the U1 of CS
K4((p + r1),(p1 + p)) is set
the U5 of CS . K4((p + r1),(p1 + p)) is set
p1 is Element of the U1 of CS
(r1 + p) + p1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 + p),p1) is Element of the U1 of CS
K4((r1 + p),p1) is set
the U5 of CS . K4((r1 + p),p1) is set
p2 + p1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p2,p1) is Element of the U1 of CS
K4(p2,p1) is set
the U5 of CS . K4(p2,p1) is set
((p + r1) + (p1 + p)) + (p2 + p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + r1) + (p1 + p)),(p2 + p1)) is Element of the U1 of CS
K4(((p + r1) + (p1 + p)),(p2 + p1)) is set
the U5 of CS . K4(((p + r1) + (p1 + p)),(p2 + p1)) is set
q is Element of the U1 of CS
((r1 + p) + p1) + q is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 + p) + p1),q) is Element of the U1 of CS
K4(((r1 + p) + p1),q) is set
the U5 of CS . K4(((r1 + p) + p1),q) is set
(((p + p1) + p2) + r) + (((r1 + p) + p1) + q) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p + p1) + p2) + r),(((r1 + p) + p1) + q)) is Element of the U1 of CS
K4((((p + p1) + p2) + r),(((r1 + p) + p1) + q)) is set
the U5 of CS . K4((((p + p1) + p2) + r),(((r1 + p) + p1) + q)) is set
r + q is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,q) is Element of the U1 of CS
K4(r,q) is set
the U5 of CS . K4(r,q) is set
(((p + r1) + (p1 + p)) + (p2 + p1)) + (r + q) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p + r1) + (p1 + p)) + (p2 + p1)),(r + q)) is Element of the U1 of CS
K4((((p + r1) + (p1 + p)) + (p2 + p1)),(r + q)) is set
the U5 of CS . K4((((p + r1) + (p1 + p)) + (p2 + p1)),(r + q)) is set
p + (p1 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,(p1 + p)) is Element of the U1 of CS
K4(p,(p1 + p)) is set
the U5 of CS . K4(p,(p1 + p)) is set
r1 + (p + (p1 + p)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r1,(p + (p1 + p))) is Element of the U1 of CS
K4(r1,(p + (p1 + p))) is set
the U5 of CS . K4(r1,(p + (p1 + p))) is set
(r1 + (p + (p1 + p))) + (p2 + p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 + (p + (p1 + p))),(p2 + p1)) is Element of the U1 of CS
K4((r1 + (p + (p1 + p))),(p2 + p1)) is set
the U5 of CS . K4((r1 + (p + (p1 + p))),(p2 + p1)) is set
((r1 + (p + (p1 + p))) + (p2 + p1)) + (r + q) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 + (p + (p1 + p))) + (p2 + p1)),(r + q)) is Element of the U1 of CS
K4(((r1 + (p + (p1 + p))) + (p2 + p1)),(r + q)) is set
the U5 of CS . K4(((r1 + (p + (p1 + p))) + (p2 + p1)),(r + q)) is set
(p + p1) + p is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + p1),p) is Element of the U1 of CS
K4((p + p1),p) is set
the U5 of CS . K4((p + p1),p) is set
r1 + ((p + p1) + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r1,((p + p1) + p)) is Element of the U1 of CS
K4(r1,((p + p1) + p)) is set
the U5 of CS . K4(r1,((p + p1) + p)) is set
(r1 + ((p + p1) + p)) + (p2 + p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 + ((p + p1) + p)),(p2 + p1)) is Element of the U1 of CS
K4((r1 + ((p + p1) + p)),(p2 + p1)) is set
the U5 of CS . K4((r1 + ((p + p1) + p)),(p2 + p1)) is set
((r1 + ((p + p1) + p)) + (p2 + p1)) + (r + q) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 + ((p + p1) + p)) + (p2 + p1)),(r + q)) is Element of the U1 of CS
K4(((r1 + ((p + p1) + p)) + (p2 + p1)),(r + q)) is set
the U5 of CS . K4(((r1 + ((p + p1) + p)) + (p2 + p1)),(r + q)) is set
(r1 + p) + (p + p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 + p),(p + p1)) is Element of the U1 of CS
K4((r1 + p),(p + p1)) is set
the U5 of CS . K4((r1 + p),(p + p1)) is set
((r1 + p) + (p + p1)) + (p2 + p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 + p) + (p + p1)),(p2 + p1)) is Element of the U1 of CS
K4(((r1 + p) + (p + p1)),(p2 + p1)) is set
the U5 of CS . K4(((r1 + p) + (p + p1)),(p2 + p1)) is set
(((r1 + p) + (p + p1)) + (p2 + p1)) + (r + q) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r1 + p) + (p + p1)) + (p2 + p1)),(r + q)) is Element of the U1 of CS
K4((((r1 + p) + (p + p1)) + (p2 + p1)),(r + q)) is set
the U5 of CS . K4((((r1 + p) + (p + p1)) + (p2 + p1)),(r + q)) is set
(p + p1) + (p2 + p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + p1),(p2 + p1)) is Element of the U1 of CS
K4((p + p1),(p2 + p1)) is set
the U5 of CS . K4((p + p1),(p2 + p1)) is set
(r1 + p) + ((p + p1) + (p2 + p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 + p),((p + p1) + (p2 + p1))) is Element of the U1 of CS
K4((r1 + p),((p + p1) + (p2 + p1))) is set
the U5 of CS . K4((r1 + p),((p + p1) + (p2 + p1))) is set
((r1 + p) + ((p + p1) + (p2 + p1))) + (r + q) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 + p) + ((p + p1) + (p2 + p1))),(r + q)) is Element of the U1 of CS
K4(((r1 + p) + ((p + p1) + (p2 + p1))),(r + q)) is set
the U5 of CS . K4(((r1 + p) + ((p + p1) + (p2 + p1))),(r + q)) is set
((p + p1) + p2) + p1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + p1) + p2),p1) is Element of the U1 of CS
K4(((p + p1) + p2),p1) is set
the U5 of CS . K4(((p + p1) + p2),p1) is set
(r1 + p) + (((p + p1) + p2) + p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 + p),(((p + p1) + p2) + p1)) is Element of the U1 of CS
K4((r1 + p),(((p + p1) + p2) + p1)) is set
the U5 of CS . K4((r1 + p),(((p + p1) + p2) + p1)) is set
((r1 + p) + (((p + p1) + p2) + p1)) + (r + q) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 + p) + (((p + p1) + p2) + p1)),(r + q)) is Element of the U1 of CS
K4(((r1 + p) + (((p + p1) + p2) + p1)),(r + q)) is set
the U5 of CS . K4(((r1 + p) + (((p + p1) + p2) + p1)),(r + q)) is set
((r1 + p) + p1) + ((p + p1) + p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 + p) + p1),((p + p1) + p2)) is Element of the U1 of CS
K4(((r1 + p) + p1),((p + p1) + p2)) is set
the U5 of CS . K4(((r1 + p) + p1),((p + p1) + p2)) is set
(((r1 + p) + p1) + ((p + p1) + p2)) + (r + q) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r1 + p) + p1) + ((p + p1) + p2)),(r + q)) is Element of the U1 of CS
K4((((r1 + p) + p1) + ((p + p1) + p2)),(r + q)) is set
the U5 of CS . K4((((r1 + p) + p1) + ((p + p1) + p2)),(r + q)) is set
((r1 + p) + p1) + (r + q) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 + p) + p1),(r + q)) is Element of the U1 of CS
K4(((r1 + p) + p1),(r + q)) is set
the U5 of CS . K4(((r1 + p) + p1),(r + q)) is set
((p + p1) + p2) + (((r1 + p) + p1) + (r + q)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + p1) + p2),(((r1 + p) + p1) + (r + q))) is Element of the U1 of CS
K4(((p + p1) + p2),(((r1 + p) + p1) + (r + q))) is set
the U5 of CS . K4(((p + p1) + p2),(((r1 + p) + p1) + (r + q))) is set
q + ((r1 + p) + p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,q,((r1 + p) + p1)) is Element of the U1 of CS
K4(q,((r1 + p) + p1)) is set
the U5 of CS . K4(q,((r1 + p) + p1)) is set
r + (q + ((r1 + p) + p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,(q + ((r1 + p) + p1))) is Element of the U1 of CS
K4(r,(q + ((r1 + p) + p1))) is set
the U5 of CS . K4(r,(q + ((r1 + p) + p1))) is set
((p + p1) + p2) + (r + (q + ((r1 + p) + p1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + p1) + p2),(r + (q + ((r1 + p) + p1)))) is Element of the U1 of CS
K4(((p + p1) + p2),(r + (q + ((r1 + p) + p1)))) is set
the U5 of CS . K4(((p + p1) + p2),(r + (q + ((r1 + p) + p1)))) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is V24() V25() Element of REAL
r1 is V24() V25() Element of REAL
r1 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,r1,p) is set
K4(r1,p) is set
the Mult of CS . K4(r1,p) is set
r * r1 is V24() V25() Element of REAL
(r * r1) * p is Element of the U1 of CS
K138( the Mult of CS,(r * r1),p) is set
K4((r * r1),p) is set
the Mult of CS . K4((r * r1),p) is set
p is V24() V25() Element of REAL
p * p1 is Element of the U1 of CS
K138( the Mult of CS,p,p1) is set
K4(p,p1) is set
the Mult of CS . K4(p,p1) is set
(r1 * p) + (p * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(r1 * p),(p * p1)) is Element of the U1 of CS
K4((r1 * p),(p * p1)) is set
the U5 of CS . K4((r1 * p),(p * p1)) is set
r * p is V24() V25() Element of REAL
(r * p) * p1 is Element of the U1 of CS
K138( the Mult of CS,(r * p),p1) is set
K4((r * p),p1) is set
the Mult of CS . K4((r * p),p1) is set
((r * r1) * p) + ((r * p) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * r1) * p),((r * p) * p1)) is Element of the U1 of CS
K4(((r * r1) * p),((r * p) * p1)) is set
the U5 of CS . K4(((r * r1) * p),((r * p) * p1)) is set
p1 is V24() V25() Element of REAL
p1 * p2 is Element of the U1 of CS
K138( the Mult of CS,p1,p2) is set
K4(p1,p2) is set
the Mult of CS . K4(p1,p2) is set
((r1 * p) + (p * p1)) + (p1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * p) + (p * p1)),(p1 * p2)) is Element of the U1 of CS
K4(((r1 * p) + (p * p1)),(p1 * p2)) is set
the U5 of CS . K4(((r1 * p) + (p * p1)),(p1 * p2)) is set
r * (((r1 * p) + (p * p1)) + (p1 * p2)) is Element of the U1 of CS
K138( the Mult of CS,r,(((r1 * p) + (p * p1)) + (p1 * p2))) is set
K4(r,(((r1 * p) + (p * p1)) + (p1 * p2))) is set
the Mult of CS . K4(r,(((r1 * p) + (p * p1)) + (p1 * p2))) is set
r * p1 is V24() V25() Element of REAL
(r * p1) * p2 is Element of the U1 of CS
K138( the Mult of CS,(r * p1),p2) is set
K4((r * p1),p2) is set
the Mult of CS . K4((r * p1),p2) is set
(((r * r1) * p) + ((r * p) * p1)) + ((r * p1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r * r1) * p) + ((r * p) * p1)),((r * p1) * p2)) is Element of the U1 of CS
K4((((r * r1) * p) + ((r * p) * p1)),((r * p1) * p2)) is set
the U5 of CS . K4((((r * r1) * p) + ((r * p) * p1)),((r * p1) * p2)) is set
r * (r1 * p) is Element of the U1 of CS
K138( the Mult of CS,r,(r1 * p)) is set
K4(r,(r1 * p)) is set
the Mult of CS . K4(r,(r1 * p)) is set
(r * (r1 * p)) + ((r * p) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * (r1 * p)),((r * p) * p1)) is Element of the U1 of CS
K4((r * (r1 * p)),((r * p) * p1)) is set
the U5 of CS . K4((r * (r1 * p)),((r * p) * p1)) is set
((r * (r1 * p)) + ((r * p) * p1)) + ((r * p1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * (r1 * p)) + ((r * p) * p1)),((r * p1) * p2)) is Element of the U1 of CS
K4(((r * (r1 * p)) + ((r * p) * p1)),((r * p1) * p2)) is set
the U5 of CS . K4(((r * (r1 * p)) + ((r * p) * p1)),((r * p1) * p2)) is set
r * (p * p1) is Element of the U1 of CS
K138( the Mult of CS,r,(p * p1)) is set
K4(r,(p * p1)) is set
the Mult of CS . K4(r,(p * p1)) is set
(r * (r1 * p)) + (r * (p * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * (r1 * p)),(r * (p * p1))) is Element of the U1 of CS
K4((r * (r1 * p)),(r * (p * p1))) is set
the U5 of CS . K4((r * (r1 * p)),(r * (p * p1))) is set
((r * (r1 * p)) + (r * (p * p1))) + ((r * p1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * (r1 * p)) + (r * (p * p1))),((r * p1) * p2)) is Element of the U1 of CS
K4(((r * (r1 * p)) + (r * (p * p1))),((r * p1) * p2)) is set
the U5 of CS . K4(((r * (r1 * p)) + (r * (p * p1))),((r * p1) * p2)) is set
r * ((r1 * p) + (p * p1)) is Element of the U1 of CS
K138( the Mult of CS,r,((r1 * p) + (p * p1))) is set
K4(r,((r1 * p) + (p * p1))) is set
the Mult of CS . K4(r,((r1 * p) + (p * p1))) is set
(r * ((r1 * p) + (p * p1))) + ((r * p1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * ((r1 * p) + (p * p1))),((r * p1) * p2)) is Element of the U1 of CS
K4((r * ((r1 * p) + (p * p1))),((r * p1) * p2)) is set
the U5 of CS . K4((r * ((r1 * p) + (p * p1))),((r * p1) * p2)) is set
r * (p1 * p2) is Element of the U1 of CS
K138( the Mult of CS,r,(p1 * p2)) is set
K4(r,(p1 * p2)) is set
the Mult of CS . K4(r,(p1 * p2)) is set
(r * ((r1 * p) + (p * p1))) + (r * (p1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * ((r1 * p) + (p * p1))),(r * (p1 * p2))) is Element of the U1 of CS
K4((r * ((r1 * p) + (p * p1))),(r * (p1 * p2))) is set
the U5 of CS . K4((r * ((r1 * p) + (p * p1))),(r * (p1 * p2))) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is V24() V25() Element of REAL
p * p1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p,p1) is set
K4(p,p1) is set
the Mult of CS . K4(p,p1) is set
p1 is V24() V25() Element of REAL
p1 * p2 is Element of the U1 of CS
K138( the Mult of CS,p1,p2) is set
K4(p1,p2) is set
the Mult of CS . K4(p1,p2) is set
(p * p1) + (p1 * p2) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(p * p1),(p1 * p2)) is Element of the U1 of CS
K4((p * p1),(p1 * p2)) is set
the U5 of CS . K4((p * p1),(p1 * p2)) is set
q is V24() V25() Element of REAL
q * p1 is Element of the U1 of CS
K138( the Mult of CS,q,p1) is set
K4(q,p1) is set
the Mult of CS . K4(q,p1) is set
p1 * q is V24() V25() Element of REAL
p + (p1 * q) is V24() V25() Element of REAL
(p + (p1 * q)) * p1 is Element of the U1 of CS
K138( the Mult of CS,(p + (p1 * q)),p1) is set
K4((p + (p1 * q)),p1) is set
the Mult of CS . K4((p + (p1 * q)),p1) is set
q1 is V24() V25() Element of REAL
q1 * r is Element of the U1 of CS
K138( the Mult of CS,q1,r) is set
K4(q1,r) is set
the Mult of CS . K4(q1,r) is set
(q * p1) + (q1 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q * p1),(q1 * r)) is Element of the U1 of CS
K4((q * p1),(q1 * r)) is set
the U5 of CS . K4((q * p1),(q1 * r)) is set
p1 * q1 is V24() V25() Element of REAL
(p1 * q1) * r is Element of the U1 of CS
K138( the Mult of CS,(p1 * q1),r) is set
K4((p1 * q1),r) is set
the Mult of CS . K4((p1 * q1),r) is set
((p + (p1 * q)) * p1) + ((p1 * q1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + (p1 * q)) * p1),((p1 * q1) * r)) is Element of the U1 of CS
K4(((p + (p1 * q)) * p1),((p1 * q1) * r)) is set
the U5 of CS . K4(((p + (p1 * q)) * p1),((p1 * q1) * r)) is set
r is V24() V25() Element of REAL
r * r1 is Element of the U1 of CS
K138( the Mult of CS,r,r1) is set
K4(r,r1) is set
the Mult of CS . K4(r,r1) is set
((q * p1) + (q1 * r)) + (r * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q * p1) + (q1 * r)),(r * r1)) is Element of the U1 of CS
K4(((q * p1) + (q1 * r)),(r * r1)) is set
the U5 of CS . K4(((q * p1) + (q1 * r)),(r * r1)) is set
p1 * r is V24() V25() Element of REAL
(p1 * r) * r1 is Element of the U1 of CS
K138( the Mult of CS,(p1 * r),r1) is set
K4((p1 * r),r1) is set
the Mult of CS . K4((p1 * r),r1) is set
(((p + (p1 * q)) * p1) + ((p1 * q1) * r)) + ((p1 * r) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p + (p1 * q)) * p1) + ((p1 * q1) * r)),((p1 * r) * r1)) is Element of the U1 of CS
K4((((p + (p1 * q)) * p1) + ((p1 * q1) * r)),((p1 * r) * r1)) is set
the U5 of CS . K4((((p + (p1 * q)) * p1) + ((p1 * q1) * r)),((p1 * r) * r1)) is set
(p1 * q) * p1 is Element of the U1 of CS
K138( the Mult of CS,(p1 * q),p1) is set
K4((p1 * q),p1) is set
the Mult of CS . K4((p1 * q),p1) is set
((p1 * q) * p1) + ((p1 * q1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p1 * q) * p1),((p1 * q1) * r)) is Element of the U1 of CS
K4(((p1 * q) * p1),((p1 * q1) * r)) is set
the U5 of CS . K4(((p1 * q) * p1),((p1 * q1) * r)) is set
(((p1 * q) * p1) + ((p1 * q1) * r)) + ((p1 * r) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p1 * q) * p1) + ((p1 * q1) * r)),((p1 * r) * r1)) is Element of the U1 of CS
K4((((p1 * q) * p1) + ((p1 * q1) * r)),((p1 * r) * r1)) is set
the U5 of CS . K4((((p1 * q) * p1) + ((p1 * q1) * r)),((p1 * r) * r1)) is set
(p * p1) + ((((p1 * q) * p1) + ((p1 * q1) * r)) + ((p1 * r) * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p * p1),((((p1 * q) * p1) + ((p1 * q1) * r)) + ((p1 * r) * r1))) is Element of the U1 of CS
K4((p * p1),((((p1 * q) * p1) + ((p1 * q1) * r)) + ((p1 * r) * r1))) is set
the U5 of CS . K4((p * p1),((((p1 * q) * p1) + ((p1 * q1) * r)) + ((p1 * r) * r1))) is set
((p1 * q1) * r) + ((p1 * r) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p1 * q1) * r),((p1 * r) * r1)) is Element of the U1 of CS
K4(((p1 * q1) * r),((p1 * r) * r1)) is set
the U5 of CS . K4(((p1 * q1) * r),((p1 * r) * r1)) is set
((p1 * q) * p1) + (((p1 * q1) * r) + ((p1 * r) * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p1 * q) * p1),(((p1 * q1) * r) + ((p1 * r) * r1))) is Element of the U1 of CS
K4(((p1 * q) * p1),(((p1 * q1) * r) + ((p1 * r) * r1))) is set
the U5 of CS . K4(((p1 * q) * p1),(((p1 * q1) * r) + ((p1 * r) * r1))) is set
(p * p1) + (((p1 * q) * p1) + (((p1 * q1) * r) + ((p1 * r) * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p * p1),(((p1 * q) * p1) + (((p1 * q1) * r) + ((p1 * r) * r1)))) is Element of the U1 of CS
K4((p * p1),(((p1 * q) * p1) + (((p1 * q1) * r) + ((p1 * r) * r1)))) is set
the U5 of CS . K4((p * p1),(((p1 * q) * p1) + (((p1 * q1) * r) + ((p1 * r) * r1)))) is set
(p * p1) + ((p1 * q) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p * p1),((p1 * q) * p1)) is Element of the U1 of CS
K4((p * p1),((p1 * q) * p1)) is set
the U5 of CS . K4((p * p1),((p1 * q) * p1)) is set
((p * p1) + ((p1 * q) * p1)) + (((p1 * q1) * r) + ((p1 * r) * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p * p1) + ((p1 * q) * p1)),(((p1 * q1) * r) + ((p1 * r) * r1))) is Element of the U1 of CS
K4(((p * p1) + ((p1 * q) * p1)),(((p1 * q1) * r) + ((p1 * r) * r1))) is set
the U5 of CS . K4(((p * p1) + ((p1 * q) * p1)),(((p1 * q1) * r) + ((p1 * r) * r1))) is set
((p + (p1 * q)) * p1) + (((p1 * q1) * r) + ((p1 * r) * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + (p1 * q)) * p1),(((p1 * q1) * r) + ((p1 * r) * r1))) is Element of the U1 of CS
K4(((p + (p1 * q)) * p1),(((p1 * q1) * r) + ((p1 * r) * r1))) is set
the U5 of CS . K4(((p + (p1 * q)) * p1),(((p1 * q1) * r) + ((p1 * r) * r1))) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is Element of the U1 of CS
p1 is V24() V25() Element of REAL
p1 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p1,p) is set
K4(p1,p) is set
the Mult of CS . K4(p1,p) is set
q is V24() V25() Element of REAL
q * p1 is Element of the U1 of CS
K138( the Mult of CS,q,p1) is set
K4(q,p1) is set
the Mult of CS . K4(q,p1) is set
(p1 * p) + (q * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(p1 * p),(q * p1)) is Element of the U1 of CS
K4((p1 * p),(q * p1)) is set
the U5 of CS . K4((p1 * p),(q * p1)) is set
q1 is V24() V25() Element of REAL
q1 * p2 is Element of the U1 of CS
K138( the Mult of CS,q1,p2) is set
K4(q1,p2) is set
the Mult of CS . K4(q1,p2) is set
((p1 * p) + (q * p1)) + (q1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p1 * p) + (q * p1)),(q1 * p2)) is Element of the U1 of CS
K4(((p1 * p) + (q * p1)),(q1 * p2)) is set
the U5 of CS . K4(((p1 * p) + (q * p1)),(q1 * p2)) is set
r is V24() V25() Element of REAL
r * r is Element of the U1 of CS
K138( the Mult of CS,r,r) is set
K4(r,r) is set
the Mult of CS . K4(r,r) is set
(((p1 * p) + (q * p1)) + (q1 * p2)) + (r * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p1 * p) + (q * p1)) + (q1 * p2)),(r * r)) is Element of the U1 of CS
K4((((p1 * p) + (q * p1)) + (q1 * p2)),(r * r)) is set
the U5 of CS . K4((((p1 * p) + (q * p1)) + (q1 * p2)),(r * r)) is set
y is V24() V25() Element of REAL
y * p is Element of the U1 of CS
K138( the Mult of CS,y,p) is set
K4(y,p) is set
the Mult of CS . K4(y,p) is set
z2 is V24() V25() Element of REAL
z2 * p1 is Element of the U1 of CS
K138( the Mult of CS,z2,p1) is set
K4(z2,p1) is set
the Mult of CS . K4(z2,p1) is set
(y * p) + (z2 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(y * p),(z2 * p1)) is Element of the U1 of CS
K4((y * p),(z2 * p1)) is set
the U5 of CS . K4((y * p),(z2 * p1)) is set
z1 is V24() V25() Element of REAL
z1 * p2 is Element of the U1 of CS
K138( the Mult of CS,z1,p2) is set
K4(z1,p2) is set
the Mult of CS . K4(z1,p2) is set
((y * p) + (z2 * p1)) + (z1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y * p) + (z2 * p1)),(z1 * p2)) is Element of the U1 of CS
K4(((y * p) + (z2 * p1)),(z1 * p2)) is set
the U5 of CS . K4(((y * p) + (z2 * p1)),(z1 * p2)) is set
x2 is V24() V25() Element of REAL
x2 * r is Element of the U1 of CS
K138( the Mult of CS,x2,r) is set
K4(x2,r) is set
the Mult of CS . K4(x2,r) is set
(((y * p) + (z2 * p1)) + (z1 * p2)) + (x2 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y * p) + (z2 * p1)) + (z1 * p2)),(x2 * r)) is Element of the U1 of CS
K4((((y * p) + (z2 * p1)) + (z1 * p2)),(x2 * r)) is set
the U5 of CS . K4((((y * p) + (z2 * p1)) + (z1 * p2)),(x2 * r)) is set
z1 is V24() V25() Element of REAL
z1 * r1 is Element of the U1 of CS
K138( the Mult of CS,z1,r1) is set
K4(z1,r1) is set
the Mult of CS . K4(z1,r1) is set
z1 * p1 is V24() V25() Element of REAL
z1 * q is V24() V25() Element of REAL
z1 * q1 is V24() V25() Element of REAL
z1 * r is V24() V25() Element of REAL
z1 is V24() V25() Element of REAL
z1 * p is Element of the U1 of CS
K138( the Mult of CS,z1,p) is set
K4(z1,p) is set
the Mult of CS . K4(z1,p) is set
(z1 * r1) + (z1 * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * r1),(z1 * p)) is Element of the U1 of CS
K4((z1 * r1),(z1 * p)) is set
the U5 of CS . K4((z1 * r1),(z1 * p)) is set
z1 * y is V24() V25() Element of REAL
(z1 * p1) + (z1 * y) is V24() V25() Element of REAL
((z1 * p1) + (z1 * y)) * p is Element of the U1 of CS
K138( the Mult of CS,((z1 * p1) + (z1 * y)),p) is set
K4(((z1 * p1) + (z1 * y)),p) is set
the Mult of CS . K4(((z1 * p1) + (z1 * y)),p) is set
z1 * z2 is V24() V25() Element of REAL
(z1 * q) + (z1 * z2) is V24() V25() Element of REAL
((z1 * q) + (z1 * z2)) * p1 is Element of the U1 of CS
K138( the Mult of CS,((z1 * q) + (z1 * z2)),p1) is set
K4(((z1 * q) + (z1 * z2)),p1) is set
the Mult of CS . K4(((z1 * q) + (z1 * z2)),p1) is set
(((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p1) + (z1 * y)) * p),(((z1 * q) + (z1 * z2)) * p1)) is Element of the U1 of CS
K4((((z1 * p1) + (z1 * y)) * p),(((z1 * q) + (z1 * z2)) * p1)) is set
the U5 of CS . K4((((z1 * p1) + (z1 * y)) * p),(((z1 * q) + (z1 * z2)) * p1)) is set
z1 * z1 is V24() V25() Element of REAL
(z1 * q1) + (z1 * z1) is V24() V25() Element of REAL
((z1 * q1) + (z1 * z1)) * p2 is Element of the U1 of CS
K138( the Mult of CS,((z1 * q1) + (z1 * z1)),p2) is set
K4(((z1 * q1) + (z1 * z1)),p2) is set
the Mult of CS . K4(((z1 * q1) + (z1 * z1)),p2) is set
((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) + (z1 * z1)) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)),(((z1 * q1) + (z1 * z1)) * p2)) is Element of the U1 of CS
K4(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)),(((z1 * q1) + (z1 * z1)) * p2)) is set
the U5 of CS . K4(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)),(((z1 * q1) + (z1 * z1)) * p2)) is set
z1 * x2 is V24() V25() Element of REAL
(z1 * r) + (z1 * x2) is V24() V25() Element of REAL
((z1 * r) + (z1 * x2)) * r is Element of the U1 of CS
K138( the Mult of CS,((z1 * r) + (z1 * x2)),r) is set
K4(((z1 * r) + (z1 * x2)),r) is set
the Mult of CS . K4(((z1 * r) + (z1 * x2)),r) is set
(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) + (z1 * z1)) * p2)) + (((z1 * r) + (z1 * x2)) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) + (z1 * z1)) * p2)),(((z1 * r) + (z1 * x2)) * r)) is Element of the U1 of CS
K4((((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) + (z1 * z1)) * p2)),(((z1 * r) + (z1 * x2)) * r)) is set
the U5 of CS . K4((((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) + (z1 * z1)) * p2)),(((z1 * r) + (z1 * x2)) * r)) is set
(z1 * p1) * p is Element of the U1 of CS
K138( the Mult of CS,(z1 * p1),p) is set
K4((z1 * p1),p) is set
the Mult of CS . K4((z1 * p1),p) is set
(z1 * q) * p1 is Element of the U1 of CS
K138( the Mult of CS,(z1 * q),p1) is set
K4((z1 * q),p1) is set
the Mult of CS . K4((z1 * q),p1) is set
((z1 * p1) * p) + ((z1 * q) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p1) * p),((z1 * q) * p1)) is Element of the U1 of CS
K4(((z1 * p1) * p),((z1 * q) * p1)) is set
the U5 of CS . K4(((z1 * p1) * p),((z1 * q) * p1)) is set
(z1 * q1) * p2 is Element of the U1 of CS
K138( the Mult of CS,(z1 * q1),p2) is set
K4((z1 * q1),p2) is set
the Mult of CS . K4((z1 * q1),p2) is set
(((z1 * p1) * p) + ((z1 * q) * p1)) + ((z1 * q1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p1) * p) + ((z1 * q) * p1)),((z1 * q1) * p2)) is Element of the U1 of CS
K4((((z1 * p1) * p) + ((z1 * q) * p1)),((z1 * q1) * p2)) is set
the U5 of CS . K4((((z1 * p1) * p) + ((z1 * q) * p1)),((z1 * q1) * p2)) is set
(z1 * r) * r is Element of the U1 of CS
K138( the Mult of CS,(z1 * r),r) is set
K4((z1 * r),r) is set
the Mult of CS . K4((z1 * r),r) is set
((((z1 * p1) * p) + ((z1 * q) * p1)) + ((z1 * q1) * p2)) + ((z1 * r) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z1 * p1) * p) + ((z1 * q) * p1)) + ((z1 * q1) * p2)),((z1 * r) * r)) is Element of the U1 of CS
K4(((((z1 * p1) * p) + ((z1 * q) * p1)) + ((z1 * q1) * p2)),((z1 * r) * r)) is set
the U5 of CS . K4(((((z1 * p1) * p) + ((z1 * q) * p1)) + ((z1 * q1) * p2)),((z1 * r) * r)) is set
(z1 * y) * p is Element of the U1 of CS
K138( the Mult of CS,(z1 * y),p) is set
K4((z1 * y),p) is set
the Mult of CS . K4((z1 * y),p) is set
(z1 * z2) * p1 is Element of the U1 of CS
K138( the Mult of CS,(z1 * z2),p1) is set
K4((z1 * z2),p1) is set
the Mult of CS . K4((z1 * z2),p1) is set
((z1 * y) * p) + ((z1 * z2) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * y) * p),((z1 * z2) * p1)) is Element of the U1 of CS
K4(((z1 * y) * p),((z1 * z2) * p1)) is set
the U5 of CS . K4(((z1 * y) * p),((z1 * z2) * p1)) is set
(z1 * z1) * p2 is Element of the U1 of CS
K138( the Mult of CS,(z1 * z1),p2) is set
K4((z1 * z1),p2) is set
the Mult of CS . K4((z1 * z1),p2) is set
(((z1 * y) * p) + ((z1 * z2) * p1)) + ((z1 * z1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * y) * p) + ((z1 * z2) * p1)),((z1 * z1) * p2)) is Element of the U1 of CS
K4((((z1 * y) * p) + ((z1 * z2) * p1)),((z1 * z1) * p2)) is set
the U5 of CS . K4((((z1 * y) * p) + ((z1 * z2) * p1)),((z1 * z1) * p2)) is set
(z1 * x2) * r is Element of the U1 of CS
K138( the Mult of CS,(z1 * x2),r) is set
K4((z1 * x2),r) is set
the Mult of CS . K4((z1 * x2),r) is set
((((z1 * y) * p) + ((z1 * z2) * p1)) + ((z1 * z1) * p2)) + ((z1 * x2) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z1 * y) * p) + ((z1 * z2) * p1)) + ((z1 * z1) * p2)),((z1 * x2) * r)) is Element of the U1 of CS
K4(((((z1 * y) * p) + ((z1 * z2) * p1)) + ((z1 * z1) * p2)),((z1 * x2) * r)) is set
the U5 of CS . K4(((((z1 * y) * p) + ((z1 * z2) * p1)) + ((z1 * z1) * p2)),((z1 * x2) * r)) is set
(((((z1 * p1) * p) + ((z1 * q) * p1)) + ((z1 * q1) * p2)) + ((z1 * r) * r)) + (((((z1 * y) * p) + ((z1 * z2) * p1)) + ((z1 * z1) * p2)) + ((z1 * x2) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((z1 * p1) * p) + ((z1 * q) * p1)) + ((z1 * q1) * p2)) + ((z1 * r) * r)),(((((z1 * y) * p) + ((z1 * z2) * p1)) + ((z1 * z1) * p2)) + ((z1 * x2) * r))) is Element of the U1 of CS
K4((((((z1 * p1) * p) + ((z1 * q) * p1)) + ((z1 * q1) * p2)) + ((z1 * r) * r)),(((((z1 * y) * p) + ((z1 * z2) * p1)) + ((z1 * z1) * p2)) + ((z1 * x2) * r))) is set
the U5 of CS . K4((((((z1 * p1) * p) + ((z1 * q) * p1)) + ((z1 * q1) * p2)) + ((z1 * r) * r)),(((((z1 * y) * p) + ((z1 * z2) * p1)) + ((z1 * z1) * p2)) + ((z1 * x2) * r))) is set
((z1 * p1) * p) + ((z1 * y) * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p1) * p),((z1 * y) * p)) is Element of the U1 of CS
K4(((z1 * p1) * p),((z1 * y) * p)) is set
the U5 of CS . K4(((z1 * p1) * p),((z1 * y) * p)) is set
((z1 * q) * p1) + ((z1 * z2) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * q) * p1),((z1 * z2) * p1)) is Element of the U1 of CS
K4(((z1 * q) * p1),((z1 * z2) * p1)) is set
the U5 of CS . K4(((z1 * q) * p1),((z1 * z2) * p1)) is set
(((z1 * p1) * p) + ((z1 * y) * p)) + (((z1 * q) * p1) + ((z1 * z2) * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p1) * p) + ((z1 * y) * p)),(((z1 * q) * p1) + ((z1 * z2) * p1))) is Element of the U1 of CS
K4((((z1 * p1) * p) + ((z1 * y) * p)),(((z1 * q) * p1) + ((z1 * z2) * p1))) is set
the U5 of CS . K4((((z1 * p1) * p) + ((z1 * y) * p)),(((z1 * q) * p1) + ((z1 * z2) * p1))) is set
((z1 * q1) * p2) + ((z1 * z1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * q1) * p2),((z1 * z1) * p2)) is Element of the U1 of CS
K4(((z1 * q1) * p2),((z1 * z1) * p2)) is set
the U5 of CS . K4(((z1 * q1) * p2),((z1 * z1) * p2)) is set
((((z1 * p1) * p) + ((z1 * y) * p)) + (((z1 * q) * p1) + ((z1 * z2) * p1))) + (((z1 * q1) * p2) + ((z1 * z1) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z1 * p1) * p) + ((z1 * y) * p)) + (((z1 * q) * p1) + ((z1 * z2) * p1))),(((z1 * q1) * p2) + ((z1 * z1) * p2))) is Element of the U1 of CS
K4(((((z1 * p1) * p) + ((z1 * y) * p)) + (((z1 * q) * p1) + ((z1 * z2) * p1))),(((z1 * q1) * p2) + ((z1 * z1) * p2))) is set
the U5 of CS . K4(((((z1 * p1) * p) + ((z1 * y) * p)) + (((z1 * q) * p1) + ((z1 * z2) * p1))),(((z1 * q1) * p2) + ((z1 * z1) * p2))) is set
((z1 * r) * r) + ((z1 * x2) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * r) * r),((z1 * x2) * r)) is Element of the U1 of CS
K4(((z1 * r) * r),((z1 * x2) * r)) is set
the U5 of CS . K4(((z1 * r) * r),((z1 * x2) * r)) is set
(((((z1 * p1) * p) + ((z1 * y) * p)) + (((z1 * q) * p1) + ((z1 * z2) * p1))) + (((z1 * q1) * p2) + ((z1 * z1) * p2))) + (((z1 * r) * r) + ((z1 * x2) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((z1 * p1) * p) + ((z1 * y) * p)) + (((z1 * q) * p1) + ((z1 * z2) * p1))) + (((z1 * q1) * p2) + ((z1 * z1) * p2))),(((z1 * r) * r) + ((z1 * x2) * r))) is Element of the U1 of CS
K4((((((z1 * p1) * p) + ((z1 * y) * p)) + (((z1 * q) * p1) + ((z1 * z2) * p1))) + (((z1 * q1) * p2) + ((z1 * z1) * p2))),(((z1 * r) * r) + ((z1 * x2) * r))) is set
the U5 of CS . K4((((((z1 * p1) * p) + ((z1 * y) * p)) + (((z1 * q) * p1) + ((z1 * z2) * p1))) + (((z1 * q1) * p2) + ((z1 * z1) * p2))),(((z1 * r) * r) + ((z1 * x2) * r))) is set
(((z1 * p1) + (z1 * y)) * p) + (((z1 * q) * p1) + ((z1 * z2) * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p1) + (z1 * y)) * p),(((z1 * q) * p1) + ((z1 * z2) * p1))) is Element of the U1 of CS
K4((((z1 * p1) + (z1 * y)) * p),(((z1 * q) * p1) + ((z1 * z2) * p1))) is set
the U5 of CS . K4((((z1 * p1) + (z1 * y)) * p),(((z1 * q) * p1) + ((z1 * z2) * p1))) is set
((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) * p1) + ((z1 * z2) * p1))) + (((z1 * q1) * p2) + ((z1 * z1) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) * p1) + ((z1 * z2) * p1))),(((z1 * q1) * p2) + ((z1 * z1) * p2))) is Element of the U1 of CS
K4(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) * p1) + ((z1 * z2) * p1))),(((z1 * q1) * p2) + ((z1 * z1) * p2))) is set
the U5 of CS . K4(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) * p1) + ((z1 * z2) * p1))),(((z1 * q1) * p2) + ((z1 * z1) * p2))) is set
(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) * p1) + ((z1 * z2) * p1))) + (((z1 * q1) * p2) + ((z1 * z1) * p2))) + (((z1 * r) * r) + ((z1 * x2) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) * p1) + ((z1 * z2) * p1))) + (((z1 * q1) * p2) + ((z1 * z1) * p2))),(((z1 * r) * r) + ((z1 * x2) * r))) is Element of the U1 of CS
K4((((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) * p1) + ((z1 * z2) * p1))) + (((z1 * q1) * p2) + ((z1 * z1) * p2))),(((z1 * r) * r) + ((z1 * x2) * r))) is set
the U5 of CS . K4((((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) * p1) + ((z1 * z2) * p1))) + (((z1 * q1) * p2) + ((z1 * z1) * p2))),(((z1 * r) * r) + ((z1 * x2) * r))) is set
((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) * p2) + ((z1 * z1) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)),(((z1 * q1) * p2) + ((z1 * z1) * p2))) is Element of the U1 of CS
K4(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)),(((z1 * q1) * p2) + ((z1 * z1) * p2))) is set
the U5 of CS . K4(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)),(((z1 * q1) * p2) + ((z1 * z1) * p2))) is set
(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) * p2) + ((z1 * z1) * p2))) + (((z1 * r) * r) + ((z1 * x2) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) * p2) + ((z1 * z1) * p2))),(((z1 * r) * r) + ((z1 * x2) * r))) is Element of the U1 of CS
K4((((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) * p2) + ((z1 * z1) * p2))),(((z1 * r) * r) + ((z1 * x2) * r))) is set
the U5 of CS . K4((((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) * p2) + ((z1 * z1) * p2))),(((z1 * r) * r) + ((z1 * x2) * r))) is set
(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) + (z1 * z1)) * p2)) + (((z1 * r) * r) + ((z1 * x2) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) + (z1 * z1)) * p2)),(((z1 * r) * r) + ((z1 * x2) * r))) is Element of the U1 of CS
K4((((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) + (z1 * z1)) * p2)),(((z1 * r) * r) + ((z1 * x2) * r))) is set
the U5 of CS . K4((((((z1 * p1) + (z1 * y)) * p) + (((z1 * q) + (z1 * z2)) * p1)) + (((z1 * q1) + (z1 * z1)) * p2)),(((z1 * r) * r) + ((z1 * x2) * r))) is set
r " is V24() V25() Element of REAL
x2 * (r ") is V24() V25() Element of REAL
- (x2 * (r ")) is V24() V25() Element of REAL
(- (x2 * (r "))) * r1 is Element of the U1 of CS
K138( the Mult of CS,(- (x2 * (r "))),r1) is set
K4((- (x2 * (r "))),r1) is set
the Mult of CS . K4((- (x2 * (r "))),r1) is set
1 * p is Element of the U1 of CS
K138( the Mult of CS,1,p) is set
K4(1,p) is set
the Mult of CS . K4(1,p) is set
((- (x2 * (r "))) * r1) + (1 * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- (x2 * (r "))) * r1),(1 * p)) is Element of the U1 of CS
K4(((- (x2 * (r "))) * r1),(1 * p)) is set
the U5 of CS . K4(((- (x2 * (r "))) * r1),(1 * p)) is set
(- (x2 * (r "))) * p1 is V24() V25() Element of REAL
1 * y is V24() V25() Element of REAL
((- (x2 * (r "))) * p1) + (1 * y) is V24() V25() Element of REAL
(- (x2 * (r "))) * q is V24() V25() Element of REAL
1 * z2 is V24() V25() Element of REAL
((- (x2 * (r "))) * q) + (1 * z2) is V24() V25() Element of REAL
(- (x2 * (r "))) * q1 is V24() V25() Element of REAL
1 * z1 is V24() V25() Element of REAL
((- (x2 * (r "))) * q1) + (1 * z1) is V24() V25() Element of REAL
(x2 * (r ")) * r is V24() V25() Element of REAL
(r ") * r is V24() V25() Element of REAL
x2 * ((r ") * r) is V24() V25() Element of REAL
x2 * 1 is V24() V25() Element of REAL
(x2 * (r ")) * q1 is V24() V25() Element of REAL
- ((x2 * (r ")) * q1) is V24() V25() Element of REAL
- (- ((x2 * (r ")) * q1)) is V24() V25() Element of REAL
(x2 * (r ")) * p1 is V24() V25() Element of REAL
- ((x2 * (r ")) * p1) is V24() V25() Element of REAL
- (- ((x2 * (r ")) * p1)) is V24() V25() Element of REAL
(x2 * (r ")) * q is V24() V25() Element of REAL
- ((x2 * (r ")) * q) is V24() V25() Element of REAL
- (- ((x2 * (r ")) * q)) is V24() V25() Element of REAL
(x2 * (r ")) * r1 is Element of the U1 of CS
K138( the Mult of CS,(x2 * (r ")),r1) is set
K4((x2 * (r ")),r1) is set
the Mult of CS . K4((x2 * (r ")),r1) is set
(- (x2 * (r "))) * r is V24() V25() Element of REAL
1 * x2 is V24() V25() Element of REAL
((- (x2 * (r "))) * r) + (1 * x2) is V24() V25() Element of REAL
(r ") * r is V24() V25() Element of REAL
x2 * ((r ") * r) is V24() V25() Element of REAL
- (x2 * ((r ") * r)) is V24() V25() Element of REAL
(- (x2 * ((r ") * r))) + x2 is V24() V25() Element of REAL
x2 * 1 is V24() V25() Element of REAL
- (x2 * 1) is V24() V25() Element of REAL
(- (x2 * 1)) + x2 is V24() V25() Element of REAL
(((- (x2 * (r "))) * p1) + (1 * y)) * p is Element of the U1 of CS
K138( the Mult of CS,(((- (x2 * (r "))) * p1) + (1 * y)),p) is set
K4((((- (x2 * (r "))) * p1) + (1 * y)),p) is set
the Mult of CS . K4((((- (x2 * (r "))) * p1) + (1 * y)),p) is set
(((- (x2 * (r "))) * q) + (1 * z2)) * p1 is Element of the U1 of CS
K138( the Mult of CS,(((- (x2 * (r "))) * q) + (1 * z2)),p1) is set
K4((((- (x2 * (r "))) * q) + (1 * z2)),p1) is set
the Mult of CS . K4((((- (x2 * (r "))) * q) + (1 * z2)),p1) is set
((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((- (x2 * (r "))) * p1) + (1 * y)) * p),((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) is Element of the U1 of CS
K4(((((- (x2 * (r "))) * p1) + (1 * y)) * p),((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) is set
the U5 of CS . K4(((((- (x2 * (r "))) * p1) + (1 * y)) * p),((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) is set
(((- (x2 * (r "))) * q1) + (1 * z1)) * p2 is Element of the U1 of CS
K138( the Mult of CS,(((- (x2 * (r "))) * q1) + (1 * z1)),p2) is set
K4((((- (x2 * (r "))) * q1) + (1 * z1)),p2) is set
the Mult of CS . K4((((- (x2 * (r "))) * q1) + (1 * z1)),p2) is set
(((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) + ((((- (x2 * (r "))) * q1) + (1 * z1)) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)),((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)) is Element of the U1 of CS
K4((((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)),((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)) is set
the U5 of CS . K4((((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)),((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)) is set
0 * r is Element of the U1 of CS
K138( the Mult of CS,0,r) is set
K4(0,r) is set
the Mult of CS . K4(0,r) is set
((((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) + ((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)) + (0 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) + ((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)),(0 * r)) is Element of the U1 of CS
K4(((((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) + ((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)),(0 * r)) is set
the U5 of CS . K4(((((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) + ((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)),(0 * r)) is set
((((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) + ((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) + ((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)),(0. CS)) is Element of the U1 of CS
K4(((((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) + ((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)),(0. CS)) is set
the U5 of CS . K4(((((((- (x2 * (r "))) * p1) + (1 * y)) * p) + ((((- (x2 * (r "))) * q) + (1 * z2)) * p1)) + ((((- (x2 * (r "))) * q1) + (1 * z1)) * p2)),(0. CS)) is set
z1 is Element of the U1 of CS
(((y * p) + (z2 * p1)) + (z1 * p2)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y * p) + (z2 * p1)) + (z1 * p2)),(0. CS)) is Element of the U1 of CS
K4((((y * p) + (z2 * p1)) + (z1 * p2)),(0. CS)) is set
the U5 of CS . K4((((y * p) + (z2 * p1)) + (z1 * p2)),(0. CS)) is set
z1 is Element of the U1 of CS
(((p1 * p) + (q * p1)) + (q1 * p2)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p1 * p) + (q * p1)) + (q1 * p2)),(0. CS)) is Element of the U1 of CS
K4((((p1 * p) + (q * p1)) + (q1 * p2)),(0. CS)) is set
the U5 of CS . K4((((p1 * p) + (q * p1)) + (q1 * p2)),(0. CS)) is set
z1 is Element of the U1 of CS
z2 is V24() V25() Element of REAL
z2 * p is Element of the U1 of CS
K138( the Mult of CS,z2,p) is set
K4(z2,p) is set
the Mult of CS . K4(z2,p) is set
p199 is V24() V25() Element of REAL
p199 * p1 is Element of the U1 of CS
K138( the Mult of CS,p199,p1) is set
K4(p199,p1) is set
the Mult of CS . K4(p199,p1) is set
(z2 * p) + (p199 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z2 * p),(p199 * p1)) is Element of the U1 of CS
K4((z2 * p),(p199 * p1)) is set
the U5 of CS . K4((z2 * p),(p199 * p1)) is set
p39 is V24() V25() Element of REAL
p39 * p2 is Element of the U1 of CS
K138( the Mult of CS,p39,p2) is set
K4(p39,p2) is set
the Mult of CS . K4(p39,p2) is set
((z2 * p) + (p199 * p1)) + (p39 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z2 * p) + (p199 * p1)),(p39 * p2)) is Element of the U1 of CS
K4(((z2 * p) + (p199 * p1)),(p39 * p2)) is set
the U5 of CS . K4(((z2 * p) + (p199 * p1)),(p39 * p2)) is set
p19 is Element of the U1 of CS
p29 is V24() V25() Element of REAL
p29 * p is Element of the U1 of CS
K138( the Mult of CS,p29,p) is set
K4(p29,p) is set
the Mult of CS . K4(p29,p) is set
q1999 is V24() V25() Element of REAL
q1999 * p1 is Element of the U1 of CS
K138( the Mult of CS,q1999,p1) is set
K4(q1999,p1) is set
the Mult of CS . K4(q1999,p1) is set
(p29 * p) + (q1999 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p29 * p),(q1999 * p1)) is Element of the U1 of CS
K4((p29 * p),(q1999 * p1)) is set
the U5 of CS . K4((p29 * p),(q1999 * p1)) is set
p2999 is V24() V25() Element of REAL
p2999 * p2 is Element of the U1 of CS
K138( the Mult of CS,p2999,p2) is set
K4(p2999,p2) is set
the Mult of CS . K4(p2999,p2) is set
((p29 * p) + (q1999 * p1)) + (p2999 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p29 * p) + (q1999 * p1)),(p2999 * p2)) is Element of the U1 of CS
K4(((p29 * p) + (q1999 * p1)),(p2999 * p2)) is set
the U5 of CS . K4(((p29 * p) + (q1999 * p1)),(p2999 * p2)) is set
r399 is Element of the U1 of CS
p29999 is V24() V25() Element of REAL
p29999 * p is Element of the U1 of CS
K138( the Mult of CS,p29999,p) is set
K4(p29999,p) is set
the Mult of CS . K4(p29999,p) is set
q3999 is V24() V25() Element of REAL
q3999 * p1 is Element of the U1 of CS
K138( the Mult of CS,q3999,p1) is set
K4(q3999,p1) is set
the Mult of CS . K4(q3999,p1) is set
(p29999 * p) + (q3999 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p29999 * p),(q3999 * p1)) is Element of the U1 of CS
K4((p29999 * p),(q3999 * p1)) is set
the U5 of CS . K4((p29999 * p),(q3999 * p1)) is set
r19 is V24() V25() Element of REAL
r19 * p2 is Element of the U1 of CS
K138( the Mult of CS,r19,p2) is set
K4(r19,p2) is set
the Mult of CS . K4(r19,p2) is set
((p29999 * p) + (q3999 * p1)) + (r19 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p29999 * p) + (q3999 * p1)),(r19 * p2)) is Element of the U1 of CS
K4(((p29999 * p) + (q3999 * p1)),(r19 * p2)) is set
the U5 of CS . K4(((p29999 * p) + (q3999 * p1)),(r19 * p2)) is set
z1 is Element of the U1 of CS
z1 is V24() V25() Element of REAL
z1 * p is Element of the U1 of CS
K138( the Mult of CS,z1,p) is set
K4(z1,p) is set
the Mult of CS . K4(z1,p) is set
z2 is V24() V25() Element of REAL
z2 * p1 is Element of the U1 of CS
K138( the Mult of CS,z2,p1) is set
K4(z2,p1) is set
the Mult of CS . K4(z2,p1) is set
(z1 * p) + (z2 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p),(z2 * p1)) is Element of the U1 of CS
K4((z1 * p),(z2 * p1)) is set
the U5 of CS . K4((z1 * p),(z2 * p1)) is set
p199 is V24() V25() Element of REAL
p199 * p2 is Element of the U1 of CS
K138( the Mult of CS,p199,p2) is set
K4(p199,p2) is set
the Mult of CS . K4(p199,p2) is set
((z1 * p) + (z2 * p1)) + (p199 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p) + (z2 * p1)),(p199 * p2)) is Element of the U1 of CS
K4(((z1 * p) + (z2 * p1)),(p199 * p2)) is set
the U5 of CS . K4(((z1 * p) + (z2 * p1)),(p199 * p2)) is set
z1 is Element of the U1 of CS
z1 is V24() V25() Element of REAL
z1 * p is Element of the U1 of CS
K138( the Mult of CS,z1,p) is set
K4(z1,p) is set
the Mult of CS . K4(z1,p) is set
z2 is V24() V25() Element of REAL
z2 * p1 is Element of the U1 of CS
K138( the Mult of CS,z2,p1) is set
K4(z2,p1) is set
the Mult of CS . K4(z2,p1) is set
(z1 * p) + (z2 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p),(z2 * p1)) is Element of the U1 of CS
K4((z1 * p),(z2 * p1)) is set
the U5 of CS . K4((z1 * p),(z2 * p1)) is set
p199 is V24() V25() Element of REAL
p199 * p2 is Element of the U1 of CS
K138( the Mult of CS,p199,p2) is set
K4(p199,p2) is set
the Mult of CS . K4(p199,p2) is set
((z1 * p) + (z2 * p1)) + (p199 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p) + (z2 * p1)),(p199 * p2)) is Element of the U1 of CS
K4(((z1 * p) + (z2 * p1)),(p199 * p2)) is set
the U5 of CS . K4(((z1 * p) + (z2 * p1)),(p199 * p2)) is set
z1 is V24() V25() Element of REAL
z1 * p is Element of the U1 of CS
K138( the Mult of CS,z1,p) is set
K4(z1,p) is set
the Mult of CS . K4(z1,p) is set
z2 is V24() V25() Element of REAL
z2 * p1 is Element of the U1 of CS
K138( the Mult of CS,z2,p1) is set
K4(z2,p1) is set
the Mult of CS . K4(z2,p1) is set
(z1 * p) + (z2 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p),(z2 * p1)) is Element of the U1 of CS
K4((z1 * p),(z2 * p1)) is set
the U5 of CS . K4((z1 * p),(z2 * p1)) is set
p199 is V24() V25() Element of REAL
p199 * p2 is Element of the U1 of CS
K138( the Mult of CS,p199,p2) is set
K4(p199,p2) is set
the Mult of CS . K4(p199,p2) is set
((z1 * p) + (z2 * p1)) + (p199 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p) + (z2 * p1)),(p199 * p2)) is Element of the U1 of CS
K4(((z1 * p) + (z2 * p1)),(p199 * p2)) is set
the U5 of CS . K4(((z1 * p) + (z2 * p1)),(p199 * p2)) is set
- z1 is V24() V25() Element of REAL
(- z1) * p is Element of the U1 of CS
K138( the Mult of CS,(- z1),p) is set
K4((- z1),p) is set
the Mult of CS . K4((- z1),p) is set
1 * z1 is Element of the U1 of CS
K138( the Mult of CS,1,z1) is set
K4(1,z1) is set
the Mult of CS . K4(1,z1) is set
((- z1) * p) + (1 * z1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- z1) * p),(1 * z1)) is Element of the U1 of CS
K4(((- z1) * p),(1 * z1)) is set
the U5 of CS . K4(((- z1) * p),(1 * z1)) is set
1 * z1 is V24() V25() Element of REAL
(- z1) + (1 * z1) is V24() V25() Element of REAL
((- z1) + (1 * z1)) * p is Element of the U1 of CS
K138( the Mult of CS,((- z1) + (1 * z1)),p) is set
K4(((- z1) + (1 * z1)),p) is set
the Mult of CS . K4(((- z1) + (1 * z1)),p) is set
1 * z2 is V24() V25() Element of REAL
(1 * z2) * p1 is Element of the U1 of CS
K138( the Mult of CS,(1 * z2),p1) is set
K4((1 * z2),p1) is set
the Mult of CS . K4((1 * z2),p1) is set
(((- z1) + (1 * z1)) * p) + ((1 * z2) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((- z1) + (1 * z1)) * p),((1 * z2) * p1)) is Element of the U1 of CS
K4((((- z1) + (1 * z1)) * p),((1 * z2) * p1)) is set
the U5 of CS . K4((((- z1) + (1 * z1)) * p),((1 * z2) * p1)) is set
1 * p199 is V24() V25() Element of REAL
(1 * p199) * p2 is Element of the U1 of CS
K138( the Mult of CS,(1 * p199),p2) is set
K4((1 * p199),p2) is set
the Mult of CS . K4((1 * p199),p2) is set
((((- z1) + (1 * z1)) * p) + ((1 * z2) * p1)) + ((1 * p199) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((- z1) + (1 * z1)) * p) + ((1 * z2) * p1)),((1 * p199) * p2)) is Element of the U1 of CS
K4(((((- z1) + (1 * z1)) * p) + ((1 * z2) * p1)),((1 * p199) * p2)) is set
the U5 of CS . K4(((((- z1) + (1 * z1)) * p) + ((1 * z2) * p1)),((1 * p199) * p2)) is set
(0. CS) + ((1 * z2) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),((1 * z2) * p1)) is Element of the U1 of CS
K4((0. CS),((1 * z2) * p1)) is set
the U5 of CS . K4((0. CS),((1 * z2) * p1)) is set
((0. CS) + ((1 * z2) * p1)) + ((1 * p199) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + ((1 * z2) * p1)),((1 * p199) * p2)) is Element of the U1 of CS
K4(((0. CS) + ((1 * z2) * p1)),((1 * p199) * p2)) is set
the U5 of CS . K4(((0. CS) + ((1 * z2) * p1)),((1 * p199) * p2)) is set
(z2 * p1) + (p199 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z2 * p1),(p199 * p2)) is Element of the U1 of CS
K4((z2 * p1),(p199 * p2)) is set
the U5 of CS . K4((z2 * p1),(p199 * p2)) is set
(z1 * p) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p),(0. CS)) is Element of the U1 of CS
K4((z1 * p),(0. CS)) is set
the U5 of CS . K4((z1 * p),(0. CS)) is set
0 * p2 is Element of the U1 of CS
K138( the Mult of CS,0,p2) is set
K4(0,p2) is set
the Mult of CS . K4(0,p2) is set
((z1 * p) + (0. CS)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p) + (0. CS)),(0 * p2)) is Element of the U1 of CS
K4(((z1 * p) + (0. CS)),(0 * p2)) is set
the U5 of CS . K4(((z1 * p) + (0. CS)),(0 * p2)) is set
((z1 * p) + (0. CS)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p) + (0. CS)),(0. CS)) is Element of the U1 of CS
K4(((z1 * p) + (0. CS)),(0. CS)) is set
the U5 of CS . K4(((z1 * p) + (0. CS)),(0. CS)) is set
(0. CS) + (z2 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(z2 * p1)) is Element of the U1 of CS
K4((0. CS),(z2 * p1)) is set
the U5 of CS . K4((0. CS),(z2 * p1)) is set
((0. CS) + (z2 * p1)) + (p199 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (z2 * p1)),(p199 * p2)) is Element of the U1 of CS
K4(((0. CS) + (z2 * p1)),(p199 * p2)) is set
the U5 of CS . K4(((0. CS) + (z2 * p1)),(p199 * p2)) is set
0 * p is Element of the U1 of CS
K138( the Mult of CS,0,p) is set
K4(0,p) is set
the Mult of CS . K4(0,p) is set
(0 * p) + (z2 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p),(z2 * p1)) is Element of the U1 of CS
K4((0 * p),(z2 * p1)) is set
the U5 of CS . K4((0 * p),(z2 * p1)) is set
((0 * p) + (z2 * p1)) + (p199 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * p) + (z2 * p1)),(p199 * p2)) is Element of the U1 of CS
K4(((0 * p) + (z2 * p1)),(p199 * p2)) is set
the U5 of CS . K4(((0 * p) + (z2 * p1)),(p199 * p2)) is set
(((0 * p) + (z2 * p1)) + (p199 * p2)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((0 * p) + (z2 * p1)) + (p199 * p2)),(0. CS)) is Element of the U1 of CS
K4((((0 * p) + (z2 * p1)) + (p199 * p2)),(0. CS)) is set
the U5 of CS . K4((((0 * p) + (z2 * p1)) + (p199 * p2)),(0. CS)) is set
0 * r is Element of the U1 of CS
K138( the Mult of CS,0,r) is set
K4(0,r) is set
the Mult of CS . K4(0,r) is set
(((0 * p) + (z2 * p1)) + (p199 * p2)) + (0 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((0 * p) + (z2 * p1)) + (p199 * p2)),(0 * r)) is Element of the U1 of CS
K4((((0 * p) + (z2 * p1)) + (p199 * p2)),(0 * r)) is set
the U5 of CS . K4((((0 * p) + (z2 * p1)) + (p199 * p2)),(0 * r)) is set
o9 is Element of the U1 of CS
p39 is Element of the U1 of CS
p29 is Element of the U1 of CS
p19 is Element of the U1 of CS
z1 is Element of the U1 of CS
z1 is Element of the U1 of CS
p199 is Element of the U1 of CS
z2 is Element of the U1 of CS
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
r1 is Element of the U1 of CS
p is V24() V25() Element of REAL
p * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p,p) is set
K4(p,p) is set
the Mult of CS . K4(p,p) is set
p1 is V24() V25() Element of REAL
p1 * p1 is Element of the U1 of CS
K138( the Mult of CS,p1,p1) is set
K4(p1,p1) is set
the Mult of CS . K4(p1,p1) is set
(p * p) + (p1 * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(p * p),(p1 * p1)) is Element of the U1 of CS
K4((p * p),(p1 * p1)) is set
the U5 of CS . K4((p * p),(p1 * p1)) is set
q is V24() V25() Element of REAL
q * p2 is Element of the U1 of CS
K138( the Mult of CS,q,p2) is set
K4(q,p2) is set
the Mult of CS . K4(q,p2) is set
q1 is V24() V25() Element of REAL
q1 * r is Element of the U1 of CS
K138( the Mult of CS,q1,r) is set
K4(q1,r) is set
the Mult of CS . K4(q1,r) is set
(q * p2) + (q1 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q * p2),(q1 * r)) is Element of the U1 of CS
K4((q * p2),(q1 * r)) is set
the U5 of CS . K4((q * p2),(q1 * r)) is set
((p * p) + (p1 * p1)) - ((q * p2) + (q1 * r)) is Element of the U1 of CS
- ((q * p2) + (q1 * r)) is Element of the U1 of CS
K176(CS,((p * p) + (p1 * p1)),(- ((q * p2) + (q1 * r)))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p * p) + (p1 * p1)),(- ((q * p2) + (q1 * r)))) is Element of the U1 of CS
K4(((p * p) + (p1 * p1)),(- ((q * p2) + (q1 * r)))) is set
the U5 of CS . K4(((p * p) + (p1 * p1)),(- ((q * p2) + (q1 * r)))) is set
(- 1) * ((q * p2) + (q1 * r)) is Element of the U1 of CS
K138( the Mult of CS,(- 1),((q * p2) + (q1 * r))) is set
K4((- 1),((q * p2) + (q1 * r))) is set
the Mult of CS . K4((- 1),((q * p2) + (q1 * r))) is set
((p * p) + (p1 * p1)) + ((- 1) * ((q * p2) + (q1 * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p * p) + (p1 * p1)),((- 1) * ((q * p2) + (q1 * r)))) is Element of the U1 of CS
K4(((p * p) + (p1 * p1)),((- 1) * ((q * p2) + (q1 * r)))) is set
the U5 of CS . K4(((p * p) + (p1 * p1)),((- 1) * ((q * p2) + (q1 * r)))) is set
(- 1) * (q * p2) is Element of the U1 of CS
K138( the Mult of CS,(- 1),(q * p2)) is set
K4((- 1),(q * p2)) is set
the Mult of CS . K4((- 1),(q * p2)) is set
(- 1) * (q1 * r) is Element of the U1 of CS
K138( the Mult of CS,(- 1),(q1 * r)) is set
K4((- 1),(q1 * r)) is set
the Mult of CS . K4((- 1),(q1 * r)) is set
((- 1) * (q * p2)) + ((- 1) * (q1 * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- 1) * (q * p2)),((- 1) * (q1 * r))) is Element of the U1 of CS
K4(((- 1) * (q * p2)),((- 1) * (q1 * r))) is set
the U5 of CS . K4(((- 1) * (q * p2)),((- 1) * (q1 * r))) is set
((p * p) + (p1 * p1)) + (((- 1) * (q * p2)) + ((- 1) * (q1 * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p * p) + (p1 * p1)),(((- 1) * (q * p2)) + ((- 1) * (q1 * r)))) is Element of the U1 of CS
K4(((p * p) + (p1 * p1)),(((- 1) * (q * p2)) + ((- 1) * (q1 * r)))) is set
the U5 of CS . K4(((p * p) + (p1 * p1)),(((- 1) * (q * p2)) + ((- 1) * (q1 * r)))) is set
(- 1) * q is V24() V25() Element of REAL
((- 1) * q) * p2 is Element of the U1 of CS
K138( the Mult of CS,((- 1) * q),p2) is set
K4(((- 1) * q),p2) is set
the Mult of CS . K4(((- 1) * q),p2) is set
(((- 1) * q) * p2) + ((- 1) * (q1 * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((- 1) * q) * p2),((- 1) * (q1 * r))) is Element of the U1 of CS
K4((((- 1) * q) * p2),((- 1) * (q1 * r))) is set
the U5 of CS . K4((((- 1) * q) * p2),((- 1) * (q1 * r))) is set
((p * p) + (p1 * p1)) + ((((- 1) * q) * p2) + ((- 1) * (q1 * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p * p) + (p1 * p1)),((((- 1) * q) * p2) + ((- 1) * (q1 * r)))) is Element of the U1 of CS
K4(((p * p) + (p1 * p1)),((((- 1) * q) * p2) + ((- 1) * (q1 * r)))) is set
the U5 of CS . K4(((p * p) + (p1 * p1)),((((- 1) * q) * p2) + ((- 1) * (q1 * r)))) is set
(- 1) * q1 is V24() V25() Element of REAL
((- 1) * q1) * r is Element of the U1 of CS
K138( the Mult of CS,((- 1) * q1),r) is set
K4(((- 1) * q1),r) is set
the Mult of CS . K4(((- 1) * q1),r) is set
(((- 1) * q) * p2) + (((- 1) * q1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((- 1) * q) * p2),(((- 1) * q1) * r)) is Element of the U1 of CS
K4((((- 1) * q) * p2),(((- 1) * q1) * r)) is set
the U5 of CS . K4((((- 1) * q) * p2),(((- 1) * q1) * r)) is set
((p * p) + (p1 * p1)) + ((((- 1) * q) * p2) + (((- 1) * q1) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p * p) + (p1 * p1)),((((- 1) * q) * p2) + (((- 1) * q1) * r))) is Element of the U1 of CS
K4(((p * p) + (p1 * p1)),((((- 1) * q) * p2) + (((- 1) * q1) * r))) is set
the U5 of CS . K4(((p * p) + (p1 * p1)),((((- 1) * q) * p2) + (((- 1) * q1) * r))) is set
((p * p) + (p1 * p1)) + (((- 1) * q) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p * p) + (p1 * p1)),(((- 1) * q) * p2)) is Element of the U1 of CS
K4(((p * p) + (p1 * p1)),(((- 1) * q) * p2)) is set
the U5 of CS . K4(((p * p) + (p1 * p1)),(((- 1) * q) * p2)) is set
(((p * p) + (p1 * p1)) + (((- 1) * q) * p2)) + (((- 1) * q1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p * p) + (p1 * p1)) + (((- 1) * q) * p2)),(((- 1) * q1) * r)) is Element of the U1 of CS
K4((((p * p) + (p1 * p1)) + (((- 1) * q) * p2)),(((- 1) * q1) * r)) is set
the U5 of CS . K4((((p * p) + (p1 * p1)) + (((- 1) * q) * p2)),(((- 1) * q1) * r)) is set
0 * p1 is Element of the U1 of CS
K138( the Mult of CS,0,p1) is set
K4(0,p1) is set
the Mult of CS . K4(0,p1) is set
(0. CS) + (0 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0 * p1)) is Element of the U1 of CS
K4((0. CS),(0 * p1)) is set
the U5 of CS . K4((0. CS),(0 * p1)) is set
(0. CS) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0. CS)) is Element of the U1 of CS
K4((0. CS),(0. CS)) is set
the U5 of CS . K4((0. CS),(0. CS)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is V24() V25() Element of REAL
p1 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p1,p) is set
K4(p1,p) is set
the Mult of CS . K4(p1,p) is set
- (p1 * p) is Element of the U1 of CS
- p1 is V24() V25() Element of REAL
(- p1) * p is Element of the U1 of CS
K138( the Mult of CS,(- p1),p) is set
K4((- p1),p) is set
the Mult of CS . K4((- p1),p) is set
- p is Element of the U1 of CS
p1 * (- p) is Element of the U1 of CS
K138( the Mult of CS,p1,(- p)) is set
K4(p1,(- p)) is set
the Mult of CS . K4(p1,(- p)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
r is V24() V25() Element of REAL
r * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,r,p) is set
K4(r,p) is set
the Mult of CS . K4(r,p) is set
r1 is V24() V25() Element of REAL
r1 * p1 is Element of the U1 of CS
K138( the Mult of CS,r1,p1) is set
K4(r1,p1) is set
the Mult of CS . K4(r1,p1) is set
(r * p) + (r1 * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(r * p),(r1 * p1)) is Element of the U1 of CS
K4((r * p),(r1 * p1)) is set
the U5 of CS . K4((r * p),(r1 * p1)) is set
p is V24() V25() Element of REAL
p * p2 is Element of the U1 of CS
K138( the Mult of CS,p,p2) is set
K4(p,p2) is set
the Mult of CS . K4(p,p2) is set
((r * p) + (r1 * p1)) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (r1 * p1)),(p * p2)) is Element of the U1 of CS
K4(((r * p) + (r1 * p1)),(p * p2)) is set
the U5 of CS . K4(((r * p) + (r1 * p1)),(p * p2)) is set
(r * p) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * p),(0. CS)) is Element of the U1 of CS
K4((r * p),(0. CS)) is set
the U5 of CS . K4((r * p),(0. CS)) is set
((r * p) + (0. CS)) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (0. CS)),(p * p2)) is Element of the U1 of CS
K4(((r * p) + (0. CS)),(p * p2)) is set
the U5 of CS . K4(((r * p) + (0. CS)),(p * p2)) is set
(r * p) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * p),(p * p2)) is Element of the U1 of CS
K4((r * p),(p * p2)) is set
the U5 of CS . K4((r * p),(p * p2)) is set
- (p * p2) is Element of the U1 of CS
- p2 is Element of the U1 of CS
p * (- p2) is Element of the U1 of CS
K138( the Mult of CS,p,(- p2)) is set
K4(p,(- p2)) is set
the Mult of CS . K4(p,(- p2)) is set
- p is V24() V25() Element of REAL
(- p) * p2 is Element of the U1 of CS
K138( the Mult of CS,(- p),p2) is set
K4((- p),p2) is set
the Mult of CS . K4((- p),p2) is set
0 * p1 is Element of the U1 of CS
K138( the Mult of CS,0,p1) is set
K4(0,p1) is set
the Mult of CS . K4(0,p1) is set
(r * p) + (0 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * p),(0 * p1)) is Element of the U1 of CS
K4((r * p),(0 * p1)) is set
the U5 of CS . K4((r * p),(0 * p1)) is set
((r * p) + (0 * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (0 * p1)),(0. CS)) is Element of the U1 of CS
K4(((r * p) + (0 * p1)),(0. CS)) is set
the U5 of CS . K4(((r * p) + (0 * p1)),(0. CS)) is set
(0. CS) + (0 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0 * p1)) is Element of the U1 of CS
K4((0. CS),(0 * p1)) is set
the U5 of CS . K4((0. CS),(0 * p1)) is set
((0. CS) + (0 * p1)) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (0 * p1)),(p * p2)) is Element of the U1 of CS
K4(((0. CS) + (0 * p1)),(p * p2)) is set
the U5 of CS . K4(((0. CS) + (0 * p1)),(p * p2)) is set
(0 * p1) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p1),(p * p2)) is Element of the U1 of CS
K4((0 * p1),(p * p2)) is set
the U5 of CS . K4((0 * p1),(p * p2)) is set
(0. CS) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(p * p2)) is Element of the U1 of CS
K4((0. CS),(p * p2)) is set
the U5 of CS . K4((0. CS),(p * p2)) is set
(0. CS) + (r1 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(r1 * p1)) is Element of the U1 of CS
K4((0. CS),(r1 * p1)) is set
the U5 of CS . K4((0. CS),(r1 * p1)) is set
((0. CS) + (r1 * p1)) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (r1 * p1)),(p * p2)) is Element of the U1 of CS
K4(((0. CS) + (r1 * p1)),(p * p2)) is set
the U5 of CS . K4(((0. CS) + (r1 * p1)),(p * p2)) is set
(r1 * p1) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * p1),(p * p2)) is Element of the U1 of CS
K4((r1 * p1),(p * p2)) is set
the U5 of CS . K4((r1 * p1),(p * p2)) is set
0 * p2 is Element of the U1 of CS
K138( the Mult of CS,0,p2) is set
K4(0,p2) is set
the Mult of CS . K4(0,p2) is set
((0. CS) + (r1 * p1)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (r1 * p1)),(0 * p2)) is Element of the U1 of CS
K4(((0. CS) + (r1 * p1)),(0 * p2)) is set
the U5 of CS . K4(((0. CS) + (r1 * p1)),(0 * p2)) is set
(r1 * p1) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * p1),(0 * p2)) is Element of the U1 of CS
K4((r1 * p1),(0 * p2)) is set
the U5 of CS . K4((r1 * p1),(0 * p2)) is set
(r1 * p1) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * p1),(0. CS)) is Element of the U1 of CS
K4((r1 * p1),(0. CS)) is set
the U5 of CS . K4((r1 * p1),(0. CS)) is set
0 * p1 is Element of the U1 of CS
K138( the Mult of CS,0,p1) is set
K4(0,p1) is set
the Mult of CS . K4(0,p1) is set
(0. CS) + (0 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0 * p1)) is Element of the U1 of CS
K4((0. CS),(0 * p1)) is set
the U5 of CS . K4((0. CS),(0 * p1)) is set
((0. CS) + (0 * p1)) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (0 * p1)),(p * p2)) is Element of the U1 of CS
K4(((0. CS) + (0 * p1)),(p * p2)) is set
the U5 of CS . K4(((0. CS) + (0 * p1)),(p * p2)) is set
(0 * p1) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p1),(p * p2)) is Element of the U1 of CS
K4((0 * p1),(p * p2)) is set
the U5 of CS . K4((0 * p1),(p * p2)) is set
(0. CS) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(p * p2)) is Element of the U1 of CS
K4((0. CS),(p * p2)) is set
the U5 of CS . K4((0. CS),(p * p2)) is set
((r * p) + (r1 * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (r1 * p1)),(0. CS)) is Element of the U1 of CS
K4(((r * p) + (r1 * p1)),(0. CS)) is set
the U5 of CS . K4(((r * p) + (r1 * p1)),(0. CS)) is set
- (r1 * p1) is Element of the U1 of CS
- p1 is Element of the U1 of CS
r1 * (- p1) is Element of the U1 of CS
K138( the Mult of CS,r1,(- p1)) is set
K4(r1,(- p1)) is set
the Mult of CS . K4(r1,(- p1)) is set
- r1 is V24() V25() Element of REAL
(- r1) * p1 is Element of the U1 of CS
K138( the Mult of CS,(- r1),p1) is set
K4((- r1),p1) is set
the Mult of CS . K4((- r1),p1) is set
0 * p1 is Element of the U1 of CS
K138( the Mult of CS,0,p1) is set
K4(0,p1) is set
the Mult of CS . K4(0,p1) is set
(r * p) + (0 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * p),(0 * p1)) is Element of the U1 of CS
K4((r * p),(0 * p1)) is set
the U5 of CS . K4((r * p),(0 * p1)) is set
((r * p) + (0 * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (0 * p1)),(0. CS)) is Element of the U1 of CS
K4(((r * p) + (0 * p1)),(0. CS)) is set
the U5 of CS . K4(((r * p) + (0 * p1)),(0. CS)) is set
0 * p2 is Element of the U1 of CS
K138( the Mult of CS,0,p2) is set
K4(0,p2) is set
the Mult of CS . K4(0,p2) is set
((0. CS) + (r1 * p1)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (r1 * p1)),(0 * p2)) is Element of the U1 of CS
K4(((0. CS) + (r1 * p1)),(0 * p2)) is set
the U5 of CS . K4(((0. CS) + (r1 * p1)),(0 * p2)) is set
(r1 * p1) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * p1),(0 * p2)) is Element of the U1 of CS
K4((r1 * p1),(0 * p2)) is set
the U5 of CS . K4((r1 * p1),(0 * p2)) is set
(r1 * p1) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * p1),(0. CS)) is Element of the U1 of CS
K4((r1 * p1),(0. CS)) is set
the U5 of CS . K4((r1 * p1),(0. CS)) is set
p " is V24() V25() Element of REAL
r " is V24() V25() Element of REAL
(r ") * r1 is V24() V25() Element of REAL
(r ") * p is V24() V25() Element of REAL
- ((r ") * p) is V24() V25() Element of REAL
- (p * p2) is Element of the U1 of CS
(r ") * (- (p * p2)) is Element of the U1 of CS
K138( the Mult of CS,(r "),(- (p * p2))) is set
K4((r "),(- (p * p2))) is set
the Mult of CS . K4((r "),(- (p * p2))) is set
(r ") * ((r * p) + (r1 * p1)) is Element of the U1 of CS
K138( the Mult of CS,(r "),((r * p) + (r1 * p1))) is set
K4((r "),((r * p) + (r1 * p1))) is set
the Mult of CS . K4((r "),((r * p) + (r1 * p1))) is set
(r ") * (r * p) is Element of the U1 of CS
K138( the Mult of CS,(r "),(r * p)) is set
K4((r "),(r * p)) is set
the Mult of CS . K4((r "),(r * p)) is set
(r ") * (r1 * p1) is Element of the U1 of CS
K138( the Mult of CS,(r "),(r1 * p1)) is set
K4((r "),(r1 * p1)) is set
the Mult of CS . K4((r "),(r1 * p1)) is set
((r ") * (r * p)) + ((r ") * (r1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r ") * (r * p)),((r ") * (r1 * p1))) is Element of the U1 of CS
K4(((r ") * (r * p)),((r ") * (r1 * p1))) is set
the U5 of CS . K4(((r ") * (r * p)),((r ") * (r1 * p1))) is set
(r ") * r is V24() V25() Element of REAL
((r ") * r) * p is Element of the U1 of CS
K138( the Mult of CS,((r ") * r),p) is set
K4(((r ") * r),p) is set
the Mult of CS . K4(((r ") * r),p) is set
(((r ") * r) * p) + ((r ") * (r1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r ") * r) * p),((r ") * (r1 * p1))) is Element of the U1 of CS
K4((((r ") * r) * p),((r ") * (r1 * p1))) is set
the U5 of CS . K4((((r ") * r) * p),((r ") * (r1 * p1))) is set
((r ") * r1) * p1 is Element of the U1 of CS
K138( the Mult of CS,((r ") * r1),p1) is set
K4(((r ") * r1),p1) is set
the Mult of CS . K4(((r ") * r1),p1) is set
(((r ") * r) * p) + (((r ") * r1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r ") * r) * p),(((r ") * r1) * p1)) is Element of the U1 of CS
K4((((r ") * r) * p),(((r ") * r1) * p1)) is set
the U5 of CS . K4((((r ") * r) * p),(((r ") * r1) * p1)) is set
1 * p is Element of the U1 of CS
K138( the Mult of CS,1,p) is set
K4(1,p) is set
the Mult of CS . K4(1,p) is set
(1 * p) + (((r ") * r1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * p),(((r ") * r1) * p1)) is Element of the U1 of CS
K4((1 * p),(((r ") * r1) * p1)) is set
the U5 of CS . K4((1 * p),(((r ") * r1) * p1)) is set
p + (((r ") * r1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,(((r ") * r1) * p1)) is Element of the U1 of CS
K4(p,(((r ") * r1) * p1)) is set
the U5 of CS . K4(p,(((r ") * r1) * p1)) is set
- p2 is Element of the U1 of CS
p * (- p2) is Element of the U1 of CS
K138( the Mult of CS,p,(- p2)) is set
K4(p,(- p2)) is set
the Mult of CS . K4(p,(- p2)) is set
(r ") * (p * (- p2)) is Element of the U1 of CS
K138( the Mult of CS,(r "),(p * (- p2))) is set
K4((r "),(p * (- p2))) is set
the Mult of CS . K4((r "),(p * (- p2))) is set
((r ") * p) * (- p2) is Element of the U1 of CS
K138( the Mult of CS,((r ") * p),(- p2)) is set
K4(((r ") * p),(- p2)) is set
the Mult of CS . K4(((r ") * p),(- p2)) is set
(- ((r ") * p)) * p2 is Element of the U1 of CS
K138( the Mult of CS,(- ((r ") * p)),p2) is set
K4((- ((r ") * p)),p2) is set
the Mult of CS . K4((- ((r ") * p)),p2) is set
- r1 is V24() V25() Element of REAL
(p ") * (- r1) is V24() V25() Element of REAL
- ((r * p) + (r1 * p1)) is Element of the U1 of CS
- (r * p) is Element of the U1 of CS
- (r1 * p1) is Element of the U1 of CS
(- (r * p)) + (- (r1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(- (r * p)),(- (r1 * p1))) is Element of the U1 of CS
K4((- (r * p)),(- (r1 * p1))) is set
the U5 of CS . K4((- (r * p)),(- (r1 * p1))) is set
- r is V24() V25() Element of REAL
(- r) * p is Element of the U1 of CS
K138( the Mult of CS,(- r),p) is set
K4((- r),p) is set
the Mult of CS . K4((- r),p) is set
((- r) * p) + (- (r1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- r) * p),(- (r1 * p1))) is Element of the U1 of CS
K4(((- r) * p),(- (r1 * p1))) is set
the U5 of CS . K4(((- r) * p),(- (r1 * p1))) is set
(- r1) * p1 is Element of the U1 of CS
K138( the Mult of CS,(- r1),p1) is set
K4((- r1),p1) is set
the Mult of CS . K4((- r1),p1) is set
((- r) * p) + ((- r1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- r) * p),((- r1) * p1)) is Element of the U1 of CS
K4(((- r) * p),((- r1) * p1)) is set
the U5 of CS . K4(((- r) * p),((- r1) * p1)) is set
(p ") * (p * p2) is Element of the U1 of CS
K138( the Mult of CS,(p "),(p * p2)) is set
K4((p "),(p * p2)) is set
the Mult of CS . K4((p "),(p * p2)) is set
(p ") * ((- r) * p) is Element of the U1 of CS
K138( the Mult of CS,(p "),((- r) * p)) is set
K4((p "),((- r) * p)) is set
the Mult of CS . K4((p "),((- r) * p)) is set
(p ") * ((- r1) * p1) is Element of the U1 of CS
K138( the Mult of CS,(p "),((- r1) * p1)) is set
K4((p "),((- r1) * p1)) is set
the Mult of CS . K4((p "),((- r1) * p1)) is set
((p ") * ((- r) * p)) + ((p ") * ((- r1) * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p ") * ((- r) * p)),((p ") * ((- r1) * p1))) is Element of the U1 of CS
K4(((p ") * ((- r) * p)),((p ") * ((- r1) * p1))) is set
the U5 of CS . K4(((p ") * ((- r) * p)),((p ") * ((- r1) * p1))) is set
(p ") * (- r) is V24() V25() Element of REAL
((p ") * (- r)) * p is Element of the U1 of CS
K138( the Mult of CS,((p ") * (- r)),p) is set
K4(((p ") * (- r)),p) is set
the Mult of CS . K4(((p ") * (- r)),p) is set
(((p ") * (- r)) * p) + ((p ") * ((- r1) * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p ") * (- r)) * p),((p ") * ((- r1) * p1))) is Element of the U1 of CS
K4((((p ") * (- r)) * p),((p ") * ((- r1) * p1))) is set
the U5 of CS . K4((((p ") * (- r)) * p),((p ") * ((- r1) * p1))) is set
((p ") * (- r1)) * p1 is Element of the U1 of CS
K138( the Mult of CS,((p ") * (- r1)),p1) is set
K4(((p ") * (- r1)),p1) is set
the Mult of CS . K4(((p ") * (- r1)),p1) is set
(((p ") * (- r)) * p) + (((p ") * (- r1)) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p ") * (- r)) * p),(((p ") * (- r1)) * p1)) is Element of the U1 of CS
K4((((p ") * (- r)) * p),(((p ") * (- r1)) * p1)) is set
the U5 of CS . K4((((p ") * (- r)) * p),(((p ") * (- r1)) * p1)) is set
(p ") * p is V24() V25() Element of REAL
((p ") * p) * p2 is Element of the U1 of CS
K138( the Mult of CS,((p ") * p),p2) is set
K4(((p ") * p),p2) is set
the Mult of CS . K4(((p ") * p),p2) is set
1 * p2 is Element of the U1 of CS
K138( the Mult of CS,1,p2) is set
K4(1,p2) is set
the Mult of CS . K4(1,p2) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
r is V24() V25() Element of REAL
r * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,r,p) is set
K4(r,p) is set
the Mult of CS . K4(r,p) is set
r1 is V24() V25() Element of REAL
r1 * p1 is Element of the U1 of CS
K138( the Mult of CS,r1,p1) is set
K4(r1,p1) is set
the Mult of CS . K4(r1,p1) is set
(r * p) + (r1 * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(r * p),(r1 * p1)) is Element of the U1 of CS
K4((r * p),(r1 * p1)) is set
the U5 of CS . K4((r * p),(r1 * p1)) is set
p is V24() V25() Element of REAL
p * p2 is Element of the U1 of CS
K138( the Mult of CS,p,p2) is set
K4(p,p2) is set
the Mult of CS . K4(p,p2) is set
((r * p) + (r1 * p1)) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (r1 * p1)),(p * p2)) is Element of the U1 of CS
K4(((r * p) + (r1 * p1)),(p * p2)) is set
the U5 of CS . K4(((r * p) + (r1 * p1)),(p * p2)) is set
((r * p) + (r1 * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (r1 * p1)),(0. CS)) is Element of the U1 of CS
K4(((r * p) + (r1 * p1)),(0. CS)) is set
the U5 of CS . K4(((r * p) + (r1 * p1)),(0. CS)) is set
- (r1 * p1) is Element of the U1 of CS
- r1 is V24() V25() Element of REAL
(- r1) * p1 is Element of the U1 of CS
K138( the Mult of CS,(- r1),p1) is set
K4((- r1),p1) is set
the Mult of CS . K4((- r1),p1) is set
(r * p) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * p),(0. CS)) is Element of the U1 of CS
K4((r * p),(0. CS)) is set
the U5 of CS . K4((r * p),(0. CS)) is set
0 * p2 is Element of the U1 of CS
K138( the Mult of CS,0,p2) is set
K4(0,p2) is set
the Mult of CS . K4(0,p2) is set
((r * p) + (0. CS)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (0. CS)),(0 * p2)) is Element of the U1 of CS
K4(((r * p) + (0. CS)),(0 * p2)) is set
the U5 of CS . K4(((r * p) + (0. CS)),(0 * p2)) is set
((r * p) + (0. CS)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (0. CS)),(0. CS)) is Element of the U1 of CS
K4(((r * p) + (0. CS)),(0. CS)) is set
the U5 of CS . K4(((r * p) + (0. CS)),(0. CS)) is set
(0. CS) + (r1 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(r1 * p1)) is Element of the U1 of CS
K4((0. CS),(r1 * p1)) is set
the U5 of CS . K4((0. CS),(r1 * p1)) is set
((0. CS) + (r1 * p1)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (r1 * p1)),(0 * p2)) is Element of the U1 of CS
K4(((0. CS) + (r1 * p1)),(0 * p2)) is set
the U5 of CS . K4(((0. CS) + (r1 * p1)),(0 * p2)) is set
((0. CS) + (r1 * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (r1 * p1)),(0. CS)) is Element of the U1 of CS
K4(((0. CS) + (r1 * p1)),(0. CS)) is set
the U5 of CS . K4(((0. CS) + (r1 * p1)),(0. CS)) is set
(r1 * p1) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * p1),(0. CS)) is Element of the U1 of CS
K4((r1 * p1),(0. CS)) is set
the U5 of CS . K4((r1 * p1),(0. CS)) is set
- ((r * p) + (r1 * p1)) is Element of the U1 of CS
- (r * p) is Element of the U1 of CS
- (r1 * p1) is Element of the U1 of CS
(- (r * p)) + (- (r1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(- (r * p)),(- (r1 * p1))) is Element of the U1 of CS
K4((- (r * p)),(- (r1 * p1))) is set
the U5 of CS . K4((- (r * p)),(- (r1 * p1))) is set
- r is V24() V25() Element of REAL
(- r) * p is Element of the U1 of CS
K138( the Mult of CS,(- r),p) is set
K4((- r),p) is set
the Mult of CS . K4((- r),p) is set
((- r) * p) + (- (r1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- r) * p),(- (r1 * p1))) is Element of the U1 of CS
K4(((- r) * p),(- (r1 * p1))) is set
the U5 of CS . K4(((- r) * p),(- (r1 * p1))) is set
- r1 is V24() V25() Element of REAL
(- r1) * p1 is Element of the U1 of CS
K138( the Mult of CS,(- r1),p1) is set
K4((- r1),p1) is set
the Mult of CS . K4((- r1),p1) is set
((- r) * p) + ((- r1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- r) * p),((- r1) * p1)) is Element of the U1 of CS
K4(((- r) * p),((- r1) * p1)) is set
the U5 of CS . K4(((- r) * p),((- r1) * p1)) is set
p " is V24() V25() Element of REAL
(p ") * (p * p2) is Element of the U1 of CS
K138( the Mult of CS,(p "),(p * p2)) is set
K4((p "),(p * p2)) is set
the Mult of CS . K4((p "),(p * p2)) is set
(p ") * ((- r) * p) is Element of the U1 of CS
K138( the Mult of CS,(p "),((- r) * p)) is set
K4((p "),((- r) * p)) is set
the Mult of CS . K4((p "),((- r) * p)) is set
(p ") * ((- r1) * p1) is Element of the U1 of CS
K138( the Mult of CS,(p "),((- r1) * p1)) is set
K4((p "),((- r1) * p1)) is set
the Mult of CS . K4((p "),((- r1) * p1)) is set
((p ") * ((- r) * p)) + ((p ") * ((- r1) * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p ") * ((- r) * p)),((p ") * ((- r1) * p1))) is Element of the U1 of CS
K4(((p ") * ((- r) * p)),((p ") * ((- r1) * p1))) is set
the U5 of CS . K4(((p ") * ((- r) * p)),((p ") * ((- r1) * p1))) is set
(p ") * (- r) is V24() V25() Element of REAL
((p ") * (- r)) * p is Element of the U1 of CS
K138( the Mult of CS,((p ") * (- r)),p) is set
K4(((p ") * (- r)),p) is set
the Mult of CS . K4(((p ") * (- r)),p) is set
(((p ") * (- r)) * p) + ((p ") * ((- r1) * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p ") * (- r)) * p),((p ") * ((- r1) * p1))) is Element of the U1 of CS
K4((((p ") * (- r)) * p),((p ") * ((- r1) * p1))) is set
the U5 of CS . K4((((p ") * (- r)) * p),((p ") * ((- r1) * p1))) is set
(p ") * (- r1) is V24() V25() Element of REAL
((p ") * (- r1)) * p1 is Element of the U1 of CS
K138( the Mult of CS,((p ") * (- r1)),p1) is set
K4(((p ") * (- r1)),p1) is set
the Mult of CS . K4(((p ") * (- r1)),p1) is set
(((p ") * (- r)) * p) + (((p ") * (- r1)) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p ") * (- r)) * p),(((p ") * (- r1)) * p1)) is Element of the U1 of CS
K4((((p ") * (- r)) * p),(((p ") * (- r1)) * p1)) is set
the U5 of CS . K4((((p ") * (- r)) * p),(((p ") * (- r1)) * p1)) is set
(p ") * p is V24() V25() Element of REAL
((p ") * p) * p2 is Element of the U1 of CS
K138( the Mult of CS,((p ") * p),p2) is set
K4(((p ") * p),p2) is set
the Mult of CS . K4(((p ") * p),p2) is set
1 * p2 is Element of the U1 of CS
K138( the Mult of CS,1,p2) is set
K4(1,p2) is set
the Mult of CS . K4(1,p2) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is V24() V25() Element of REAL
p2 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p2,p) is set
K4(p2,p) is set
the Mult of CS . K4(p2,p) is set
1 * p1 is Element of the U1 of CS
K138( the Mult of CS,1,p1) is set
K4(1,p1) is set
the Mult of CS . K4(1,p1) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is V24() V25() Element of REAL
p * p2 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p,p2) is set
K4(p,p2) is set
the Mult of CS . K4(p,p2) is set
p1 + (p * p2) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,p1,(p * p2)) is Element of the U1 of CS
K4(p1,(p * p2)) is set
the U5 of CS . K4(p1,(p * p2)) is set
p1 is V24() V25() Element of REAL
p1 * r1 is Element of the U1 of CS
K138( the Mult of CS,p1,r1) is set
K4(p1,r1) is set
the Mult of CS . K4(p1,r1) is set
p1 + (p1 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p1,(p1 * r1)) is Element of the U1 of CS
K4(p1,(p1 * r1)) is set
the U5 of CS . K4(p1,(p1 * r1)) is set
q is V24() V25() Element of REAL
q * (p1 + (p1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,q,(p1 + (p1 * r1))) is set
K4(q,(p1 + (p1 * r1))) is set
the Mult of CS . K4(q,(p1 + (p1 * r1))) is set
q * p1 is Element of the U1 of CS
K138( the Mult of CS,q,p1) is set
K4(q,p1) is set
the Mult of CS . K4(q,p1) is set
q * (p1 * r1) is Element of the U1 of CS
K138( the Mult of CS,q,(p1 * r1)) is set
K4(q,(p1 * r1)) is set
the Mult of CS . K4(q,(p1 * r1)) is set
(q * p1) + (q * (p1 * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q * p1),(q * (p1 * r1))) is Element of the U1 of CS
K4((q * p1),(q * (p1 * r1))) is set
the U5 of CS . K4((q * p1),(q * (p1 * r1))) is set
q * p1 is V24() V25() Element of REAL
(q * p1) * r1 is Element of the U1 of CS
K138( the Mult of CS,(q * p1),r1) is set
K4((q * p1),r1) is set
the Mult of CS . K4((q * p1),r1) is set
(q * p1) + ((q * p1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q * p1),((q * p1) * r1)) is Element of the U1 of CS
K4((q * p1),((q * p1) * r1)) is set
the U5 of CS . K4((q * p1),((q * p1) * r1)) is set
- (q * p1) is Element of the U1 of CS
(- (q * p1)) + (p1 + (p * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(- (q * p1)),(p1 + (p * p2))) is Element of the U1 of CS
K4((- (q * p1)),(p1 + (p * p2))) is set
the U5 of CS . K4((- (q * p1)),(p1 + (p * p2))) is set
(- (q * p1)) + (q * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(- (q * p1)),(q * p1)) is Element of the U1 of CS
K4((- (q * p1)),(q * p1)) is set
the U5 of CS . K4((- (q * p1)),(q * p1)) is set
((- (q * p1)) + (q * p1)) + ((q * p1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- (q * p1)) + (q * p1)),((q * p1) * r1)) is Element of the U1 of CS
K4(((- (q * p1)) + (q * p1)),((q * p1) * r1)) is set
the U5 of CS . K4(((- (q * p1)) + (q * p1)),((q * p1) * r1)) is set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
(0. CS) + ((q * p1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),((q * p1) * r1)) is Element of the U1 of CS
K4((0. CS),((q * p1) * r1)) is set
the U5 of CS . K4((0. CS),((q * p1) * r1)) is set
(- (q * p1)) + p1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(- (q * p1)),p1) is Element of the U1 of CS
K4((- (q * p1)),p1) is set
the U5 of CS . K4((- (q * p1)),p1) is set
((- (q * p1)) + p1) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- (q * p1)) + p1),(p * p2)) is Element of the U1 of CS
K4(((- (q * p1)) + p1),(p * p2)) is set
the U5 of CS . K4(((- (q * p1)) + p1),(p * p2)) is set
- q is V24() V25() Element of REAL
(- q) * p1 is Element of the U1 of CS
K138( the Mult of CS,(- q),p1) is set
K4((- q),p1) is set
the Mult of CS . K4((- q),p1) is set
((- q) * p1) + p1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- q) * p1),p1) is Element of the U1 of CS
K4(((- q) * p1),p1) is set
the U5 of CS . K4(((- q) * p1),p1) is set
(((- q) * p1) + p1) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((- q) * p1) + p1),(p * p2)) is Element of the U1 of CS
K4((((- q) * p1) + p1),(p * p2)) is set
the U5 of CS . K4((((- q) * p1) + p1),(p * p2)) is set
1 * p1 is Element of the U1 of CS
K138( the Mult of CS,1,p1) is set
K4(1,p1) is set
the Mult of CS . K4(1,p1) is set
((- q) * p1) + (1 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- q) * p1),(1 * p1)) is Element of the U1 of CS
K4(((- q) * p1),(1 * p1)) is set
the U5 of CS . K4(((- q) * p1),(1 * p1)) is set
(((- q) * p1) + (1 * p1)) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((- q) * p1) + (1 * p1)),(p * p2)) is Element of the U1 of CS
K4((((- q) * p1) + (1 * p1)),(p * p2)) is set
the U5 of CS . K4((((- q) * p1) + (1 * p1)),(p * p2)) is set
(- q) + 1 is V24() V25() Element of REAL
((- q) + 1) * p1 is Element of the U1 of CS
K138( the Mult of CS,((- q) + 1),p1) is set
K4(((- q) + 1),p1) is set
the Mult of CS . K4(((- q) + 1),p1) is set
(((- q) + 1) * p1) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((- q) + 1) * p1),(p * p2)) is Element of the U1 of CS
K4((((- q) + 1) * p1),(p * p2)) is set
the U5 of CS . K4((((- q) + 1) * p1),(p * p2)) is set
- ((q * p1) * r1) is Element of the U1 of CS
((((- q) + 1) * p1) + (p * p2)) + (- ((q * p1) * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((- q) + 1) * p1) + (p * p2)),(- ((q * p1) * r1))) is Element of the U1 of CS
K4(((((- q) + 1) * p1) + (p * p2)),(- ((q * p1) * r1))) is set
the U5 of CS . K4(((((- q) + 1) * p1) + (p * p2)),(- ((q * p1) * r1))) is set
- (q * p1) is V24() V25() Element of REAL
(- (q * p1)) * r1 is Element of the U1 of CS
K138( the Mult of CS,(- (q * p1)),r1) is set
K4((- (q * p1)),r1) is set
the Mult of CS . K4((- (q * p1)),r1) is set
((((- q) + 1) * p1) + (p * p2)) + ((- (q * p1)) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((- q) + 1) * p1) + (p * p2)),((- (q * p1)) * r1)) is Element of the U1 of CS
K4(((((- q) + 1) * p1) + (p * p2)),((- (q * p1)) * r1)) is set
the U5 of CS . K4(((((- q) + 1) * p1) + (p * p2)),((- (q * p1)) * r1)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is V24() V25() Element of REAL
p2 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p2,p) is set
K4(p2,p) is set
the Mult of CS . K4(p2,p) is set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is Element of the U1 of CS
p1 is V24() V25() Element of REAL
p1 * r1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p1,r1) is set
K4(p1,r1) is set
the Mult of CS . K4(p1,r1) is set
r + (p1 * r1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,r,(p1 * r1)) is Element of the U1 of CS
K4(r,(p1 * r1)) is set
the U5 of CS . K4(r,(p1 * r1)) is set
q is V24() V25() Element of REAL
q * p is Element of the U1 of CS
K138( the Mult of CS,q,p) is set
K4(q,p) is set
the Mult of CS . K4(q,p) is set
r + (q * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,(q * p)) is Element of the U1 of CS
K4(r,(q * p)) is set
the U5 of CS . K4(r,(q * p)) is set
q1 is V24() V25() Element of REAL
q1 * p1 is Element of the U1 of CS
K138( the Mult of CS,q1,p1) is set
K4(q1,p1) is set
the Mult of CS . K4(q1,p1) is set
r is V24() V25() Element of REAL
r * p2 is Element of the U1 of CS
K138( the Mult of CS,r,p2) is set
K4(r,p2) is set
the Mult of CS . K4(r,p2) is set
(q1 * p1) + (r * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q1 * p1),(r * p2)) is Element of the U1 of CS
K4((q1 * p1),(r * p2)) is set
the U5 of CS . K4((q1 * p1),(r * p2)) is set
q1 + r is V24() V25() Element of REAL
(q1 + r) * r is Element of the U1 of CS
K138( the Mult of CS,(q1 + r),r) is set
K4((q1 + r),r) is set
the Mult of CS . K4((q1 + r),r) is set
q1 * p1 is V24() V25() Element of REAL
(q1 * p1) * r1 is Element of the U1 of CS
K138( the Mult of CS,(q1 * p1),r1) is set
K4((q1 * p1),r1) is set
the Mult of CS . K4((q1 * p1),r1) is set
((q1 + r) * r) + ((q1 * p1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 + r) * r),((q1 * p1) * r1)) is Element of the U1 of CS
K4(((q1 + r) * r),((q1 * p1) * r1)) is set
the U5 of CS . K4(((q1 + r) * r),((q1 * p1) * r1)) is set
r * q is V24() V25() Element of REAL
(r * q) * p is Element of the U1 of CS
K138( the Mult of CS,(r * q),p) is set
K4((r * q),p) is set
the Mult of CS . K4((r * q),p) is set
(((q1 + r) * r) + ((q1 * p1) * r1)) + ((r * q) * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q1 + r) * r) + ((q1 * p1) * r1)),((r * q) * p)) is Element of the U1 of CS
K4((((q1 + r) * r) + ((q1 * p1) * r1)),((r * q) * p)) is set
the U5 of CS . K4((((q1 + r) * r) + ((q1 * p1) * r1)),((r * q) * p)) is set
q1 * r is Element of the U1 of CS
K138( the Mult of CS,q1,r) is set
K4(q1,r) is set
the Mult of CS . K4(q1,r) is set
q1 * (p1 * r1) is Element of the U1 of CS
K138( the Mult of CS,q1,(p1 * r1)) is set
K4(q1,(p1 * r1)) is set
the Mult of CS . K4(q1,(p1 * r1)) is set
(q1 * r) + (q1 * (p1 * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q1 * r),(q1 * (p1 * r1))) is Element of the U1 of CS
K4((q1 * r),(q1 * (p1 * r1))) is set
the U5 of CS . K4((q1 * r),(q1 * (p1 * r1))) is set
r * (r + (q * p)) is Element of the U1 of CS
K138( the Mult of CS,r,(r + (q * p))) is set
K4(r,(r + (q * p))) is set
the Mult of CS . K4(r,(r + (q * p))) is set
((q1 * r) + (q1 * (p1 * r1))) + (r * (r + (q * p))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + (q1 * (p1 * r1))),(r * (r + (q * p)))) is Element of the U1 of CS
K4(((q1 * r) + (q1 * (p1 * r1))),(r * (r + (q * p)))) is set
the U5 of CS . K4(((q1 * r) + (q1 * (p1 * r1))),(r * (r + (q * p)))) is set
r * r is Element of the U1 of CS
K138( the Mult of CS,r,r) is set
K4(r,r) is set
the Mult of CS . K4(r,r) is set
r * (q * p) is Element of the U1 of CS
K138( the Mult of CS,r,(q * p)) is set
K4(r,(q * p)) is set
the Mult of CS . K4(r,(q * p)) is set
(r * r) + (r * (q * p)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * r),(r * (q * p))) is Element of the U1 of CS
K4((r * r),(r * (q * p))) is set
the U5 of CS . K4((r * r),(r * (q * p))) is set
((q1 * r) + (q1 * (p1 * r1))) + ((r * r) + (r * (q * p))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + (q1 * (p1 * r1))),((r * r) + (r * (q * p)))) is Element of the U1 of CS
K4(((q1 * r) + (q1 * (p1 * r1))),((r * r) + (r * (q * p)))) is set
the U5 of CS . K4(((q1 * r) + (q1 * (p1 * r1))),((r * r) + (r * (q * p)))) is set
(q1 * r) + ((q1 * p1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q1 * r),((q1 * p1) * r1)) is Element of the U1 of CS
K4((q1 * r),((q1 * p1) * r1)) is set
the U5 of CS . K4((q1 * r),((q1 * p1) * r1)) is set
((q1 * r) + ((q1 * p1) * r1)) + ((r * r) + (r * (q * p))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + ((q1 * p1) * r1)),((r * r) + (r * (q * p)))) is Element of the U1 of CS
K4(((q1 * r) + ((q1 * p1) * r1)),((r * r) + (r * (q * p)))) is set
the U5 of CS . K4(((q1 * r) + ((q1 * p1) * r1)),((r * r) + (r * (q * p)))) is set
(r * r) + ((r * q) * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * r),((r * q) * p)) is Element of the U1 of CS
K4((r * r),((r * q) * p)) is set
the U5 of CS . K4((r * r),((r * q) * p)) is set
((q1 * r) + ((q1 * p1) * r1)) + ((r * r) + ((r * q) * p)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + ((q1 * p1) * r1)),((r * r) + ((r * q) * p))) is Element of the U1 of CS
K4(((q1 * r) + ((q1 * p1) * r1)),((r * r) + ((r * q) * p))) is set
the U5 of CS . K4(((q1 * r) + ((q1 * p1) * r1)),((r * r) + ((r * q) * p))) is set
((q1 * r) + ((q1 * p1) * r1)) + (r * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + ((q1 * p1) * r1)),(r * r)) is Element of the U1 of CS
K4(((q1 * r) + ((q1 * p1) * r1)),(r * r)) is set
the U5 of CS . K4(((q1 * r) + ((q1 * p1) * r1)),(r * r)) is set
(((q1 * r) + ((q1 * p1) * r1)) + (r * r)) + ((r * q) * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q1 * r) + ((q1 * p1) * r1)) + (r * r)),((r * q) * p)) is Element of the U1 of CS
K4((((q1 * r) + ((q1 * p1) * r1)) + (r * r)),((r * q) * p)) is set
the U5 of CS . K4((((q1 * r) + ((q1 * p1) * r1)) + (r * r)),((r * q) * p)) is set
(q1 * r) + (r * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q1 * r),(r * r)) is Element of the U1 of CS
K4((q1 * r),(r * r)) is set
the U5 of CS . K4((q1 * r),(r * r)) is set
((q1 * r) + (r * r)) + ((q1 * p1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + (r * r)),((q1 * p1) * r1)) is Element of the U1 of CS
K4(((q1 * r) + (r * r)),((q1 * p1) * r1)) is set
the U5 of CS . K4(((q1 * r) + (r * r)),((q1 * p1) * r1)) is set
(((q1 * r) + (r * r)) + ((q1 * p1) * r1)) + ((r * q) * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q1 * r) + (r * r)) + ((q1 * p1) * r1)),((r * q) * p)) is Element of the U1 of CS
K4((((q1 * r) + (r * r)) + ((q1 * p1) * r1)),((r * q) * p)) is set
the U5 of CS . K4((((q1 * r) + (r * r)) + ((q1 * p1) * r1)),((r * q) * p)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
0 * r is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,0,r) is set
K4(0,r) is set
the Mult of CS . K4(0,r) is set
r1 is V24() V25() Element of REAL
r1 * p1 is Element of the U1 of CS
K138( the Mult of CS,r1,p1) is set
K4(r1,p1) is set
the Mult of CS . K4(r1,p1) is set
(0 * r) + (r1 * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(0 * r),(r1 * p1)) is Element of the U1 of CS
K4((0 * r),(r1 * p1)) is set
the U5 of CS . K4((0 * r),(r1 * p1)) is set
p is V24() V25() Element of REAL
p * p2 is Element of the U1 of CS
K138( the Mult of CS,p,p2) is set
K4(p,p2) is set
the Mult of CS . K4(p,p2) is set
(r1 * p1) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * p1),(p * p2)) is Element of the U1 of CS
K4((r1 * p1),(p * p2)) is set
the U5 of CS . K4((r1 * p1),(p * p2)) is set
((0 * r) + (r1 * p1)) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * r) + (r1 * p1)),(p * p2)) is Element of the U1 of CS
K4(((0 * r) + (r1 * p1)),(p * p2)) is set
the U5 of CS . K4(((0 * r) + (r1 * p1)),(p * p2)) is set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
(0. CS) + (r1 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(r1 * p1)) is Element of the U1 of CS
K4((0. CS),(r1 * p1)) is set
the U5 of CS . K4((0. CS),(r1 * p1)) is set
((0. CS) + (r1 * p1)) + (p * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + (r1 * p1)),(p * p2)) is Element of the U1 of CS
K4(((0. CS) + (r1 * p1)),(p * p2)) is set
the U5 of CS . K4(((0. CS) + (r1 * p1)),(p * p2)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
0 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,0,p) is set
K4(0,p) is set
the Mult of CS . K4(0,p) is set
p1 is Element of the U1 of CS
0 * p1 is Element of the U1 of CS
K138( the Mult of CS,0,p1) is set
K4(0,p1) is set
the Mult of CS . K4(0,p1) is set
(0 * p) + (0 * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(0 * p),(0 * p1)) is Element of the U1 of CS
K4((0 * p),(0 * p1)) is set
the U5 of CS . K4((0 * p),(0 * p1)) is set
(0. CS) + (0 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0 * p1)) is Element of the U1 of CS
K4((0. CS),(0 * p1)) is set
the U5 of CS . K4((0. CS),(0 * p1)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
0 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,0,p) is set
K4(0,p) is set
the Mult of CS . K4(0,p) is set
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is V24() V25() Element of REAL
- r is V24() V25() Element of REAL
r1 is V24() V25() Element of REAL
r * r1 is V24() V25() Element of REAL
(r * r1) * p1 is Element of the U1 of CS
K138( the Mult of CS,(r * r1),p1) is set
K4((r * r1),p1) is set
the Mult of CS . K4((r * r1),p1) is set
(0 * p) + ((r * r1) * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(0 * p),((r * r1) * p1)) is Element of the U1 of CS
K4((0 * p),((r * r1) * p1)) is set
the U5 of CS . K4((0 * p),((r * r1) * p1)) is set
r1 * p1 is Element of the U1 of CS
K138( the Mult of CS,r1,p1) is set
K4(r1,p1) is set
the Mult of CS . K4(r1,p1) is set
p is V24() V25() Element of REAL
(- r) * p is V24() V25() Element of REAL
((- r) * p) * p2 is Element of the U1 of CS
K138( the Mult of CS,((- r) * p),p2) is set
K4(((- r) * p),p2) is set
the Mult of CS . K4(((- r) * p),p2) is set
((0 * p) + ((r * r1) * p1)) + (((- r) * p) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * p) + ((r * r1) * p1)),(((- r) * p) * p2)) is Element of the U1 of CS
K4(((0 * p) + ((r * r1) * p1)),(((- r) * p) * p2)) is set
the U5 of CS . K4(((0 * p) + ((r * r1) * p1)),(((- r) * p) * p2)) is set
p * p2 is Element of the U1 of CS
K138( the Mult of CS,p,p2) is set
K4(p,p2) is set
the Mult of CS . K4(p,p2) is set
(r1 * p1) - (p * p2) is Element of the U1 of CS
- (p * p2) is Element of the U1 of CS
K176(CS,(r1 * p1),(- (p * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r1 * p1),(- (p * p2))) is Element of the U1 of CS
K4((r1 * p1),(- (p * p2))) is set
the U5 of CS . K4((r1 * p1),(- (p * p2))) is set
r * ((r1 * p1) - (p * p2)) is Element of the U1 of CS
K138( the Mult of CS,r,((r1 * p1) - (p * p2))) is set
K4(r,((r1 * p1) - (p * p2))) is set
the Mult of CS . K4(r,((r1 * p1) - (p * p2))) is set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
(0. CS) + ((r * r1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),((r * r1) * p1)) is Element of the U1 of CS
K4((0. CS),((r * r1) * p1)) is set
the U5 of CS . K4((0. CS),((r * r1) * p1)) is set
((0. CS) + ((r * r1) * p1)) + (((- r) * p) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + ((r * r1) * p1)),(((- r) * p) * p2)) is Element of the U1 of CS
K4(((0. CS) + ((r * r1) * p1)),(((- r) * p) * p2)) is set
the U5 of CS . K4(((0. CS) + ((r * r1) * p1)),(((- r) * p) * p2)) is set
((r * r1) * p1) + (((- r) * p) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * r1) * p1),(((- r) * p) * p2)) is Element of the U1 of CS
K4(((r * r1) * p1),(((- r) * p) * p2)) is set
the U5 of CS . K4(((r * r1) * p1),(((- r) * p) * p2)) is set
r * (r1 * p1) is Element of the U1 of CS
K138( the Mult of CS,r,(r1 * p1)) is set
K4(r,(r1 * p1)) is set
the Mult of CS . K4(r,(r1 * p1)) is set
- p is V24() V25() Element of REAL
r * (- p) is V24() V25() Element of REAL
(r * (- p)) * p2 is Element of the U1 of CS
K138( the Mult of CS,(r * (- p)),p2) is set
K4((r * (- p)),p2) is set
the Mult of CS . K4((r * (- p)),p2) is set
(r * (r1 * p1)) + ((r * (- p)) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * (r1 * p1)),((r * (- p)) * p2)) is Element of the U1 of CS
K4((r * (r1 * p1)),((r * (- p)) * p2)) is set
the U5 of CS . K4((r * (r1 * p1)),((r * (- p)) * p2)) is set
(- p) * p2 is Element of the U1 of CS
K138( the Mult of CS,(- p),p2) is set
K4((- p),p2) is set
the Mult of CS . K4((- p),p2) is set
r * ((- p) * p2) is Element of the U1 of CS
K138( the Mult of CS,r,((- p) * p2)) is set
K4(r,((- p) * p2)) is set
the Mult of CS . K4(r,((- p) * p2)) is set
(r * (r1 * p1)) + (r * ((- p) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * (r1 * p1)),(r * ((- p) * p2))) is Element of the U1 of CS
K4((r * (r1 * p1)),(r * ((- p) * p2))) is set
the U5 of CS . K4((r * (r1 * p1)),(r * ((- p) * p2))) is set
r * (- (p * p2)) is Element of the U1 of CS
K138( the Mult of CS,r,(- (p * p2))) is set
K4(r,(- (p * p2))) is set
the Mult of CS . K4(r,(- (p * p2))) is set
(r * (r1 * p1)) + (r * (- (p * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * (r1 * p1)),(r * (- (p * p2)))) is Element of the U1 of CS
K4((r * (r1 * p1)),(r * (- (p * p2)))) is set
the U5 of CS . K4((r * (r1 * p1)),(r * (- (p * p2)))) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
q is Element of the U1 of CS
q1 is Element of the U1 of CS
r is Element of the U1 of CS
z2 is V24() V25() Element of REAL
z2 * p1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,z2,p1) is set
K4(z2,p1) is set
the Mult of CS . K4(z2,p1) is set
y is V24() V25() Element of REAL
y * r is Element of the U1 of CS
K138( the Mult of CS,y,r) is set
K4(y,r) is set
the Mult of CS . K4(y,r) is set
p + (y * r) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,p,(y * r)) is Element of the U1 of CS
K4(p,(y * r)) is set
the U5 of CS . K4(p,(y * r)) is set
x2 is V24() V25() Element of REAL
x2 * r1 is Element of the U1 of CS
K138( the Mult of CS,x2,r1) is set
K4(x2,r1) is set
the Mult of CS . K4(x2,r1) is set
z1 is V24() V25() Element of REAL
z1 * p1 is Element of the U1 of CS
K138( the Mult of CS,z1,p1) is set
K4(z1,p1) is set
the Mult of CS . K4(z1,p1) is set
p + (z1 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,(z1 * p1)) is Element of the U1 of CS
K4(p,(z1 * p1)) is set
the U5 of CS . K4(p,(z1 * p1)) is set
z1 is V24() V25() Element of REAL
z1 * p is Element of the U1 of CS
K138( the Mult of CS,z1,p) is set
K4(z1,p) is set
the Mult of CS . K4(z1,p) is set
z1 is V24() V25() Element of REAL
z1 * p2 is Element of the U1 of CS
K138( the Mult of CS,z1,p2) is set
K4(z1,p2) is set
the Mult of CS . K4(z1,p2) is set
p + (z1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,(z1 * p2)) is Element of the U1 of CS
K4(p,(z1 * p2)) is set
the U5 of CS . K4(p,(z1 * p2)) is set
o9 is V24() V25() Element of REAL
o9 * p1 is Element of the U1 of CS
K138( the Mult of CS,o9,p1) is set
K4(o9,p1) is set
the Mult of CS . K4(o9,p1) is set
p19 is V24() V25() Element of REAL
p19 * p2 is Element of the U1 of CS
K138( the Mult of CS,p19,p2) is set
K4(p19,p2) is set
the Mult of CS . K4(p19,p2) is set
(o9 * p1) + (p19 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(o9 * p1),(p19 * p2)) is Element of the U1 of CS
K4((o9 * p1),(p19 * p2)) is set
the U5 of CS . K4((o9 * p1),(p19 * p2)) is set
p29 is V24() V25() Element of REAL
p29 * p2 is Element of the U1 of CS
K138( the Mult of CS,p29,p2) is set
K4(p29,p2) is set
the Mult of CS . K4(p29,p2) is set
q1999 is V24() V25() Element of REAL
q1999 * r is Element of the U1 of CS
K138( the Mult of CS,q1999,r) is set
K4(q1999,r) is set
the Mult of CS . K4(q1999,r) is set
(p29 * p2) + (q1999 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p29 * p2),(q1999 * r)) is Element of the U1 of CS
K4((p29 * p2),(q1999 * r)) is set
the U5 of CS . K4((p29 * p2),(q1999 * r)) is set
p2999 is V24() V25() Element of REAL
p2999 * (p + (z1 * p2)) is Element of the U1 of CS
K138( the Mult of CS,p2999,(p + (z1 * p2))) is set
K4(p2999,(p + (z1 * p2))) is set
the Mult of CS . K4(p2999,(p + (z1 * p2))) is set
r399 is V24() V25() Element of REAL
r399 * (p + (y * r)) is Element of the U1 of CS
K138( the Mult of CS,r399,(p + (y * r))) is set
K4(r399,(p + (y * r))) is set
the Mult of CS . K4(r399,(p + (y * r))) is set
(p2999 * (p + (z1 * p2))) + (r399 * (p + (y * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p2999 * (p + (z1 * p2))),(r399 * (p + (y * r)))) is Element of the U1 of CS
K4((p2999 * (p + (z1 * p2))),(r399 * (p + (y * r)))) is set
the U5 of CS . K4((p2999 * (p + (z1 * p2))),(r399 * (p + (y * r)))) is set
p29999 is V24() V25() Element of REAL
p29999 * p1 is Element of the U1 of CS
K138( the Mult of CS,p29999,p1) is set
K4(p29999,p1) is set
the Mult of CS . K4(p29999,p1) is set
q3999 is V24() V25() Element of REAL
q3999 * r is Element of the U1 of CS
K138( the Mult of CS,q3999,r) is set
K4(q3999,r) is set
the Mult of CS . K4(q3999,r) is set
(p29999 * p1) + (q3999 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p29999 * p1),(q3999 * r)) is Element of the U1 of CS
K4((p29999 * p1),(q3999 * r)) is set
the U5 of CS . K4((p29999 * p1),(q3999 * r)) is set
p2999 + r399 is V24() V25() Element of REAL
(p2999 + r399) * p is Element of the U1 of CS
K138( the Mult of CS,(p2999 + r399),p) is set
K4((p2999 + r399),p) is set
the Mult of CS . K4((p2999 + r399),p) is set
p2999 * z1 is V24() V25() Element of REAL
(p2999 * z1) * p2 is Element of the U1 of CS
K138( the Mult of CS,(p2999 * z1),p2) is set
K4((p2999 * z1),p2) is set
the Mult of CS . K4((p2999 * z1),p2) is set
((p2999 + r399) * p) + ((p2999 * z1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p2999 + r399) * p),((p2999 * z1) * p2)) is Element of the U1 of CS
K4(((p2999 + r399) * p),((p2999 * z1) * p2)) is set
the U5 of CS . K4(((p2999 + r399) * p),((p2999 * z1) * p2)) is set
r399 * y is V24() V25() Element of REAL
(r399 * y) * r is Element of the U1 of CS
K138( the Mult of CS,(r399 * y),r) is set
K4((r399 * y),r) is set
the Mult of CS . K4((r399 * y),r) is set
(((p2999 + r399) * p) + ((p2999 * z1) * p2)) + ((r399 * y) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p2999 + r399) * p) + ((p2999 * z1) * p2)),((r399 * y) * r)) is Element of the U1 of CS
K4((((p2999 + r399) * p) + ((p2999 * z1) * p2)),((r399 * y) * r)) is set
the U5 of CS . K4((((p2999 + r399) * p) + ((p2999 * z1) * p2)),((r399 * y) * r)) is set
r19 is V24() V25() Element of REAL
r19 * (p + (z1 * p1)) is Element of the U1 of CS
K138( the Mult of CS,r19,(p + (z1 * p1))) is set
K4(r19,(p + (z1 * p1))) is set
the Mult of CS . K4(r19,(p + (z1 * p1))) is set
p19999 is V24() V25() Element of REAL
p19999 * (p + (z1 * p2)) is Element of the U1 of CS
K138( the Mult of CS,p19999,(p + (z1 * p2))) is set
K4(p19999,(p + (z1 * p2))) is set
the Mult of CS . K4(p19999,(p + (z1 * p2))) is set
(r19 * (p + (z1 * p1))) + (p19999 * (p + (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r19 * (p + (z1 * p1))),(p19999 * (p + (z1 * p2)))) is Element of the U1 of CS
K4((r19 * (p + (z1 * p1))),(p19999 * (p + (z1 * p2)))) is set
the U5 of CS . K4((r19 * (p + (z1 * p1))),(p19999 * (p + (z1 * p2)))) is set
r19 + p19999 is V24() V25() Element of REAL
(r19 + p19999) * p is Element of the U1 of CS
K138( the Mult of CS,(r19 + p19999),p) is set
K4((r19 + p19999),p) is set
the Mult of CS . K4((r19 + p19999),p) is set
r19 * z1 is V24() V25() Element of REAL
(r19 * z1) * p1 is Element of the U1 of CS
K138( the Mult of CS,(r19 * z1),p1) is set
K4((r19 * z1),p1) is set
the Mult of CS . K4((r19 * z1),p1) is set
((r19 + p19999) * p) + ((r19 * z1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r19 + p19999) * p),((r19 * z1) * p1)) is Element of the U1 of CS
K4(((r19 + p19999) * p),((r19 * z1) * p1)) is set
the U5 of CS . K4(((r19 + p19999) * p),((r19 * z1) * p1)) is set
p19999 * z1 is V24() V25() Element of REAL
(p19999 * z1) * p2 is Element of the U1 of CS
K138( the Mult of CS,(p19999 * z1),p2) is set
K4((p19999 * z1),p2) is set
the Mult of CS . K4((p19999 * z1),p2) is set
(((r19 + p19999) * p) + ((r19 * z1) * p1)) + ((p19999 * z1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r19 + p19999) * p) + ((r19 * z1) * p1)),((p19999 * z1) * p2)) is Element of the U1 of CS
K4((((r19 + p19999) * p) + ((r19 * z1) * p1)),((p19999 * z1) * p2)) is set
the U5 of CS . K4((((r19 + p19999) * p) + ((r19 * z1) * p1)),((p19999 * z1) * p2)) is set
q399 is V24() V25() Element of REAL
q399 * (p + (z1 * p1)) is Element of the U1 of CS
K138( the Mult of CS,q399,(p + (z1 * p1))) is set
K4(q399,(p + (z1 * p1))) is set
the Mult of CS . K4(q399,(p + (z1 * p1))) is set
r29 is V24() V25() Element of REAL
r29 * (p + (y * r)) is Element of the U1 of CS
K138( the Mult of CS,r29,(p + (y * r))) is set
K4(r29,(p + (y * r))) is set
the Mult of CS . K4(r29,(p + (y * r))) is set
(q399 * (p + (z1 * p1))) + (r29 * (p + (y * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q399 * (p + (z1 * p1))),(r29 * (p + (y * r)))) is Element of the U1 of CS
K4((q399 * (p + (z1 * p1))),(r29 * (p + (y * r)))) is set
the U5 of CS . K4((q399 * (p + (z1 * p1))),(r29 * (p + (y * r)))) is set
q399 + r29 is V24() V25() Element of REAL
(q399 + r29) * p is Element of the U1 of CS
K138( the Mult of CS,(q399 + r29),p) is set
K4((q399 + r29),p) is set
the Mult of CS . K4((q399 + r29),p) is set
q399 * z1 is V24() V25() Element of REAL
(q399 * z1) * p1 is Element of the U1 of CS
K138( the Mult of CS,(q399 * z1),p1) is set
K4((q399 * z1),p1) is set
the Mult of CS . K4((q399 * z1),p1) is set
((q399 + r29) * p) + ((q399 * z1) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q399 + r29) * p),((q399 * z1) * p1)) is Element of the U1 of CS
K4(((q399 + r29) * p),((q399 * z1) * p1)) is set
the U5 of CS . K4(((q399 + r29) * p),((q399 * z1) * p1)) is set
r29 * y is V24() V25() Element of REAL
(r29 * y) * r is Element of the U1 of CS
K138( the Mult of CS,(r29 * y),r) is set
K4((r29 * y),r) is set
the Mult of CS . K4((r29 * y),r) is set
(((q399 + r29) * p) + ((q399 * z1) * p1)) + ((r29 * y) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q399 + r29) * p) + ((q399 * z1) * p1)),((r29 * y) * r)) is Element of the U1 of CS
K4((((q399 + r29) * p) + ((q399 * z1) * p1)),((r29 * y) * r)) is set
the U5 of CS . K4((((q399 + r29) * p) + ((q399 * z1) * p1)),((r29 * y) * r)) is set
0 * p is Element of the U1 of CS
K138( the Mult of CS,0,p) is set
K4(0,p) is set
the Mult of CS . K4(0,p) is set
(0 * p) + (o9 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p),(o9 * p1)) is Element of the U1 of CS
K4((0 * p),(o9 * p1)) is set
the U5 of CS . K4((0 * p),(o9 * p1)) is set
((0 * p) + (o9 * p1)) + (p19 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * p) + (o9 * p1)),(p19 * p2)) is Element of the U1 of CS
K4(((0 * p) + (o9 * p1)),(p19 * p2)) is set
the U5 of CS . K4(((0 * p) + (o9 * p1)),(p19 * p2)) is set
(0 * p) + (p29 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p),(p29 * p2)) is Element of the U1 of CS
K4((0 * p),(p29 * p2)) is set
the U5 of CS . K4((0 * p),(p29 * p2)) is set
((0 * p) + (p29 * p2)) + (q1999 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * p) + (p29 * p2)),(q1999 * r)) is Element of the U1 of CS
K4(((0 * p) + (p29 * p2)),(q1999 * r)) is set
the U5 of CS . K4(((0 * p) + (p29 * p2)),(q1999 * r)) is set
(0 * p) + (p29999 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p),(p29999 * p1)) is Element of the U1 of CS
K4((0 * p),(p29999 * p1)) is set
the U5 of CS . K4((0 * p),(p29999 * p1)) is set
((0 * p) + (p29999 * p1)) + (q3999 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * p) + (p29999 * p1)),(q3999 * r)) is Element of the U1 of CS
K4(((0 * p) + (p29999 * p1)),(q3999 * r)) is set
the U5 of CS . K4(((0 * p) + (p29999 * p1)),(q3999 * r)) is set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
(z1 * p2) - (y * r) is Element of the U1 of CS
- (y * r) is Element of the U1 of CS
K176(CS,(z1 * p2),(- (y * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p2),(- (y * r))) is Element of the U1 of CS
K4((z1 * p2),(- (y * r))) is set
the U5 of CS . K4((z1 * p2),(- (y * r))) is set
(z1 * p1) - (y * r) is Element of the U1 of CS
K176(CS,(z1 * p1),(- (y * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p1),(- (y * r))) is Element of the U1 of CS
K4((z1 * p1),(- (y * r))) is set
the U5 of CS . K4((z1 * p1),(- (y * r))) is set
(z1 * p1) - (z1 * p2) is Element of the U1 of CS
- (z1 * p2) is Element of the U1 of CS
K176(CS,(z1 * p1),(- (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p1),(- (z1 * p2))) is Element of the U1 of CS
K4((z1 * p1),(- (z1 * p2))) is set
the U5 of CS . K4((z1 * p1),(- (z1 * p2))) is set
- p2999 is V24() V25() Element of REAL
p2999 * ((z1 * p2) - (y * r)) is Element of the U1 of CS
K138( the Mult of CS,p2999,((z1 * p2) - (y * r))) is set
K4(p2999,((z1 * p2) - (y * r))) is set
the Mult of CS . K4(p2999,((z1 * p2) - (y * r))) is set
- r19 is V24() V25() Element of REAL
r19 * ((z1 * p1) - (z1 * p2)) is Element of the U1 of CS
K138( the Mult of CS,r19,((z1 * p1) - (z1 * p2))) is set
K4(r19,((z1 * p1) - (z1 * p2))) is set
the Mult of CS . K4(r19,((z1 * p1) - (z1 * p2))) is set
- q399 is V24() V25() Element of REAL
q399 * ((z1 * p1) - (y * r)) is Element of the U1 of CS
K138( the Mult of CS,q399,((z1 * p1) - (y * r))) is set
K4(q399,((z1 * p1) - (y * r))) is set
the Mult of CS . K4(q399,((z1 * p1) - (y * r))) is set
1 * ((z1 * p2) - (y * r)) is Element of the U1 of CS
K138( the Mult of CS,1,((z1 * p2) - (y * r))) is set
K4(1,((z1 * p2) - (y * r))) is set
the Mult of CS . K4(1,((z1 * p2) - (y * r))) is set
(- 1) * ((z1 * p1) - (y * r)) is Element of the U1 of CS
K138( the Mult of CS,(- 1),((z1 * p1) - (y * r))) is set
K4((- 1),((z1 * p1) - (y * r))) is set
the Mult of CS . K4((- 1),((z1 * p1) - (y * r))) is set
(1 * ((z1 * p2) - (y * r))) + ((- 1) * ((z1 * p1) - (y * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * ((z1 * p2) - (y * r))),((- 1) * ((z1 * p1) - (y * r)))) is Element of the U1 of CS
K4((1 * ((z1 * p2) - (y * r))),((- 1) * ((z1 * p1) - (y * r)))) is set
the U5 of CS . K4((1 * ((z1 * p2) - (y * r))),((- 1) * ((z1 * p1) - (y * r)))) is set
1 * ((z1 * p1) - (z1 * p2)) is Element of the U1 of CS
K138( the Mult of CS,1,((z1 * p1) - (z1 * p2))) is set
K4(1,((z1 * p1) - (z1 * p2))) is set
the Mult of CS . K4(1,((z1 * p1) - (z1 * p2))) is set
((1 * ((z1 * p2) - (y * r))) + ((- 1) * ((z1 * p1) - (y * r)))) + (1 * ((z1 * p1) - (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((1 * ((z1 * p2) - (y * r))) + ((- 1) * ((z1 * p1) - (y * r)))),(1 * ((z1 * p1) - (z1 * p2)))) is Element of the U1 of CS
K4(((1 * ((z1 * p2) - (y * r))) + ((- 1) * ((z1 * p1) - (y * r)))),(1 * ((z1 * p1) - (z1 * p2)))) is set
the U5 of CS . K4(((1 * ((z1 * p2) - (y * r))) + ((- 1) * ((z1 * p1) - (y * r)))),(1 * ((z1 * p1) - (z1 * p2)))) is set
((z1 * p2) - (y * r)) + ((- 1) * ((z1 * p1) - (y * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p2) - (y * r)),((- 1) * ((z1 * p1) - (y * r)))) is Element of the U1 of CS
K4(((z1 * p2) - (y * r)),((- 1) * ((z1 * p1) - (y * r)))) is set
the U5 of CS . K4(((z1 * p2) - (y * r)),((- 1) * ((z1 * p1) - (y * r)))) is set
(((z1 * p2) - (y * r)) + ((- 1) * ((z1 * p1) - (y * r)))) + (1 * ((z1 * p1) - (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p2) - (y * r)) + ((- 1) * ((z1 * p1) - (y * r)))),(1 * ((z1 * p1) - (z1 * p2)))) is Element of the U1 of CS
K4((((z1 * p2) - (y * r)) + ((- 1) * ((z1 * p1) - (y * r)))),(1 * ((z1 * p1) - (z1 * p2)))) is set
the U5 of CS . K4((((z1 * p2) - (y * r)) + ((- 1) * ((z1 * p1) - (y * r)))),(1 * ((z1 * p1) - (z1 * p2)))) is set
(((z1 * p2) - (y * r)) + ((- 1) * ((z1 * p1) - (y * r)))) + ((z1 * p1) - (z1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p2) - (y * r)) + ((- 1) * ((z1 * p1) - (y * r)))),((z1 * p1) - (z1 * p2))) is Element of the U1 of CS
K4((((z1 * p2) - (y * r)) + ((- 1) * ((z1 * p1) - (y * r)))),((z1 * p1) - (z1 * p2))) is set
the U5 of CS . K4((((z1 * p2) - (y * r)) + ((- 1) * ((z1 * p1) - (y * r)))),((z1 * p1) - (z1 * p2))) is set
- ((z1 * p1) - (y * r)) is Element of the U1 of CS
((z1 * p2) - (y * r)) + (- ((z1 * p1) - (y * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p2) - (y * r)),(- ((z1 * p1) - (y * r)))) is Element of the U1 of CS
K4(((z1 * p2) - (y * r)),(- ((z1 * p1) - (y * r)))) is set
the U5 of CS . K4(((z1 * p2) - (y * r)),(- ((z1 * p1) - (y * r)))) is set
(((z1 * p2) - (y * r)) + (- ((z1 * p1) - (y * r)))) + ((z1 * p1) - (z1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p2) - (y * r)) + (- ((z1 * p1) - (y * r)))),((z1 * p1) - (z1 * p2))) is Element of the U1 of CS
K4((((z1 * p2) - (y * r)) + (- ((z1 * p1) - (y * r)))),((z1 * p1) - (z1 * p2))) is set
the U5 of CS . K4((((z1 * p2) - (y * r)) + (- ((z1 * p1) - (y * r)))),((z1 * p1) - (z1 * p2))) is set
(z1 * p2) + (- (y * r)) is Element of the U1 of CS
- (z1 * p1) is Element of the U1 of CS
(y * r) + (- (z1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(y * r),(- (z1 * p1))) is Element of the U1 of CS
K4((y * r),(- (z1 * p1))) is set
the U5 of CS . K4((y * r),(- (z1 * p1))) is set
((z1 * p2) + (- (y * r))) + ((y * r) + (- (z1 * p1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p2) + (- (y * r))),((y * r) + (- (z1 * p1)))) is Element of the U1 of CS
K4(((z1 * p2) + (- (y * r))),((y * r) + (- (z1 * p1)))) is set
the U5 of CS . K4(((z1 * p2) + (- (y * r))),((y * r) + (- (z1 * p1)))) is set
(((z1 * p2) + (- (y * r))) + ((y * r) + (- (z1 * p1)))) + ((z1 * p1) - (z1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p2) + (- (y * r))) + ((y * r) + (- (z1 * p1)))),((z1 * p1) - (z1 * p2))) is Element of the U1 of CS
K4((((z1 * p2) + (- (y * r))) + ((y * r) + (- (z1 * p1)))),((z1 * p1) - (z1 * p2))) is set
the U5 of CS . K4((((z1 * p2) + (- (y * r))) + ((y * r) + (- (z1 * p1)))),((z1 * p1) - (z1 * p2))) is set
((z1 * p2) + (- (y * r))) + (y * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p2) + (- (y * r))),(y * r)) is Element of the U1 of CS
K4(((z1 * p2) + (- (y * r))),(y * r)) is set
the U5 of CS . K4(((z1 * p2) + (- (y * r))),(y * r)) is set
(((z1 * p2) + (- (y * r))) + (y * r)) + (- (z1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p2) + (- (y * r))) + (y * r)),(- (z1 * p1))) is Element of the U1 of CS
K4((((z1 * p2) + (- (y * r))) + (y * r)),(- (z1 * p1))) is set
the U5 of CS . K4((((z1 * p2) + (- (y * r))) + (y * r)),(- (z1 * p1))) is set
(z1 * p1) + (- (z1 * p2)) is Element of the U1 of CS
((((z1 * p2) + (- (y * r))) + (y * r)) + (- (z1 * p1))) + ((z1 * p1) + (- (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((z1 * p2) + (- (y * r))) + (y * r)) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is Element of the U1 of CS
K4(((((z1 * p2) + (- (y * r))) + (y * r)) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is set
the U5 of CS . K4(((((z1 * p2) + (- (y * r))) + (y * r)) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is set
(- (y * r)) + (y * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(- (y * r)),(y * r)) is Element of the U1 of CS
K4((- (y * r)),(y * r)) is set
the U5 of CS . K4((- (y * r)),(y * r)) is set
(z1 * p2) + ((- (y * r)) + (y * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p2),((- (y * r)) + (y * r))) is Element of the U1 of CS
K4((z1 * p2),((- (y * r)) + (y * r))) is set
the U5 of CS . K4((z1 * p2),((- (y * r)) + (y * r))) is set
((z1 * p2) + ((- (y * r)) + (y * r))) + (- (z1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p2) + ((- (y * r)) + (y * r))),(- (z1 * p1))) is Element of the U1 of CS
K4(((z1 * p2) + ((- (y * r)) + (y * r))),(- (z1 * p1))) is set
the U5 of CS . K4(((z1 * p2) + ((- (y * r)) + (y * r))),(- (z1 * p1))) is set
(((z1 * p2) + ((- (y * r)) + (y * r))) + (- (z1 * p1))) + ((z1 * p1) + (- (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p2) + ((- (y * r)) + (y * r))) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is Element of the U1 of CS
K4((((z1 * p2) + ((- (y * r)) + (y * r))) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is set
the U5 of CS . K4((((z1 * p2) + ((- (y * r)) + (y * r))) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
(z1 * p2) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p2),(0. CS)) is Element of the U1 of CS
K4((z1 * p2),(0. CS)) is set
the U5 of CS . K4((z1 * p2),(0. CS)) is set
((z1 * p2) + (0. CS)) + (- (z1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p2) + (0. CS)),(- (z1 * p1))) is Element of the U1 of CS
K4(((z1 * p2) + (0. CS)),(- (z1 * p1))) is set
the U5 of CS . K4(((z1 * p2) + (0. CS)),(- (z1 * p1))) is set
(((z1 * p2) + (0. CS)) + (- (z1 * p1))) + ((z1 * p1) + (- (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((z1 * p2) + (0. CS)) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is Element of the U1 of CS
K4((((z1 * p2) + (0. CS)) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is set
the U5 of CS . K4((((z1 * p2) + (0. CS)) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is set
(z1 * p2) + (- (z1 * p1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p2),(- (z1 * p1))) is Element of the U1 of CS
K4((z1 * p2),(- (z1 * p1))) is set
the U5 of CS . K4((z1 * p2),(- (z1 * p1))) is set
((z1 * p2) + (- (z1 * p1))) + ((z1 * p1) + (- (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z1 * p2) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is Element of the U1 of CS
K4(((z1 * p2) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is set
the U5 of CS . K4(((z1 * p2) + (- (z1 * p1))),((z1 * p1) + (- (z1 * p2)))) is set
(- (z1 * p1)) + ((z1 * p1) + (- (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(- (z1 * p1)),((z1 * p1) + (- (z1 * p2)))) is Element of the U1 of CS
K4((- (z1 * p1)),((z1 * p1) + (- (z1 * p2)))) is set
the U5 of CS . K4((- (z1 * p1)),((z1 * p1) + (- (z1 * p2)))) is set
(z1 * p2) + ((- (z1 * p1)) + ((z1 * p1) + (- (z1 * p2)))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p2),((- (z1 * p1)) + ((z1 * p1) + (- (z1 * p2))))) is Element of the U1 of CS
K4((z1 * p2),((- (z1 * p1)) + ((z1 * p1) + (- (z1 * p2))))) is set
the U5 of CS . K4((z1 * p2),((- (z1 * p1)) + ((z1 * p1) + (- (z1 * p2))))) is set
(- (z1 * p1)) + (z1 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(- (z1 * p1)),(z1 * p1)) is Element of the U1 of CS
K4((- (z1 * p1)),(z1 * p1)) is set
the U5 of CS . K4((- (z1 * p1)),(z1 * p1)) is set
((- (z1 * p1)) + (z1 * p1)) + (- (z1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((- (z1 * p1)) + (z1 * p1)),(- (z1 * p2))) is Element of the U1 of CS
K4(((- (z1 * p1)) + (z1 * p1)),(- (z1 * p2))) is set
the U5 of CS . K4(((- (z1 * p1)) + (z1 * p1)),(- (z1 * p2))) is set
(z1 * p2) + (((- (z1 * p1)) + (z1 * p1)) + (- (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p2),(((- (z1 * p1)) + (z1 * p1)) + (- (z1 * p2)))) is Element of the U1 of CS
K4((z1 * p2),(((- (z1 * p1)) + (z1 * p1)) + (- (z1 * p2)))) is set
the U5 of CS . K4((z1 * p2),(((- (z1 * p1)) + (z1 * p1)) + (- (z1 * p2)))) is set
(0. CS) + (- (z1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(- (z1 * p2))) is Element of the U1 of CS
K4((0. CS),(- (z1 * p2))) is set
the U5 of CS . K4((0. CS),(- (z1 * p2))) is set
(z1 * p2) + ((0. CS) + (- (z1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p2),((0. CS) + (- (z1 * p2)))) is Element of the U1 of CS
K4((z1 * p2),((0. CS) + (- (z1 * p2)))) is set
the U5 of CS . K4((z1 * p2),((0. CS) + (- (z1 * p2)))) is set
(z1 * p2) + (- (z1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z1 * p2),(- (z1 * p2))) is Element of the U1 of CS
K4((z1 * p2),(- (z1 * p2))) is set
the U5 of CS . K4((z1 * p2),(- (z1 * p2))) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is V24() V25() Element of REAL
p2 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p2,p) is set
K4(p2,p) is set
the Mult of CS . K4(p2,p) is set
1 * p1 is Element of the U1 of CS
K138( the Mult of CS,1,p1) is set
K4(1,p1) is set
the Mult of CS . K4(1,p1) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is V24() V25() Element of REAL
r * p1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,r,p1) is set
K4(r,p1) is set
the Mult of CS . K4(r,p1) is set
r1 is V24() V25() Element of REAL
r1 * p2 is Element of the U1 of CS
K138( the Mult of CS,r1,p2) is set
K4(r1,p2) is set
the Mult of CS . K4(r1,p2) is set
r1 * r is V24() V25() Element of REAL
(r1 * r) * p1 is Element of the U1 of CS
K138( the Mult of CS,(r1 * r),p1) is set
K4((r1 * r),p1) is set
the Mult of CS . K4((r1 * r),p1) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is V24() V25() Element of REAL
p * p1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p,p1) is set
K4(p,p1) is set
the Mult of CS . K4(p,p1) is set
p1 is V24() V25() Element of REAL
p1 * p2 is Element of the U1 of CS
K138( the Mult of CS,p1,p2) is set
K4(p1,p2) is set
the Mult of CS . K4(p1,p2) is set
(p * p1) + (p1 * p2) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(p * p1),(p1 * p2)) is Element of the U1 of CS
K4((p * p1),(p1 * p2)) is set
the U5 of CS . K4((p * p1),(p1 * p2)) is set
p1 * r is Element of the U1 of CS
K138( the Mult of CS,p1,r) is set
K4(p1,r) is set
the Mult of CS . K4(p1,r) is set
(p1 * r) + (p * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p1 * r),(p * p1)) is Element of the U1 of CS
K4((p1 * r),(p * p1)) is set
the U5 of CS . K4((p1 * r),(p * p1)) is set
q is V24() V25() Element of REAL
q * r1 is Element of the U1 of CS
K138( the Mult of CS,q,r1) is set
K4(q,r1) is set
the Mult of CS . K4(q,r1) is set
r + (q * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,(q * r1)) is Element of the U1 of CS
K4(r,(q * r1)) is set
the U5 of CS . K4(r,(q * r1)) is set
p1 * q is V24() V25() Element of REAL
(p1 * q) * r1 is Element of the U1 of CS
K138( the Mult of CS,(p1 * q),r1) is set
K4((p1 * q),r1) is set
the Mult of CS . K4((p1 * q),r1) is set
((p1 * r) + (p * p1)) + ((p1 * q) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p1 * r) + (p * p1)),((p1 * q) * r1)) is Element of the U1 of CS
K4(((p1 * r) + (p * p1)),((p1 * q) * r1)) is set
the U5 of CS . K4(((p1 * r) + (p * p1)),((p1 * q) * r1)) is set
p1 * (q * r1) is Element of the U1 of CS
K138( the Mult of CS,p1,(q * r1)) is set
K4(p1,(q * r1)) is set
the Mult of CS . K4(p1,(q * r1)) is set
(p1 * r) + (p1 * (q * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p1 * r),(p1 * (q * r1))) is Element of the U1 of CS
K4((p1 * r),(p1 * (q * r1))) is set
the U5 of CS . K4((p1 * r),(p1 * (q * r1))) is set
(p * p1) + ((p1 * r) + (p1 * (q * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p * p1),((p1 * r) + (p1 * (q * r1)))) is Element of the U1 of CS
K4((p * p1),((p1 * r) + (p1 * (q * r1)))) is set
the U5 of CS . K4((p * p1),((p1 * r) + (p1 * (q * r1)))) is set
(p * p1) + (p1 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p * p1),(p1 * r)) is Element of the U1 of CS
K4((p * p1),(p1 * r)) is set
the U5 of CS . K4((p * p1),(p1 * r)) is set
((p * p1) + (p1 * r)) + (p1 * (q * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p * p1) + (p1 * r)),(p1 * (q * r1))) is Element of the U1 of CS
K4(((p * p1) + (p1 * r)),(p1 * (q * r1))) is set
the U5 of CS . K4(((p * p1) + (p1 * r)),(p1 * (q * r1))) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is V24() V25() Element of REAL
p * p1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p,p1) is set
K4(p,p1) is set
the Mult of CS . K4(p,p1) is set
p1 is V24() V25() Element of REAL
p1 * p2 is Element of the U1 of CS
K138( the Mult of CS,p1,p2) is set
K4(p1,p2) is set
the Mult of CS . K4(p1,p2) is set
(p * p1) + (p1 * p2) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(p * p1),(p1 * p2)) is Element of the U1 of CS
K4((p * p1),(p1 * p2)) is set
the U5 of CS . K4((p * p1),(p1 * p2)) is set
p1 * r is Element of the U1 of CS
K138( the Mult of CS,p1,r) is set
K4(p1,r) is set
the Mult of CS . K4(p1,r) is set
q is V24() V25() Element of REAL
q * r1 is Element of the U1 of CS
K138( the Mult of CS,q,r1) is set
K4(q,r1) is set
the Mult of CS . K4(q,r1) is set
r + (q * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,(q * r1)) is Element of the U1 of CS
K4(r,(q * r1)) is set
the U5 of CS . K4(r,(q * r1)) is set
p1 * q is V24() V25() Element of REAL
(p1 * q) * r1 is Element of the U1 of CS
K138( the Mult of CS,(p1 * q),r1) is set
K4((p1 * q),r1) is set
the Mult of CS . K4((p1 * q),r1) is set
(p1 * r) + ((p1 * q) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p1 * r),((p1 * q) * r1)) is Element of the U1 of CS
K4((p1 * r),((p1 * q) * r1)) is set
the U5 of CS . K4((p1 * r),((p1 * q) * r1)) is set
((p1 * r) + ((p1 * q) * r1)) + (p * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p1 * r) + ((p1 * q) * r1)),(p * p1)) is Element of the U1 of CS
K4(((p1 * r) + ((p1 * q) * r1)),(p * p1)) is set
the U5 of CS . K4(((p1 * r) + ((p1 * q) * r1)),(p * p1)) is set
(p1 * r) + (p * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p1 * r),(p * p1)) is Element of the U1 of CS
K4((p1 * r),(p * p1)) is set
the U5 of CS . K4((p1 * r),(p * p1)) is set
((p1 * r) + (p * p1)) + ((p1 * q) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p1 * r) + (p * p1)),((p1 * q) * r1)) is Element of the U1 of CS
K4(((p1 * r) + (p * p1)),((p1 * q) * r1)) is set
the U5 of CS . K4(((p1 * r) + (p * p1)),((p1 * q) * r1)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is V24() V25() Element of REAL
p2 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p2,p) is set
K4(p2,p) is set
the Mult of CS . K4(p2,p) is set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is V24() V25() Element of REAL
r1 * p1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,r1,p1) is set
K4(r1,p1) is set
the Mult of CS . K4(r1,p1) is set
p is V24() V25() Element of REAL
p * p is Element of the U1 of CS
K138( the Mult of CS,p,p) is set
K4(p,p) is set
the Mult of CS . K4(p,p) is set
p1 is V24() V25() Element of REAL
p1 * p2 is Element of the U1 of CS
K138( the Mult of CS,p1,p2) is set
K4(p1,p2) is set
the Mult of CS . K4(p1,p2) is set
p1 * r1 is V24() V25() Element of REAL
(p1 * r1) * p1 is Element of the U1 of CS
K138( the Mult of CS,(p1 * r1),p1) is set
K4((p1 * r1),p1) is set
the Mult of CS . K4((p1 * r1),p1) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is Element of the U1 of CS
p1 is V24() V25() Element of REAL
p1 * r1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p1,r1) is set
K4(p1,r1) is set
the Mult of CS . K4(p1,r1) is set
r + (p1 * r1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,r,(p1 * r1)) is Element of the U1 of CS
K4(r,(p1 * r1)) is set
the U5 of CS . K4(r,(p1 * r1)) is set
q is V24() V25() Element of REAL
q * p is Element of the U1 of CS
K138( the Mult of CS,q,p) is set
K4(q,p) is set
the Mult of CS . K4(q,p) is set
r + (q * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,(q * p)) is Element of the U1 of CS
K4(r,(q * p)) is set
the U5 of CS . K4(r,(q * p)) is set
q1 is V24() V25() Element of REAL
q1 * p1 is Element of the U1 of CS
K138( the Mult of CS,q1,p1) is set
K4(q1,p1) is set
the Mult of CS . K4(q1,p1) is set
r is V24() V25() Element of REAL
r * p2 is Element of the U1 of CS
K138( the Mult of CS,r,p2) is set
K4(r,p2) is set
the Mult of CS . K4(r,p2) is set
(q1 * p1) + (r * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q1 * p1),(r * p2)) is Element of the U1 of CS
K4((q1 * p1),(r * p2)) is set
the U5 of CS . K4((q1 * p1),(r * p2)) is set
q1 + r is V24() V25() Element of REAL
(q1 + r) * r is Element of the U1 of CS
K138( the Mult of CS,(q1 + r),r) is set
K4((q1 + r),r) is set
the Mult of CS . K4((q1 + r),r) is set
q1 * p1 is V24() V25() Element of REAL
(q1 * p1) * r1 is Element of the U1 of CS
K138( the Mult of CS,(q1 * p1),r1) is set
K4((q1 * p1),r1) is set
the Mult of CS . K4((q1 * p1),r1) is set
((q1 + r) * r) + ((q1 * p1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 + r) * r),((q1 * p1) * r1)) is Element of the U1 of CS
K4(((q1 + r) * r),((q1 * p1) * r1)) is set
the U5 of CS . K4(((q1 + r) * r),((q1 * p1) * r1)) is set
r * q is V24() V25() Element of REAL
(r * q) * p is Element of the U1 of CS
K138( the Mult of CS,(r * q),p) is set
K4((r * q),p) is set
the Mult of CS . K4((r * q),p) is set
(((q1 + r) * r) + ((q1 * p1) * r1)) + ((r * q) * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q1 + r) * r) + ((q1 * p1) * r1)),((r * q) * p)) is Element of the U1 of CS
K4((((q1 + r) * r) + ((q1 * p1) * r1)),((r * q) * p)) is set
the U5 of CS . K4((((q1 + r) * r) + ((q1 * p1) * r1)),((r * q) * p)) is set
q1 * r is Element of the U1 of CS
K138( the Mult of CS,q1,r) is set
K4(q1,r) is set
the Mult of CS . K4(q1,r) is set
q1 * (p1 * r1) is Element of the U1 of CS
K138( the Mult of CS,q1,(p1 * r1)) is set
K4(q1,(p1 * r1)) is set
the Mult of CS . K4(q1,(p1 * r1)) is set
(q1 * r) + (q1 * (p1 * r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q1 * r),(q1 * (p1 * r1))) is Element of the U1 of CS
K4((q1 * r),(q1 * (p1 * r1))) is set
the U5 of CS . K4((q1 * r),(q1 * (p1 * r1))) is set
r * (r + (q * p)) is Element of the U1 of CS
K138( the Mult of CS,r,(r + (q * p))) is set
K4(r,(r + (q * p))) is set
the Mult of CS . K4(r,(r + (q * p))) is set
((q1 * r) + (q1 * (p1 * r1))) + (r * (r + (q * p))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + (q1 * (p1 * r1))),(r * (r + (q * p)))) is Element of the U1 of CS
K4(((q1 * r) + (q1 * (p1 * r1))),(r * (r + (q * p)))) is set
the U5 of CS . K4(((q1 * r) + (q1 * (p1 * r1))),(r * (r + (q * p)))) is set
r * r is Element of the U1 of CS
K138( the Mult of CS,r,r) is set
K4(r,r) is set
the Mult of CS . K4(r,r) is set
r * (q * p) is Element of the U1 of CS
K138( the Mult of CS,r,(q * p)) is set
K4(r,(q * p)) is set
the Mult of CS . K4(r,(q * p)) is set
(r * r) + (r * (q * p)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * r),(r * (q * p))) is Element of the U1 of CS
K4((r * r),(r * (q * p))) is set
the U5 of CS . K4((r * r),(r * (q * p))) is set
((q1 * r) + (q1 * (p1 * r1))) + ((r * r) + (r * (q * p))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + (q1 * (p1 * r1))),((r * r) + (r * (q * p)))) is Element of the U1 of CS
K4(((q1 * r) + (q1 * (p1 * r1))),((r * r) + (r * (q * p)))) is set
the U5 of CS . K4(((q1 * r) + (q1 * (p1 * r1))),((r * r) + (r * (q * p)))) is set
(q1 * r) + ((q1 * p1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q1 * r),((q1 * p1) * r1)) is Element of the U1 of CS
K4((q1 * r),((q1 * p1) * r1)) is set
the U5 of CS . K4((q1 * r),((q1 * p1) * r1)) is set
((q1 * r) + ((q1 * p1) * r1)) + ((r * r) + (r * (q * p))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + ((q1 * p1) * r1)),((r * r) + (r * (q * p)))) is Element of the U1 of CS
K4(((q1 * r) + ((q1 * p1) * r1)),((r * r) + (r * (q * p)))) is set
the U5 of CS . K4(((q1 * r) + ((q1 * p1) * r1)),((r * r) + (r * (q * p)))) is set
(r * r) + ((r * q) * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * r),((r * q) * p)) is Element of the U1 of CS
K4((r * r),((r * q) * p)) is set
the U5 of CS . K4((r * r),((r * q) * p)) is set
((q1 * r) + ((q1 * p1) * r1)) + ((r * r) + ((r * q) * p)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + ((q1 * p1) * r1)),((r * r) + ((r * q) * p))) is Element of the U1 of CS
K4(((q1 * r) + ((q1 * p1) * r1)),((r * r) + ((r * q) * p))) is set
the U5 of CS . K4(((q1 * r) + ((q1 * p1) * r1)),((r * r) + ((r * q) * p))) is set
((q1 * r) + ((q1 * p1) * r1)) + (r * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + ((q1 * p1) * r1)),(r * r)) is Element of the U1 of CS
K4(((q1 * r) + ((q1 * p1) * r1)),(r * r)) is set
the U5 of CS . K4(((q1 * r) + ((q1 * p1) * r1)),(r * r)) is set
(((q1 * r) + ((q1 * p1) * r1)) + (r * r)) + ((r * q) * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q1 * r) + ((q1 * p1) * r1)) + (r * r)),((r * q) * p)) is Element of the U1 of CS
K4((((q1 * r) + ((q1 * p1) * r1)) + (r * r)),((r * q) * p)) is set
the U5 of CS . K4((((q1 * r) + ((q1 * p1) * r1)) + (r * r)),((r * q) * p)) is set
(q1 * r) + (r * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q1 * r),(r * r)) is Element of the U1 of CS
K4((q1 * r),(r * r)) is set
the U5 of CS . K4((q1 * r),(r * r)) is set
((q1 * r) + (r * r)) + ((q1 * p1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 * r) + (r * r)),((q1 * p1) * r1)) is Element of the U1 of CS
K4(((q1 * r) + (r * r)),((q1 * p1) * r1)) is set
the U5 of CS . K4(((q1 * r) + (r * r)),((q1 * p1) * r1)) is set
(((q1 * r) + (r * r)) + ((q1 * p1) * r1)) + ((r * q) * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q1 * r) + (r * r)) + ((q1 * p1) * r1)),((r * q) * p)) is Element of the U1 of CS
K4((((q1 * r) + (r * r)) + ((q1 * p1) * r1)),((r * q) * p)) is set
the U5 of CS . K4((((q1 * r) + (r * r)) + ((q1 * p1) * r1)),((r * q) * p)) is set
CS is V24() V25() Element of REAL
p is V24() V25() Element of REAL
p1 is V24() V25() Element of REAL
p * p1 is V24() V25() Element of REAL
CS * p1 is V24() V25() Element of REAL
(p * p1) - (CS * p1) is V24() V25() Element of REAL
p - CS is V24() V25() Element of REAL
(p - CS) * p1 is V24() V25() Element of REAL
CS is V24() V25() Element of REAL
p is V24() V25() Element of REAL
p1 is V24() V25() Element of REAL
p * p1 is V24() V25() Element of REAL
p2 is V24() V25() Element of REAL
p * p2 is V24() V25() Element of REAL
(p * p1) - (p * p2) is V24() V25() Element of REAL
CS * p2 is V24() V25() Element of REAL
(p * p2) - (CS * p2) is V24() V25() Element of REAL
((p * p2) - (CS * p2)) " is V24() V25() Element of REAL
((p * p1) - (p * p2)) * (((p * p2) - (CS * p2)) ") is V24() V25() Element of REAL
r is V24() V25() Element of REAL
p is V24() V25() Element of REAL
r + p is V24() V25() Element of REAL
r1 is V24() V25() Element of REAL
p1 is V24() V25() Element of REAL
r1 + p1 is V24() V25() Element of REAL
r * CS is V24() V25() Element of REAL
r1 * p is V24() V25() Element of REAL
p * p1 is V24() V25() Element of REAL
p1 * p2 is V24() V25() Element of REAL
(((p * p1) - (p * p2)) * (((p * p2) - (CS * p2)) ")) * p is V24() V25() Element of REAL
r * (p * p2) is V24() V25() Element of REAL
p * (p * p2) is V24() V25() Element of REAL
(r * (p * p2)) + (p * (p * p2)) is V24() V25() Element of REAL
(r1 + p1) * (p * p2) is V24() V25() Element of REAL
r * (CS * p2) is V24() V25() Element of REAL
(r1 * p) * p2 is V24() V25() Element of REAL
p1 * p is V24() V25() Element of REAL
p * (p1 * p) is V24() V25() Element of REAL
(p1 * p2) * p is V24() V25() Element of REAL
p * ((p * p1) - (p * p2)) is V24() V25() Element of REAL
r * ((p * p2) - (CS * p2)) is V24() V25() Element of REAL
((p * p2) - (CS * p2)) * (((p * p2) - (CS * p2)) ") is V24() V25() Element of REAL
r * (((p * p2) - (CS * p2)) * (((p * p2) - (CS * p2)) ")) is V24() V25() Element of REAL
(p * ((p * p1) - (p * p2))) * (((p * p2) - (CS * p2)) ") is V24() V25() Element of REAL
r * 1 is V24() V25() Element of REAL
CS is V24() V25() Element of REAL
p is V24() V25() Element of REAL
p * CS is V24() V25() Element of REAL
p1 is V24() V25() Element of REAL
p1 * CS is V24() V25() Element of REAL
(p1 * CS) - (p * CS) is V24() V25() Element of REAL
((p1 * CS) - (p * CS)) " is V24() V25() Element of REAL
p2 is V24() V25() Element of REAL
p2 * (((p1 * CS) - (p * CS)) ") is V24() V25() Element of REAL
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is V24() V25() Element of REAL
p is V24() V25() Element of REAL
r1 * p is V24() V25() Element of REAL
p1 is V24() V25() Element of REAL
r1 * p1 is V24() V25() Element of REAL
(r1 * p) - (r1 * p1) is V24() V25() Element of REAL
p - p1 is V24() V25() Element of REAL
p1 * p is V24() V25() Element of REAL
q is V24() V25() Element of REAL
q * p1 is V24() V25() Element of REAL
(r1 * p1) - (q * p1) is V24() V25() Element of REAL
((r1 * p1) - (q * p1)) " is V24() V25() Element of REAL
((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ") is V24() V25() Element of REAL
(r1 * p) - (q * p1) is V24() V25() Element of REAL
((r1 * p) - (q * p1)) * p1 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,((r1 * p) - (q * p1)),p1) is set
K4(((r1 * p) - (q * p1)),p1) is set
the Mult of CS . K4(((r1 * p) - (q * p1)),p1) is set
q * r1 is V24() V25() Element of REAL
(q * r1) * (p - p1) is V24() V25() Element of REAL
((q * r1) * (p - p1)) * p2 is Element of the U1 of CS
K138( the Mult of CS,((q * r1) * (p - p1)),p2) is set
K4(((q * r1) * (p - p1)),p2) is set
the Mult of CS . K4(((q * r1) * (p - p1)),p2) is set
(((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(((r1 * p) - (q * p1)) * p1),(((q * r1) * (p - p1)) * p2)) is Element of the U1 of CS
K4((((r1 * p) - (q * p1)) * p1),(((q * r1) * (p - p1)) * p2)) is set
the U5 of CS . K4((((r1 * p) - (q * p1)) * p1),(((q * r1) * (p - p1)) * p2)) is set
r1 - q is V24() V25() Element of REAL
(p1 * p) * (r1 - q) is V24() V25() Element of REAL
((p1 * p) * (r1 - q)) * r is Element of the U1 of CS
K138( the Mult of CS,((p1 * p) * (r1 - q)),r) is set
K4(((p1 * p) * (r1 - q)),r) is set
the Mult of CS . K4(((p1 * p) * (r1 - q)),r) is set
((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2)) + (((p1 * p) * (r1 - q)) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2)),(((p1 * p) * (r1 - q)) * r)) is Element of the U1 of CS
K4(((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2)),(((p1 * p) * (r1 - q)) * r)) is set
the U5 of CS . K4(((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2)),(((p1 * p) * (r1 - q)) * r)) is set
q1 is V24() V25() Element of REAL
r is V24() V25() Element of REAL
(((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r is V24() V25() Element of REAL
q1 + r is V24() V25() Element of REAL
(q1 + r) * p1 is Element of the U1 of CS
K138( the Mult of CS,(q1 + r),p1) is set
K4((q1 + r),p1) is set
the Mult of CS . K4((q1 + r),p1) is set
q1 * q is V24() V25() Element of REAL
(q1 * q) * p2 is Element of the U1 of CS
K138( the Mult of CS,(q1 * q),p2) is set
K4((q1 * q),p2) is set
the Mult of CS . K4((q1 * q),p2) is set
((q1 + r) * p1) + ((q1 * q) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q1 + r) * p1),((q1 * q) * p2)) is Element of the U1 of CS
K4(((q1 + r) * p1),((q1 * q) * p2)) is set
the U5 of CS . K4(((q1 + r) * p1),((q1 * q) * p2)) is set
r * p is V24() V25() Element of REAL
(r * p) * r is Element of the U1 of CS
K138( the Mult of CS,(r * p),r) is set
K4((r * p),r) is set
the Mult of CS . K4((r * p),r) is set
(((q1 + r) * p1) + ((q1 * q) * p2)) + ((r * p) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q1 + r) * p1) + ((q1 * q) * p2)),((r * p) * r)) is Element of the U1 of CS
K4((((q1 + r) * p1) + ((q1 * q) * p2)),((r * p) * r)) is set
the U5 of CS . K4((((q1 + r) * p1) + ((q1 * q) * p2)),((r * p) * r)) is set
r * (((r1 * p1) - (q * p1)) ") is V24() V25() Element of REAL
(r * (((r1 * p1) - (q * p1)) ")) * (((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2)) + (((p1 * p) * (r1 - q)) * r)) is Element of the U1 of CS
K138( the Mult of CS,(r * (((r1 * p1) - (q * p1)) ")),(((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2)) + (((p1 * p) * (r1 - q)) * r))) is set
K4((r * (((r1 * p1) - (q * p1)) ")),(((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2)) + (((p1 * p) * (r1 - q)) * r))) is set
the Mult of CS . K4((r * (((r1 * p1) - (q * p1)) ")),(((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2)) + (((p1 * p) * (r1 - q)) * r))) is set
r * 1 is V24() V25() Element of REAL
(r * 1) * p is V24() V25() Element of REAL
((r * 1) * p) * r is Element of the U1 of CS
K138( the Mult of CS,((r * 1) * p),r) is set
K4(((r * 1) * p),r) is set
the Mult of CS . K4(((r * 1) * p),r) is set
(((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1)) is V24() V25() Element of REAL
r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1))) is V24() V25() Element of REAL
(r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1)))) * p is V24() V25() Element of REAL
((r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1)))) * p) * r is Element of the U1 of CS
K138( the Mult of CS,((r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1)))) * p),r) is set
K4(((r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1)))) * p),r) is set
the Mult of CS . K4(((r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1)))) * p),r) is set
p * p1 is V24() V25() Element of REAL
(p * p1) * (r1 - q) is V24() V25() Element of REAL
(r * (((r1 * p1) - (q * p1)) ")) * ((p * p1) * (r1 - q)) is V24() V25() Element of REAL
((r * (((r1 * p1) - (q * p1)) ")) * ((p * p1) * (r1 - q))) * r is Element of the U1 of CS
K138( the Mult of CS,((r * (((r1 * p1) - (q * p1)) ")) * ((p * p1) * (r1 - q))),r) is set
K4(((r * (((r1 * p1) - (q * p1)) ")) * ((p * p1) * (r1 - q))),r) is set
the Mult of CS . K4(((r * (((r1 * p1) - (q * p1)) ")) * ((p * p1) * (r1 - q))),r) is set
(r * (((r1 * p1) - (q * p1)) ")) * (((p1 * p) * (r1 - q)) * r) is Element of the U1 of CS
K138( the Mult of CS,(r * (((r1 * p1) - (q * p1)) ")),(((p1 * p) * (r1 - q)) * r)) is set
K4((r * (((r1 * p1) - (q * p1)) ")),(((p1 * p) * (r1 - q)) * r)) is set
the Mult of CS . K4((r * (((r1 * p1) - (q * p1)) ")),(((p1 * p) * (r1 - q)) * r)) is set
((((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r) * q is V24() V25() Element of REAL
(((((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r) * q) * p2 is Element of the U1 of CS
K138( the Mult of CS,(((((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r) * q),p2) is set
K4((((((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r) * q),p2) is set
the Mult of CS . K4((((((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r) * q),p2) is set
(r * (((r1 * p1) - (q * p1)) ")) * ((q * r1) * (p - p1)) is V24() V25() Element of REAL
((r * (((r1 * p1) - (q * p1)) ")) * ((q * r1) * (p - p1))) * p2 is Element of the U1 of CS
K138( the Mult of CS,((r * (((r1 * p1) - (q * p1)) ")) * ((q * r1) * (p - p1))),p2) is set
K4(((r * (((r1 * p1) - (q * p1)) ")) * ((q * r1) * (p - p1))),p2) is set
the Mult of CS . K4(((r * (((r1 * p1) - (q * p1)) ")) * ((q * r1) * (p - p1))),p2) is set
(r * (((r1 * p1) - (q * p1)) ")) * (((q * r1) * (p - p1)) * p2) is Element of the U1 of CS
K138( the Mult of CS,(r * (((r1 * p1) - (q * p1)) ")),(((q * r1) * (p - p1)) * p2)) is set
K4((r * (((r1 * p1) - (q * p1)) ")),(((q * r1) * (p - p1)) * p2)) is set
the Mult of CS . K4((r * (((r1 * p1) - (q * p1)) ")),(((q * r1) * (p - p1)) * p2)) is set
((((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r) + (r * 1) is V24() V25() Element of REAL
(((((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r) + (r * 1)) * p1 is Element of the U1 of CS
K138( the Mult of CS,(((((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r) + (r * 1)),p1) is set
K4((((((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r) + (r * 1)),p1) is set
the Mult of CS . K4((((((r1 * p) - (r1 * p1)) * (((r1 * p1) - (q * p1)) ")) * r) + (r * 1)),p1) is set
((r1 * p) - (r1 * p1)) * (r * (((r1 * p1) - (q * p1)) ")) is V24() V25() Element of REAL
(((r1 * p) - (r1 * p1)) * (r * (((r1 * p1) - (q * p1)) "))) + (r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1)))) is V24() V25() Element of REAL
((((r1 * p) - (r1 * p1)) * (r * (((r1 * p1) - (q * p1)) "))) + (r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1))))) * p1 is Element of the U1 of CS
K138( the Mult of CS,((((r1 * p) - (r1 * p1)) * (r * (((r1 * p1) - (q * p1)) "))) + (r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1))))),p1) is set
K4(((((r1 * p) - (r1 * p1)) * (r * (((r1 * p1) - (q * p1)) "))) + (r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1))))),p1) is set
the Mult of CS . K4(((((r1 * p) - (r1 * p1)) * (r * (((r1 * p1) - (q * p1)) "))) + (r * ((((r1 * p1) - (q * p1)) ") * ((r1 * p1) - (q * p1))))),p1) is set
- (r1 * p1) is V24() V25() Element of REAL
(r1 * p) + (- (r1 * p1)) is V24() V25() Element of REAL
((r1 * p) + (- (r1 * p1))) + (r1 * p1) is V24() V25() Element of REAL
(((r1 * p) + (- (r1 * p1))) + (r1 * p1)) - (q * p1) is V24() V25() Element of REAL
(r * (((r1 * p1) - (q * p1)) ")) * ((((r1 * p) + (- (r1 * p1))) + (r1 * p1)) - (q * p1)) is V24() V25() Element of REAL
((r * (((r1 * p1) - (q * p1)) ")) * ((((r1 * p) + (- (r1 * p1))) + (r1 * p1)) - (q * p1))) * p1 is Element of the U1 of CS
K138( the Mult of CS,((r * (((r1 * p1) - (q * p1)) ")) * ((((r1 * p) + (- (r1 * p1))) + (r1 * p1)) - (q * p1))),p1) is set
K4(((r * (((r1 * p1) - (q * p1)) ")) * ((((r1 * p) + (- (r1 * p1))) + (r1 * p1)) - (q * p1))),p1) is set
the Mult of CS . K4(((r * (((r1 * p1) - (q * p1)) ")) * ((((r1 * p) + (- (r1 * p1))) + (r1 * p1)) - (q * p1))),p1) is set
(r * (((r1 * p1) - (q * p1)) ")) * (((r1 * p) - (q * p1)) * p1) is Element of the U1 of CS
K138( the Mult of CS,(r * (((r1 * p1) - (q * p1)) ")),(((r1 * p) - (q * p1)) * p1)) is set
K4((r * (((r1 * p1) - (q * p1)) ")),(((r1 * p) - (q * p1)) * p1)) is set
the Mult of CS . K4((r * (((r1 * p1) - (q * p1)) ")),(((r1 * p) - (q * p1)) * p1)) is set
(r * (((r1 * p1) - (q * p1)) ")) * ((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2)) is Element of the U1 of CS
K138( the Mult of CS,(r * (((r1 * p1) - (q * p1)) ")),((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2))) is set
K4((r * (((r1 * p1) - (q * p1)) ")),((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2))) is set
the Mult of CS . K4((r * (((r1 * p1) - (q * p1)) ")),((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2))) is set
((r * (((r1 * p1) - (q * p1)) ")) * ((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2))) + ((r * (((r1 * p1) - (q * p1)) ")) * (((p1 * p) * (r1 - q)) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * (((r1 * p1) - (q * p1)) ")) * ((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2))),((r * (((r1 * p1) - (q * p1)) ")) * (((p1 * p) * (r1 - q)) * r))) is Element of the U1 of CS
K4(((r * (((r1 * p1) - (q * p1)) ")) * ((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2))),((r * (((r1 * p1) - (q * p1)) ")) * (((p1 * p) * (r1 - q)) * r))) is set
the U5 of CS . K4(((r * (((r1 * p1) - (q * p1)) ")) * ((((r1 * p) - (q * p1)) * p1) + (((q * r1) * (p - p1)) * p2))),((r * (((r1 * p1) - (q * p1)) ")) * (((p1 * p) * (r1 - q)) * r))) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p + p1 is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,p,p1) is Element of the U1 of CS
K4(p,p1) is set
the U5 of CS . K4(p,p1) is set
p2 is Element of the U1 of CS
(p + p1) + p2 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + p1),p2) is Element of the U1 of CS
K4((p + p1),p2) is set
the U5 of CS . K4((p + p1),p2) is set
r is Element of the U1 of CS
p + r is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,r) is Element of the U1 of CS
K4(p,r) is set
the U5 of CS . K4(p,r) is set
r1 is Element of the U1 of CS
r + r1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,r1) is Element of the U1 of CS
K4(r,r1) is set
the U5 of CS . K4(r,r1) is set
p1 + r1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p1,r1) is Element of the U1 of CS
K4(p1,r1) is set
the U5 of CS . K4(p1,r1) is set
(p + r) + (p1 + r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + r),(p1 + r1)) is Element of the U1 of CS
K4((p + r),(p1 + r1)) is set
the U5 of CS . K4((p + r),(p1 + r1)) is set
p is Element of the U1 of CS
(r + r1) + p is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + r1),p) is Element of the U1 of CS
K4((r + r1),p) is set
the U5 of CS . K4((r + r1),p) is set
((p + p1) + p2) + ((r + r1) + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + p1) + p2),((r + r1) + p)) is Element of the U1 of CS
K4(((p + p1) + p2),((r + r1) + p)) is set
the U5 of CS . K4(((p + p1) + p2),((r + r1) + p)) is set
p2 + p is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p2,p) is Element of the U1 of CS
K4(p2,p) is set
the U5 of CS . K4(p2,p) is set
((p + r) + (p1 + r1)) + (p2 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + r) + (p1 + r1)),(p2 + p)) is Element of the U1 of CS
K4(((p + r) + (p1 + r1)),(p2 + p)) is set
the U5 of CS . K4(((p + r) + (p1 + r1)),(p2 + p)) is set
p + (p1 + r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,(p1 + r1)) is Element of the U1 of CS
K4(p,(p1 + r1)) is set
the U5 of CS . K4(p,(p1 + r1)) is set
r + (p + (p1 + r1)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,(p + (p1 + r1))) is Element of the U1 of CS
K4(r,(p + (p1 + r1))) is set
the U5 of CS . K4(r,(p + (p1 + r1))) is set
(r + (p + (p1 + r1))) + (p2 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + (p + (p1 + r1))),(p2 + p)) is Element of the U1 of CS
K4((r + (p + (p1 + r1))),(p2 + p)) is set
the U5 of CS . K4((r + (p + (p1 + r1))),(p2 + p)) is set
(p + p1) + r1 is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + p1),r1) is Element of the U1 of CS
K4((p + p1),r1) is set
the U5 of CS . K4((p + p1),r1) is set
r + ((p + p1) + r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,r,((p + p1) + r1)) is Element of the U1 of CS
K4(r,((p + p1) + r1)) is set
the U5 of CS . K4(r,((p + p1) + r1)) is set
(r + ((p + p1) + r1)) + (p2 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + ((p + p1) + r1)),(p2 + p)) is Element of the U1 of CS
K4((r + ((p + p1) + r1)),(p2 + p)) is set
the U5 of CS . K4((r + ((p + p1) + r1)),(p2 + p)) is set
(r + r1) + (p + p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + r1),(p + p1)) is Element of the U1 of CS
K4((r + r1),(p + p1)) is set
the U5 of CS . K4((r + r1),(p + p1)) is set
((r + r1) + (p + p1)) + (p2 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r + r1) + (p + p1)),(p2 + p)) is Element of the U1 of CS
K4(((r + r1) + (p + p1)),(p2 + p)) is set
the U5 of CS . K4(((r + r1) + (p + p1)),(p2 + p)) is set
(p + p1) + (p2 + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + p1),(p2 + p)) is Element of the U1 of CS
K4((p + p1),(p2 + p)) is set
the U5 of CS . K4((p + p1),(p2 + p)) is set
(r + r1) + ((p + p1) + (p2 + p)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + r1),((p + p1) + (p2 + p))) is Element of the U1 of CS
K4((r + r1),((p + p1) + (p2 + p))) is set
the U5 of CS . K4((r + r1),((p + p1) + (p2 + p))) is set
((p + p1) + p2) + p is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p + p1) + p2),p) is Element of the U1 of CS
K4(((p + p1) + p2),p) is set
the U5 of CS . K4(((p + p1) + p2),p) is set
(r + r1) + (((p + p1) + p2) + p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r + r1),(((p + p1) + p2) + p)) is Element of the U1 of CS
K4((r + r1),(((p + p1) + p2) + p)) is set
the U5 of CS . K4((r + r1),(((p + p1) + p2) + p)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
1 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,1,p) is set
K4(1,p) is set
the Mult of CS . K4(1,p) is set
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is Element of the U1 of CS
p1 is V24() V25() Element of REAL
p1 * p2 is Element of the U1 of CS
K138( the Mult of CS,p1,p2) is set
K4(p1,p2) is set
the Mult of CS . K4(p1,p2) is set
p1 + (p1 * p2) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,p1,(p1 * p2)) is Element of the U1 of CS
K4(p1,(p1 * p2)) is set
the U5 of CS . K4(p1,(p1 * p2)) is set
q is V24() V25() Element of REAL
p1 * q is V24() V25() Element of REAL
q * r is Element of the U1 of CS
K138( the Mult of CS,q,r) is set
K4(q,r) is set
the Mult of CS . K4(q,r) is set
(p1 + (p1 * p2)) + (q * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p1 + (p1 * p2)),(q * r)) is Element of the U1 of CS
K4((p1 + (p1 * p2)),(q * r)) is set
the U5 of CS . K4((p1 + (p1 * p2)),(q * r)) is set
q1 is V24() V25() Element of REAL
q1 * p1 is V24() V25() Element of REAL
p1 - q1 is V24() V25() Element of REAL
q1 * p2 is Element of the U1 of CS
K138( the Mult of CS,q1,p2) is set
K4(q1,p2) is set
the Mult of CS . K4(q1,p2) is set
p1 + (q1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p1,(q1 * p2)) is Element of the U1 of CS
K4(p1,(q1 * p2)) is set
the U5 of CS . K4(p1,(q1 * p2)) is set
q1 - p1 is V24() V25() Element of REAL
r is V24() V25() Element of REAL
q1 * r is V24() V25() Element of REAL
(p1 * q) - (q1 * r) is V24() V25() Element of REAL
((p1 * q) - (q1 * r)) * p1 is Element of the U1 of CS
K138( the Mult of CS,((p1 * q) - (q1 * r)),p1) is set
K4(((p1 * q) - (q1 * r)),p1) is set
the Mult of CS . K4(((p1 * q) - (q1 * r)),p1) is set
q - r is V24() V25() Element of REAL
(q1 * p1) * (q - r) is V24() V25() Element of REAL
((q1 * p1) * (q - r)) * p2 is Element of the U1 of CS
K138( the Mult of CS,((q1 * p1) * (q - r)),p2) is set
K4(((q1 * p1) * (q - r)),p2) is set
the Mult of CS . K4(((q1 * p1) * (q - r)),p2) is set
(((p1 * q) - (q1 * r)) * p1) + (((q1 * p1) * (q - r)) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p1 * q) - (q1 * r)) * p1),(((q1 * p1) * (q - r)) * p2)) is Element of the U1 of CS
K4((((p1 * q) - (q1 * r)) * p1),(((q1 * p1) * (q - r)) * p2)) is set
the U5 of CS . K4((((p1 * q) - (q1 * r)) * p1),(((q1 * p1) * (q - r)) * p2)) is set
r * q is V24() V25() Element of REAL
(r * q) * (p1 - q1) is V24() V25() Element of REAL
((r * q) * (p1 - q1)) * r is Element of the U1 of CS
K138( the Mult of CS,((r * q) * (p1 - q1)),r) is set
K4(((r * q) * (p1 - q1)),r) is set
the Mult of CS . K4(((r * q) * (p1 - q1)),r) is set
((((p1 * q) - (q1 * r)) * p1) + (((q1 * p1) * (q - r)) * p2)) + (((r * q) * (p1 - q1)) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((p1 * q) - (q1 * r)) * p1) + (((q1 * p1) * (q - r)) * p2)),(((r * q) * (p1 - q1)) * r)) is Element of the U1 of CS
K4(((((p1 * q) - (q1 * r)) * p1) + (((q1 * p1) * (q - r)) * p2)),(((r * q) * (p1 - q1)) * r)) is set
the U5 of CS . K4(((((p1 * q) - (q1 * r)) * p1) + (((q1 * p1) * (q - r)) * p2)),(((r * q) * (p1 - q1)) * r)) is set
r * r is Element of the U1 of CS
K138( the Mult of CS,r,r) is set
K4(r,r) is set
the Mult of CS . K4(r,r) is set
(p1 + (q1 * p2)) + (r * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p1 + (q1 * p2)),(r * r)) is Element of the U1 of CS
K4((p1 + (q1 * p2)),(r * r)) is set
the U5 of CS . K4((p1 + (q1 * p2)),(r * r)) is set
(q1 * r) - (p1 * q) is V24() V25() Element of REAL
r - q is V24() V25() Element of REAL
(q1 * p1) * (r - q) is V24() V25() Element of REAL
(r * q) * (q1 - p1) is V24() V25() Element of REAL
y is V24() V25() Element of REAL
z2 is V24() V25() Element of REAL
y + z2 is V24() V25() Element of REAL
y * p1 is V24() V25() Element of REAL
z2 * q1 is V24() V25() Element of REAL
(y * p1) + (z2 * q1) is V24() V25() Element of REAL
y * q is V24() V25() Element of REAL
z2 * r is V24() V25() Element of REAL
(y * q) + (z2 * r) is V24() V25() Element of REAL
y * r1 is Element of the U1 of CS
K138( the Mult of CS,y,r1) is set
K4(y,r1) is set
the Mult of CS . K4(y,r1) is set
(1 * p) + (y * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * p),(y * r1)) is Element of the U1 of CS
K4((1 * p),(y * r1)) is set
the U5 of CS . K4((1 * p),(y * r1)) is set
z2 * p is Element of the U1 of CS
K138( the Mult of CS,z2,p) is set
K4(z2,p) is set
the Mult of CS . K4(z2,p) is set
((1 * p) + (y * r1)) + (z2 * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((1 * p) + (y * r1)),(z2 * p)) is Element of the U1 of CS
K4(((1 * p) + (y * r1)),(z2 * p)) is set
the U5 of CS . K4(((1 * p) + (y * r1)),(z2 * p)) is set
p + (y * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,(y * r1)) is Element of the U1 of CS
K4(p,(y * r1)) is set
the U5 of CS . K4(p,(y * r1)) is set
(p + (y * r1)) + (z2 * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + (y * r1)),(z2 * p)) is Element of the U1 of CS
K4((p + (y * r1)),(z2 * p)) is set
the U5 of CS . K4((p + (y * r1)),(z2 * p)) is set
(y * r1) + (z2 * p) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(y * r1),(z2 * p)) is Element of the U1 of CS
K4((y * r1),(z2 * p)) is set
the U5 of CS . K4((y * r1),(z2 * p)) is set
p + ((y * r1) + (z2 * p)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,((y * r1) + (z2 * p))) is Element of the U1 of CS
K4(p,((y * r1) + (z2 * p))) is set
the U5 of CS . K4(p,((y * r1) + (z2 * p))) is set
y * (p1 + (p1 * p2)) is Element of the U1 of CS
K138( the Mult of CS,y,(p1 + (p1 * p2))) is set
K4(y,(p1 + (p1 * p2))) is set
the Mult of CS . K4(y,(p1 + (p1 * p2))) is set
y * (q * r) is Element of the U1 of CS
K138( the Mult of CS,y,(q * r)) is set
K4(y,(q * r)) is set
the Mult of CS . K4(y,(q * r)) is set
(y * (p1 + (p1 * p2))) + (y * (q * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(y * (p1 + (p1 * p2))),(y * (q * r))) is Element of the U1 of CS
K4((y * (p1 + (p1 * p2))),(y * (q * r))) is set
the U5 of CS . K4((y * (p1 + (p1 * p2))),(y * (q * r))) is set
z2 * ((p1 + (q1 * p2)) + (r * r)) is Element of the U1 of CS
K138( the Mult of CS,z2,((p1 + (q1 * p2)) + (r * r))) is set
K4(z2,((p1 + (q1 * p2)) + (r * r))) is set
the Mult of CS . K4(z2,((p1 + (q1 * p2)) + (r * r))) is set
((y * (p1 + (p1 * p2))) + (y * (q * r))) + (z2 * ((p1 + (q1 * p2)) + (r * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y * (p1 + (p1 * p2))) + (y * (q * r))),(z2 * ((p1 + (q1 * p2)) + (r * r)))) is Element of the U1 of CS
K4(((y * (p1 + (p1 * p2))) + (y * (q * r))),(z2 * ((p1 + (q1 * p2)) + (r * r)))) is set
the U5 of CS . K4(((y * (p1 + (p1 * p2))) + (y * (q * r))),(z2 * ((p1 + (q1 * p2)) + (r * r)))) is set
y * p1 is Element of the U1 of CS
K138( the Mult of CS,y,p1) is set
K4(y,p1) is set
the Mult of CS . K4(y,p1) is set
y * (p1 * p2) is Element of the U1 of CS
K138( the Mult of CS,y,(p1 * p2)) is set
K4(y,(p1 * p2)) is set
the Mult of CS . K4(y,(p1 * p2)) is set
(y * p1) + (y * (p1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(y * p1),(y * (p1 * p2))) is Element of the U1 of CS
K4((y * p1),(y * (p1 * p2))) is set
the U5 of CS . K4((y * p1),(y * (p1 * p2))) is set
((y * p1) + (y * (p1 * p2))) + (y * (q * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y * p1) + (y * (p1 * p2))),(y * (q * r))) is Element of the U1 of CS
K4(((y * p1) + (y * (p1 * p2))),(y * (q * r))) is set
the U5 of CS . K4(((y * p1) + (y * (p1 * p2))),(y * (q * r))) is set
(((y * p1) + (y * (p1 * p2))) + (y * (q * r))) + (z2 * ((p1 + (q1 * p2)) + (r * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y * p1) + (y * (p1 * p2))) + (y * (q * r))),(z2 * ((p1 + (q1 * p2)) + (r * r)))) is Element of the U1 of CS
K4((((y * p1) + (y * (p1 * p2))) + (y * (q * r))),(z2 * ((p1 + (q1 * p2)) + (r * r)))) is set
the U5 of CS . K4((((y * p1) + (y * (p1 * p2))) + (y * (q * r))),(z2 * ((p1 + (q1 * p2)) + (r * r)))) is set
z2 * (p1 + (q1 * p2)) is Element of the U1 of CS
K138( the Mult of CS,z2,(p1 + (q1 * p2))) is set
K4(z2,(p1 + (q1 * p2))) is set
the Mult of CS . K4(z2,(p1 + (q1 * p2))) is set
z2 * (r * r) is Element of the U1 of CS
K138( the Mult of CS,z2,(r * r)) is set
K4(z2,(r * r)) is set
the Mult of CS . K4(z2,(r * r)) is set
(z2 * (p1 + (q1 * p2))) + (z2 * (r * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z2 * (p1 + (q1 * p2))),(z2 * (r * r))) is Element of the U1 of CS
K4((z2 * (p1 + (q1 * p2))),(z2 * (r * r))) is set
the U5 of CS . K4((z2 * (p1 + (q1 * p2))),(z2 * (r * r))) is set
(((y * p1) + (y * (p1 * p2))) + (y * (q * r))) + ((z2 * (p1 + (q1 * p2))) + (z2 * (r * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y * p1) + (y * (p1 * p2))) + (y * (q * r))),((z2 * (p1 + (q1 * p2))) + (z2 * (r * r)))) is Element of the U1 of CS
K4((((y * p1) + (y * (p1 * p2))) + (y * (q * r))),((z2 * (p1 + (q1 * p2))) + (z2 * (r * r)))) is set
the U5 of CS . K4((((y * p1) + (y * (p1 * p2))) + (y * (q * r))),((z2 * (p1 + (q1 * p2))) + (z2 * (r * r)))) is set
z2 * p1 is Element of the U1 of CS
K138( the Mult of CS,z2,p1) is set
K4(z2,p1) is set
the Mult of CS . K4(z2,p1) is set
z2 * (q1 * p2) is Element of the U1 of CS
K138( the Mult of CS,z2,(q1 * p2)) is set
K4(z2,(q1 * p2)) is set
the Mult of CS . K4(z2,(q1 * p2)) is set
(z2 * p1) + (z2 * (q1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(z2 * p1),(z2 * (q1 * p2))) is Element of the U1 of CS
K4((z2 * p1),(z2 * (q1 * p2))) is set
the U5 of CS . K4((z2 * p1),(z2 * (q1 * p2))) is set
((z2 * p1) + (z2 * (q1 * p2))) + (z2 * (r * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((z2 * p1) + (z2 * (q1 * p2))),(z2 * (r * r))) is Element of the U1 of CS
K4(((z2 * p1) + (z2 * (q1 * p2))),(z2 * (r * r))) is set
the U5 of CS . K4(((z2 * p1) + (z2 * (q1 * p2))),(z2 * (r * r))) is set
(((y * p1) + (y * (p1 * p2))) + (y * (q * r))) + (((z2 * p1) + (z2 * (q1 * p2))) + (z2 * (r * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y * p1) + (y * (p1 * p2))) + (y * (q * r))),(((z2 * p1) + (z2 * (q1 * p2))) + (z2 * (r * r)))) is Element of the U1 of CS
K4((((y * p1) + (y * (p1 * p2))) + (y * (q * r))),(((z2 * p1) + (z2 * (q1 * p2))) + (z2 * (r * r)))) is set
the U5 of CS . K4((((y * p1) + (y * (p1 * p2))) + (y * (q * r))),(((z2 * p1) + (z2 * (q1 * p2))) + (z2 * (r * r)))) is set
(y * p1) + (z2 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(y * p1),(z2 * p1)) is Element of the U1 of CS
K4((y * p1),(z2 * p1)) is set
the U5 of CS . K4((y * p1),(z2 * p1)) is set
(y * (p1 * p2)) + (z2 * (q1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(y * (p1 * p2)),(z2 * (q1 * p2))) is Element of the U1 of CS
K4((y * (p1 * p2)),(z2 * (q1 * p2))) is set
the U5 of CS . K4((y * (p1 * p2)),(z2 * (q1 * p2))) is set
((y * p1) + (z2 * p1)) + ((y * (p1 * p2)) + (z2 * (q1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y * p1) + (z2 * p1)),((y * (p1 * p2)) + (z2 * (q1 * p2)))) is Element of the U1 of CS
K4(((y * p1) + (z2 * p1)),((y * (p1 * p2)) + (z2 * (q1 * p2)))) is set
the U5 of CS . K4(((y * p1) + (z2 * p1)),((y * (p1 * p2)) + (z2 * (q1 * p2)))) is set
(y * (q * r)) + (z2 * (r * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(y * (q * r)),(z2 * (r * r))) is Element of the U1 of CS
K4((y * (q * r)),(z2 * (r * r))) is set
the U5 of CS . K4((y * (q * r)),(z2 * (r * r))) is set
(((y * p1) + (z2 * p1)) + ((y * (p1 * p2)) + (z2 * (q1 * p2)))) + ((y * (q * r)) + (z2 * (r * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y * p1) + (z2 * p1)) + ((y * (p1 * p2)) + (z2 * (q1 * p2)))),((y * (q * r)) + (z2 * (r * r)))) is Element of the U1 of CS
K4((((y * p1) + (z2 * p1)) + ((y * (p1 * p2)) + (z2 * (q1 * p2)))),((y * (q * r)) + (z2 * (r * r)))) is set
the U5 of CS . K4((((y * p1) + (z2 * p1)) + ((y * (p1 * p2)) + (z2 * (q1 * p2)))),((y * (q * r)) + (z2 * (r * r)))) is set
(y + z2) * p1 is Element of the U1 of CS
K138( the Mult of CS,(y + z2),p1) is set
K4((y + z2),p1) is set
the Mult of CS . K4((y + z2),p1) is set
((y + z2) * p1) + ((y * (p1 * p2)) + (z2 * (q1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y + z2) * p1),((y * (p1 * p2)) + (z2 * (q1 * p2)))) is Element of the U1 of CS
K4(((y + z2) * p1),((y * (p1 * p2)) + (z2 * (q1 * p2)))) is set
the U5 of CS . K4(((y + z2) * p1),((y * (p1 * p2)) + (z2 * (q1 * p2)))) is set
(((y + z2) * p1) + ((y * (p1 * p2)) + (z2 * (q1 * p2)))) + ((y * (q * r)) + (z2 * (r * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y + z2) * p1) + ((y * (p1 * p2)) + (z2 * (q1 * p2)))),((y * (q * r)) + (z2 * (r * r)))) is Element of the U1 of CS
K4((((y + z2) * p1) + ((y * (p1 * p2)) + (z2 * (q1 * p2)))),((y * (q * r)) + (z2 * (r * r)))) is set
the U5 of CS . K4((((y + z2) * p1) + ((y * (p1 * p2)) + (z2 * (q1 * p2)))),((y * (q * r)) + (z2 * (r * r)))) is set
(y * p1) * p2 is Element of the U1 of CS
K138( the Mult of CS,(y * p1),p2) is set
K4((y * p1),p2) is set
the Mult of CS . K4((y * p1),p2) is set
((y * p1) * p2) + (z2 * (q1 * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y * p1) * p2),(z2 * (q1 * p2))) is Element of the U1 of CS
K4(((y * p1) * p2),(z2 * (q1 * p2))) is set
the U5 of CS . K4(((y * p1) * p2),(z2 * (q1 * p2))) is set
((y + z2) * p1) + (((y * p1) * p2) + (z2 * (q1 * p2))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y + z2) * p1),(((y * p1) * p2) + (z2 * (q1 * p2)))) is Element of the U1 of CS
K4(((y + z2) * p1),(((y * p1) * p2) + (z2 * (q1 * p2)))) is set
the U5 of CS . K4(((y + z2) * p1),(((y * p1) * p2) + (z2 * (q1 * p2)))) is set
(((y + z2) * p1) + (((y * p1) * p2) + (z2 * (q1 * p2)))) + ((y * (q * r)) + (z2 * (r * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y + z2) * p1) + (((y * p1) * p2) + (z2 * (q1 * p2)))),((y * (q * r)) + (z2 * (r * r)))) is Element of the U1 of CS
K4((((y + z2) * p1) + (((y * p1) * p2) + (z2 * (q1 * p2)))),((y * (q * r)) + (z2 * (r * r)))) is set
the U5 of CS . K4((((y + z2) * p1) + (((y * p1) * p2) + (z2 * (q1 * p2)))),((y * (q * r)) + (z2 * (r * r)))) is set
(z2 * q1) * p2 is Element of the U1 of CS
K138( the Mult of CS,(z2 * q1),p2) is set
K4((z2 * q1),p2) is set
the Mult of CS . K4((z2 * q1),p2) is set
((y * p1) * p2) + ((z2 * q1) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y * p1) * p2),((z2 * q1) * p2)) is Element of the U1 of CS
K4(((y * p1) * p2),((z2 * q1) * p2)) is set
the U5 of CS . K4(((y * p1) * p2),((z2 * q1) * p2)) is set
((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y + z2) * p1),(((y * p1) * p2) + ((z2 * q1) * p2))) is Element of the U1 of CS
K4(((y + z2) * p1),(((y * p1) * p2) + ((z2 * q1) * p2))) is set
the U5 of CS . K4(((y + z2) * p1),(((y * p1) * p2) + ((z2 * q1) * p2))) is set
(((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))) + ((y * (q * r)) + (z2 * (r * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))),((y * (q * r)) + (z2 * (r * r)))) is Element of the U1 of CS
K4((((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))),((y * (q * r)) + (z2 * (r * r)))) is set
the U5 of CS . K4((((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))),((y * (q * r)) + (z2 * (r * r)))) is set
(y * q) * r is Element of the U1 of CS
K138( the Mult of CS,(y * q),r) is set
K4((y * q),r) is set
the Mult of CS . K4((y * q),r) is set
((y * q) * r) + (z2 * (r * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y * q) * r),(z2 * (r * r))) is Element of the U1 of CS
K4(((y * q) * r),(z2 * (r * r))) is set
the U5 of CS . K4(((y * q) * r),(z2 * (r * r))) is set
(((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))) + (((y * q) * r) + (z2 * (r * r))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))),(((y * q) * r) + (z2 * (r * r)))) is Element of the U1 of CS
K4((((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))),(((y * q) * r) + (z2 * (r * r)))) is set
the U5 of CS . K4((((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))),(((y * q) * r) + (z2 * (r * r)))) is set
(z2 * r) * r is Element of the U1 of CS
K138( the Mult of CS,(z2 * r),r) is set
K4((z2 * r),r) is set
the Mult of CS . K4((z2 * r),r) is set
((y * q) * r) + ((z2 * r) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y * q) * r),((z2 * r) * r)) is Element of the U1 of CS
K4(((y * q) * r),((z2 * r) * r)) is set
the U5 of CS . K4(((y * q) * r),((z2 * r) * r)) is set
(((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))) + (((y * q) * r) + ((z2 * r) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))),(((y * q) * r) + ((z2 * r) * r))) is Element of the U1 of CS
K4((((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))),(((y * q) * r) + ((z2 * r) * r))) is set
the U5 of CS . K4((((y + z2) * p1) + (((y * p1) * p2) + ((z2 * q1) * p2))),(((y * q) * r) + ((z2 * r) * r))) is set
((y * p1) + (z2 * q1)) * p2 is Element of the U1 of CS
K138( the Mult of CS,((y * p1) + (z2 * q1)),p2) is set
K4(((y * p1) + (z2 * q1)),p2) is set
the Mult of CS . K4(((y * p1) + (z2 * q1)),p2) is set
((y + z2) * p1) + (((y * p1) + (z2 * q1)) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((y + z2) * p1),(((y * p1) + (z2 * q1)) * p2)) is Element of the U1 of CS
K4(((y + z2) * p1),(((y * p1) + (z2 * q1)) * p2)) is set
the U5 of CS . K4(((y + z2) * p1),(((y * p1) + (z2 * q1)) * p2)) is set
(((y + z2) * p1) + (((y * p1) + (z2 * q1)) * p2)) + (((y * q) * r) + ((z2 * r) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y + z2) * p1) + (((y * p1) + (z2 * q1)) * p2)),(((y * q) * r) + ((z2 * r) * r))) is Element of the U1 of CS
K4((((y + z2) * p1) + (((y * p1) + (z2 * q1)) * p2)),(((y * q) * r) + ((z2 * r) * r))) is set
the U5 of CS . K4((((y + z2) * p1) + (((y * p1) + (z2 * q1)) * p2)),(((y * q) * r) + ((z2 * r) * r))) is set
((q1 * r) - (p1 * q)) * p1 is Element of the U1 of CS
K138( the Mult of CS,((q1 * r) - (p1 * q)),p1) is set
K4(((q1 * r) - (p1 * q)),p1) is set
the Mult of CS . K4(((q1 * r) - (p1 * q)),p1) is set
((q1 * p1) * (r - q)) * p2 is Element of the U1 of CS
K138( the Mult of CS,((q1 * p1) * (r - q)),p2) is set
K4(((q1 * p1) * (r - q)),p2) is set
the Mult of CS . K4(((q1 * p1) * (r - q)),p2) is set
(((q1 * r) - (p1 * q)) * p1) + (((q1 * p1) * (r - q)) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q1 * r) - (p1 * q)) * p1),(((q1 * p1) * (r - q)) * p2)) is Element of the U1 of CS
K4((((q1 * r) - (p1 * q)) * p1),(((q1 * p1) * (r - q)) * p2)) is set
the U5 of CS . K4((((q1 * r) - (p1 * q)) * p1),(((q1 * p1) * (r - q)) * p2)) is set
((r * q) * (q1 - p1)) * r is Element of the U1 of CS
K138( the Mult of CS,((r * q) * (q1 - p1)),r) is set
K4(((r * q) * (q1 - p1)),r) is set
the Mult of CS . K4(((r * q) * (q1 - p1)),r) is set
((((q1 * r) - (p1 * q)) * p1) + (((q1 * p1) * (r - q)) * p2)) + (((r * q) * (q1 - p1)) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((q1 * r) - (p1 * q)) * p1) + (((q1 * p1) * (r - q)) * p2)),(((r * q) * (q1 - p1)) * r)) is Element of the U1 of CS
K4(((((q1 * r) - (p1 * q)) * p1) + (((q1 * p1) * (r - q)) * p2)),(((r * q) * (q1 - p1)) * r)) is set
the U5 of CS . K4(((((q1 * r) - (p1 * q)) * p1) + (((q1 * p1) * (r - q)) * p2)),(((r * q) * (q1 - p1)) * r)) is set
(((p1 * q) - (q1 * r)) * p1) + (((q1 * r) - (p1 * q)) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((p1 * q) - (q1 * r)) * p1),(((q1 * r) - (p1 * q)) * p1)) is Element of the U1 of CS
K4((((p1 * q) - (q1 * r)) * p1),(((q1 * r) - (p1 * q)) * p1)) is set
the U5 of CS . K4((((p1 * q) - (q1 * r)) * p1),(((q1 * r) - (p1 * q)) * p1)) is set
(((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q1 * p1) * (q - r)) * p2),(((q1 * p1) * (r - q)) * p2)) is Element of the U1 of CS
K4((((q1 * p1) * (q - r)) * p2),(((q1 * p1) * (r - q)) * p2)) is set
the U5 of CS . K4((((q1 * p1) * (q - r)) * p2),(((q1 * p1) * (r - q)) * p2)) is set
((((p1 * q) - (q1 * r)) * p1) + (((q1 * r) - (p1 * q)) * p1)) + ((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((p1 * q) - (q1 * r)) * p1) + (((q1 * r) - (p1 * q)) * p1)),((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))) is Element of the U1 of CS
K4(((((p1 * q) - (q1 * r)) * p1) + (((q1 * r) - (p1 * q)) * p1)),((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))) is set
the U5 of CS . K4(((((p1 * q) - (q1 * r)) * p1) + (((q1 * r) - (p1 * q)) * p1)),((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))) is set
(((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r * q) * (p1 - q1)) * r),(((r * q) * (q1 - p1)) * r)) is Element of the U1 of CS
K4((((r * q) * (p1 - q1)) * r),(((r * q) * (q1 - p1)) * r)) is set
the U5 of CS . K4((((r * q) * (p1 - q1)) * r),(((r * q) * (q1 - p1)) * r)) is set
(((((p1 * q) - (q1 * r)) * p1) + (((q1 * r) - (p1 * q)) * p1)) + ((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))) + ((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((p1 * q) - (q1 * r)) * p1) + (((q1 * r) - (p1 * q)) * p1)) + ((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))),((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r))) is Element of the U1 of CS
K4((((((p1 * q) - (q1 * r)) * p1) + (((q1 * r) - (p1 * q)) * p1)) + ((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))),((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r))) is set
the U5 of CS . K4((((((p1 * q) - (q1 * r)) * p1) + (((q1 * r) - (p1 * q)) * p1)) + ((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))),((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r))) is set
((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q)) is V24() V25() Element of REAL
(((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1 is Element of the U1 of CS
K138( the Mult of CS,(((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))),p1) is set
K4((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))),p1) is set
the Mult of CS . K4((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))),p1) is set
((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1),((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))) is Element of the U1 of CS
K4(((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1),((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))) is set
the U5 of CS . K4(((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1),((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))) is set
(((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))) + ((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))),((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r))) is Element of the U1 of CS
K4((((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))),((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r))) is set
the U5 of CS . K4((((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) * p2) + (((q1 * p1) * (r - q)) * p2))),((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r))) is set
((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q)) is V24() V25() Element of REAL
(((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2 is Element of the U1 of CS
K138( the Mult of CS,(((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))),p2) is set
K4((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))),p2) is set
the Mult of CS . K4((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))),p2) is set
((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1),((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) is Element of the U1 of CS
K4(((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1),((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) is set
the U5 of CS . K4(((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1),((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) is set
(((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) + ((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)),((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r))) is Element of the U1 of CS
K4((((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)),((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r))) is set
the U5 of CS . K4((((((p1 * q) - (q1 * r)) + ((q1 * r) - (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)),((((r * q) * (p1 - q1)) * r) + (((r * q) * (q1 - p1)) * r))) is set
- (q1 * r) is V24() V25() Element of REAL
(p1 * q) + (- (q1 * r)) is V24() V25() Element of REAL
((p1 * q) + (- (q1 * r))) + (q1 * r) is V24() V25() Element of REAL
- (p1 * q) is V24() V25() Element of REAL
(((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q)) is V24() V25() Element of REAL
((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))) * p1 is Element of the U1 of CS
K138( the Mult of CS,((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))),p1) is set
K4(((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))),p1) is set
the Mult of CS . K4(((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))),p1) is set
(((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))) * p1),((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) is Element of the U1 of CS
K4((((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))) * p1),((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) is set
the U5 of CS . K4((((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))) * p1),((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) is set
((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1)) is V24() V25() Element of REAL
(((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))) * r is Element of the U1 of CS
K138( the Mult of CS,(((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))),r) is set
K4((((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))),r) is set
the Mult of CS . K4((((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))),r) is set
((((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) + ((((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)),((((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))) * r)) is Element of the U1 of CS
K4(((((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)),((((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))) * r)) is set
the U5 of CS . K4(((((((p1 * q) + (- (q1 * r))) + (q1 * r)) + (- (p1 * q))) * p1) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)),((((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))) * r)) is set
(0. CS) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) is Element of the U1 of CS
K4((0. CS),((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) is set
the U5 of CS . K4((0. CS),((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) is set
((0. CS) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)) + ((((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0. CS) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)),((((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))) * r)) is Element of the U1 of CS
K4(((0. CS) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)),((((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))) * r)) is set
the U5 of CS . K4(((0. CS) + ((((q1 * p1) * (q - r)) + ((q1 * p1) * (r - q))) * p2)),((((r * q) * (p1 - q1)) + ((r * q) * (q1 - p1))) * r)) is set
0 * p2 is Element of the U1 of CS
K138( the Mult of CS,0,p2) is set
K4(0,p2) is set
the Mult of CS . K4(0,p2) is set
- ((r * q) * (p1 - q1)) is V24() V25() Element of REAL
((r * q) * (p1 - q1)) + (- ((r * q) * (p1 - q1))) is V24() V25() Element of REAL
(((r * q) * (p1 - q1)) + (- ((r * q) * (p1 - q1)))) * r is Element of the U1 of CS
K138( the Mult of CS,(((r * q) * (p1 - q1)) + (- ((r * q) * (p1 - q1)))),r) is set
K4((((r * q) * (p1 - q1)) + (- ((r * q) * (p1 - q1)))),r) is set
the Mult of CS . K4((((r * q) * (p1 - q1)) + (- ((r * q) * (p1 - q1)))),r) is set
(0 * p2) + ((((r * q) * (p1 - q1)) + (- ((r * q) * (p1 - q1)))) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0 * p2),((((r * q) * (p1 - q1)) + (- ((r * q) * (p1 - q1)))) * r)) is Element of the U1 of CS
K4((0 * p2),((((r * q) * (p1 - q1)) + (- ((r * q) * (p1 - q1)))) * r)) is set
the U5 of CS . K4((0 * p2),((((r * q) * (p1 - q1)) + (- ((r * q) * (p1 - q1)))) * r)) is set
0 * r is Element of the U1 of CS
K138( the Mult of CS,0,r) is set
K4(0,r) is set
the Mult of CS . K4(0,r) is set
(0. CS) + (0 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0 * r)) is Element of the U1 of CS
K4((0. CS),(0 * r)) is set
the U5 of CS . K4((0. CS),(0 * r)) is set
(0. CS) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0. CS)) is Element of the U1 of CS
K4((0. CS),(0. CS)) is set
the U5 of CS . K4((0. CS),(0. CS)) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is V24() V25() Element of REAL
p * p2 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,p,p2) is set
K4(p,p2) is set
the Mult of CS . K4(p,p2) is set
p1 + (p * p2) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,p1,(p * p2)) is Element of the U1 of CS
K4(p1,(p * p2)) is set
the U5 of CS . K4(p1,(p * p2)) is set
p1 is V24() V25() Element of REAL
p1 * r is Element of the U1 of CS
K138( the Mult of CS,p1,r) is set
K4(p1,r) is set
the Mult of CS . K4(p1,r) is set
(p1 + (p * p2)) + (p1 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p1 + (p * p2)),(p1 * r)) is Element of the U1 of CS
K4((p1 + (p * p2)),(p1 * r)) is set
the U5 of CS . K4((p1 + (p * p2)),(p1 * r)) is set
r is V24() V25() Element of REAL
r * p1 is Element of the U1 of CS
K138( the Mult of CS,r,p1) is set
K4(r,p1) is set
the Mult of CS . K4(r,p1) is set
q is V24() V25() Element of REAL
q * p2 is Element of the U1 of CS
K138( the Mult of CS,q,p2) is set
K4(q,p2) is set
the Mult of CS . K4(q,p2) is set
(r * p1) + (q * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * p1),(q * p2)) is Element of the U1 of CS
K4((r * p1),(q * p2)) is set
the U5 of CS . K4((r * p1),(q * p2)) is set
r * p1 is V24() V25() Element of REAL
(r * p1) * r is Element of the U1 of CS
K138( the Mult of CS,(r * p1),r) is set
K4((r * p1),r) is set
the Mult of CS . K4((r * p1),r) is set
((r * p1) + (q * p2)) + ((r * p1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p1) + (q * p2)),((r * p1) * r)) is Element of the U1 of CS
K4(((r * p1) + (q * p2)),((r * p1) * r)) is set
the U5 of CS . K4(((r * p1) + (q * p2)),((r * p1) * r)) is set
y is V24() V25() Element of REAL
y * p is V24() V25() Element of REAL
r * p is Element of the U1 of CS
K138( the Mult of CS,r,p) is set
K4(r,p) is set
the Mult of CS . K4(r,p) is set
r * (p * p2) is Element of the U1 of CS
K138( the Mult of CS,r,(p * p2)) is set
K4(r,(p * p2)) is set
the Mult of CS . K4(r,(p * p2)) is set
(r * p1) + (r * (p * p2)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * p1),(r * (p * p2))) is Element of the U1 of CS
K4((r * p1),(r * (p * p2))) is set
the U5 of CS . K4((r * p1),(r * (p * p2))) is set
((r * p1) + (r * (p * p2))) + ((r * p1) * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p1) + (r * (p * p2))),((r * p1) * r)) is Element of the U1 of CS
K4(((r * p1) + (r * (p * p2))),((r * p1) * r)) is set
the U5 of CS . K4(((r * p1) + (r * (p * p2))),((r * p1) * r)) is set
r * (p1 * r) is Element of the U1 of CS
K138( the Mult of CS,r,(p1 * r)) is set
K4(r,(p1 * r)) is set
the Mult of CS . K4(r,(p1 * r)) is set
((r * p1) + (r * (p * p2))) + (r * (p1 * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p1) + (r * (p * p2))),(r * (p1 * r))) is Element of the U1 of CS
K4(((r * p1) + (r * (p * p2))),(r * (p1 * r))) is set
the U5 of CS . K4(((r * p1) + (r * (p * p2))),(r * (p1 * r))) is set
r * (p1 + (p * p2)) is Element of the U1 of CS
K138( the Mult of CS,r,(p1 + (p * p2))) is set
K4(r,(p1 + (p * p2))) is set
the Mult of CS . K4(r,(p1 + (p * p2))) is set
(r * (p1 + (p * p2))) + (r * (p1 * r)) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r * (p1 + (p * p2))),(r * (p1 * r))) is Element of the U1 of CS
K4((r * (p1 + (p * p2))),(r * (p1 * r))) is set
the U5 of CS . K4((r * (p1 + (p * p2))),(r * (p1 * r))) is set
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
q is Element of the U1 of CS
q1 is Element of the U1 of CS
r is Element of the U1 of CS
z2 is V24() V25() Element of REAL
z2 * r is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,z2,r) is set
K4(z2,r) is set
the Mult of CS . K4(z2,r) is set
y is V24() V25() Element of REAL
y * p1 is Element of the U1 of CS
K138( the Mult of CS,y,p1) is set
K4(y,p1) is set
the Mult of CS . K4(y,p1) is set
p + (y * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,p,(y * p1)) is Element of the U1 of CS
K4(p,(y * p1)) is set
the U5 of CS . K4(p,(y * p1)) is set
x2 is V24() V25() Element of REAL
x2 * p1 is Element of the U1 of CS
K138( the Mult of CS,x2,p1) is set
K4(x2,p1) is set
the Mult of CS . K4(x2,p1) is set
z1 is V24() V25() Element of REAL
z1 * r1 is Element of the U1 of CS
K138( the Mult of CS,z1,r1) is set
K4(z1,r1) is set
the Mult of CS . K4(z1,r1) is set
p + (z1 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,(z1 * r1)) is Element of the U1 of CS
K4(p,(z1 * r1)) is set
the U5 of CS . K4(p,(z1 * r1)) is set
z1 is V24() V25() Element of REAL
z1 * p is Element of the U1 of CS
K138( the Mult of CS,z1,p) is set
K4(z1,p) is set
the Mult of CS . K4(z1,p) is set
z1 is V24() V25() Element of REAL
z1 * r1 is Element of the U1 of CS
K138( the Mult of CS,z1,r1) is set
K4(z1,r1) is set
the Mult of CS . K4(z1,r1) is set
p + (z1 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,(z1 * r1)) is Element of the U1 of CS
K4(p,(z1 * r1)) is set
the U5 of CS . K4(p,(z1 * r1)) is set
p199 is V24() V25() Element of REAL
p199 * p2 is Element of the U1 of CS
K138( the Mult of CS,p199,p2) is set
K4(p199,p2) is set
the Mult of CS . K4(p199,p2) is set
z2 is V24() V25() Element of REAL
z2 * p1 is Element of the U1 of CS
K138( the Mult of CS,z2,p1) is set
K4(z2,p1) is set
the Mult of CS . K4(z2,p1) is set
p + (z2 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,p,(z2 * p1)) is Element of the U1 of CS
K4(p,(z2 * p1)) is set
the U5 of CS . K4(p,(z2 * p1)) is set
q1999 is V24() V25() Element of REAL
q1999 * p1 is Element of the U1 of CS
K138( the Mult of CS,q1999,p1) is set
K4(q1999,p1) is set
the Mult of CS . K4(q1999,p1) is set
p2999 is V24() V25() Element of REAL
p2999 * (p + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,p2999,(p + (z1 * r1))) is set
K4(p2999,(p + (z1 * r1))) is set
the Mult of CS . K4(p2999,(p + (z1 * r1))) is set
(q1999 * p1) + (p2999 * (p + (z1 * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q1999 * p1),(p2999 * (p + (z1 * r1)))) is Element of the U1 of CS
K4((q1999 * p1),(p2999 * (p + (z1 * r1)))) is set
the U5 of CS . K4((q1999 * p1),(p2999 * (p + (z1 * r1)))) is set
r399 is V24() V25() Element of REAL
r399 * (p + (z2 * p1)) is Element of the U1 of CS
K138( the Mult of CS,r399,(p + (z2 * p1))) is set
K4(r399,(p + (z2 * p1))) is set
the Mult of CS . K4(r399,(p + (z2 * p1))) is set
p29999 is V24() V25() Element of REAL
p29999 * (p + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,p29999,(p + (z1 * r1))) is set
K4(p29999,(p + (z1 * r1))) is set
the Mult of CS . K4(p29999,(p + (z1 * r1))) is set
(r399 * (p + (z2 * p1))) + (p29999 * (p + (z1 * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r399 * (p + (z2 * p1))),(p29999 * (p + (z1 * r1)))) is Element of the U1 of CS
K4((r399 * (p + (z2 * p1))),(p29999 * (p + (z1 * r1)))) is set
the U5 of CS . K4((r399 * (p + (z2 * p1))),(p29999 * (p + (z1 * r1)))) is set
q3999 is V24() V25() Element of REAL
q3999 * (p + (y * p1)) is Element of the U1 of CS
K138( the Mult of CS,q3999,(p + (y * p1))) is set
K4(q3999,(p + (y * p1))) is set
the Mult of CS . K4(q3999,(p + (y * p1))) is set
r19 is V24() V25() Element of REAL
r19 * (p + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,r19,(p + (z1 * r1))) is set
K4(r19,(p + (z1 * r1))) is set
the Mult of CS . K4(r19,(p + (z1 * r1))) is set
(q3999 * (p + (y * p1))) + (r19 * (p + (z1 * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q3999 * (p + (y * p1))),(r19 * (p + (z1 * r1)))) is Element of the U1 of CS
K4((q3999 * (p + (y * p1))),(r19 * (p + (z1 * r1)))) is set
the U5 of CS . K4((q3999 * (p + (y * p1))),(r19 * (p + (z1 * r1)))) is set
r399 + p29999 is V24() V25() Element of REAL
(r399 + p29999) * p is Element of the U1 of CS
K138( the Mult of CS,(r399 + p29999),p) is set
K4((r399 + p29999),p) is set
the Mult of CS . K4((r399 + p29999),p) is set
r399 * z2 is V24() V25() Element of REAL
(r399 * z2) * p1 is Element of the U1 of CS
K138( the Mult of CS,(r399 * z2),p1) is set
K4((r399 * z2),p1) is set
the Mult of CS . K4((r399 * z2),p1) is set
((r399 + p29999) * p) + ((r399 * z2) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r399 + p29999) * p),((r399 * z2) * p1)) is Element of the U1 of CS
K4(((r399 + p29999) * p),((r399 * z2) * p1)) is set
the U5 of CS . K4(((r399 + p29999) * p),((r399 * z2) * p1)) is set
p29999 * z1 is V24() V25() Element of REAL
(p29999 * z1) * r1 is Element of the U1 of CS
K138( the Mult of CS,(p29999 * z1),r1) is set
K4((p29999 * z1),r1) is set
the Mult of CS . K4((p29999 * z1),r1) is set
(((r399 + p29999) * p) + ((r399 * z2) * p1)) + ((p29999 * z1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r399 + p29999) * p) + ((r399 * z2) * p1)),((p29999 * z1) * r1)) is Element of the U1 of CS
K4((((r399 + p29999) * p) + ((r399 * z2) * p1)),((p29999 * z1) * r1)) is set
the U5 of CS . K4((((r399 + p29999) * p) + ((r399 * z2) * p1)),((p29999 * z1) * r1)) is set
p19999 is V24() V25() Element of REAL
p19999 * p1 is Element of the U1 of CS
K138( the Mult of CS,p19999,p1) is set
K4(p19999,p1) is set
the Mult of CS . K4(p19999,p1) is set
q399 is V24() V25() Element of REAL
q399 * (p + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,q399,(p + (z1 * r1))) is set
K4(q399,(p + (z1 * r1))) is set
the Mult of CS . K4(q399,(p + (z1 * r1))) is set
(p19999 * p1) + (q399 * (p + (z1 * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p19999 * p1),(q399 * (p + (z1 * r1)))) is Element of the U1 of CS
K4((p19999 * p1),(q399 * (p + (z1 * r1)))) is set
the U5 of CS . K4((p19999 * p1),(q399 * (p + (z1 * r1)))) is set
r29 is V24() V25() Element of REAL
r29 * r1 is Element of the U1 of CS
K138( the Mult of CS,r29,r1) is set
K4(r29,r1) is set
the Mult of CS . K4(r29,r1) is set
p3999 is V24() V25() Element of REAL
p3999 * (p + (y * p1)) is Element of the U1 of CS
K138( the Mult of CS,p3999,(p + (y * p1))) is set
K4(p3999,(p + (y * p1))) is set
the Mult of CS . K4(p3999,(p + (y * p1))) is set
(r29 * r1) + (p3999 * (p + (y * p1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r29 * r1),(p3999 * (p + (y * p1)))) is Element of the U1 of CS
K4((r29 * r1),(p3999 * (p + (y * p1)))) is set
the U5 of CS . K4((r29 * r1),(p3999 * (p + (y * p1)))) is set
q399 * p is Element of the U1 of CS
K138( the Mult of CS,q399,p) is set
K4(q399,p) is set
the Mult of CS . K4(q399,p) is set
(q399 * p) + (p19999 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q399 * p),(p19999 * p1)) is Element of the U1 of CS
K4((q399 * p),(p19999 * p1)) is set
the U5 of CS . K4((q399 * p),(p19999 * p1)) is set
q399 * z1 is V24() V25() Element of REAL
(q399 * z1) * r1 is Element of the U1 of CS
K138( the Mult of CS,(q399 * z1),r1) is set
K4((q399 * z1),r1) is set
the Mult of CS . K4((q399 * z1),r1) is set
((q399 * p) + (p19999 * p1)) + ((q399 * z1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q399 * p) + (p19999 * p1)),((q399 * z1) * r1)) is Element of the U1 of CS
K4(((q399 * p) + (p19999 * p1)),((q399 * z1) * r1)) is set
the U5 of CS . K4(((q399 * p) + (p19999 * p1)),((q399 * z1) * r1)) is set
q29999 is V24() V25() Element of REAL
q29999 * r1 is Element of the U1 of CS
K138( the Mult of CS,q29999,r1) is set
K4(q29999,r1) is set
the Mult of CS . K4(q29999,r1) is set
r199 is V24() V25() Element of REAL
r199 * (p + (z2 * p1)) is Element of the U1 of CS
K138( the Mult of CS,r199,(p + (z2 * p1))) is set
K4(r199,(p + (z2 * p1))) is set
the Mult of CS . K4(r199,(p + (z2 * p1))) is set
(q29999 * r1) + (r199 * (p + (z2 * p1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(q29999 * r1),(r199 * (p + (z2 * p1)))) is Element of the U1 of CS
K4((q29999 * r1),(r199 * (p + (z2 * p1)))) is set
the U5 of CS . K4((q29999 * r1),(r199 * (p + (z2 * p1)))) is set
p2999 * p is Element of the U1 of CS
K138( the Mult of CS,p2999,p) is set
K4(p2999,p) is set
the Mult of CS . K4(p2999,p) is set
(p2999 * p) + (q1999 * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p2999 * p),(q1999 * p1)) is Element of the U1 of CS
K4((p2999 * p),(q1999 * p1)) is set
the U5 of CS . K4((p2999 * p),(q1999 * p1)) is set
p2999 * z1 is V24() V25() Element of REAL
(p2999 * z1) * r1 is Element of the U1 of CS
K138( the Mult of CS,(p2999 * z1),r1) is set
K4((p2999 * z1),r1) is set
the Mult of CS . K4((p2999 * z1),r1) is set
((p2999 * p) + (q1999 * p1)) + ((p2999 * z1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p2999 * p) + (q1999 * p1)),((p2999 * z1) * r1)) is Element of the U1 of CS
K4(((p2999 * p) + (q1999 * p1)),((p2999 * z1) * r1)) is set
the U5 of CS . K4(((p2999 * p) + (q1999 * p1)),((p2999 * z1) * r1)) is set
p3999 * p is Element of the U1 of CS
K138( the Mult of CS,p3999,p) is set
K4(p3999,p) is set
the Mult of CS . K4(p3999,p) is set
p3999 * y is V24() V25() Element of REAL
(p3999 * y) * p1 is Element of the U1 of CS
K138( the Mult of CS,(p3999 * y),p1) is set
K4((p3999 * y),p1) is set
the Mult of CS . K4((p3999 * y),p1) is set
(p3999 * p) + ((p3999 * y) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p3999 * p),((p3999 * y) * p1)) is Element of the U1 of CS
K4((p3999 * p),((p3999 * y) * p1)) is set
the U5 of CS . K4((p3999 * p),((p3999 * y) * p1)) is set
((p3999 * p) + ((p3999 * y) * p1)) + (r29 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((p3999 * p) + ((p3999 * y) * p1)),(r29 * r1)) is Element of the U1 of CS
K4(((p3999 * p) + ((p3999 * y) * p1)),(r29 * r1)) is set
the U5 of CS . K4(((p3999 * p) + ((p3999 * y) * p1)),(r29 * r1)) is set
r199 * p is Element of the U1 of CS
K138( the Mult of CS,r199,p) is set
K4(r199,p) is set
the Mult of CS . K4(r199,p) is set
r199 * z2 is V24() V25() Element of REAL
(r199 * z2) * p1 is Element of the U1 of CS
K138( the Mult of CS,(r199 * z2),p1) is set
K4((r199 * z2),p1) is set
the Mult of CS . K4((r199 * z2),p1) is set
(r199 * p) + ((r199 * z2) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(r199 * p),((r199 * z2) * p1)) is Element of the U1 of CS
K4((r199 * p),((r199 * z2) * p1)) is set
the U5 of CS . K4((r199 * p),((r199 * z2) * p1)) is set
((r199 * p) + ((r199 * z2) * p1)) + (q29999 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r199 * p) + ((r199 * z2) * p1)),(q29999 * r1)) is Element of the U1 of CS
K4(((r199 * p) + ((r199 * z2) * p1)),(q29999 * r1)) is set
the U5 of CS . K4(((r199 * p) + ((r199 * z2) * p1)),(q29999 * r1)) is set
q3999 + r19 is V24() V25() Element of REAL
(q3999 + r19) * p is Element of the U1 of CS
K138( the Mult of CS,(q3999 + r19),p) is set
K4((q3999 + r19),p) is set
the Mult of CS . K4((q3999 + r19),p) is set
q3999 * y is V24() V25() Element of REAL
(q3999 * y) * p1 is Element of the U1 of CS
K138( the Mult of CS,(q3999 * y),p1) is set
K4((q3999 * y),p1) is set
the Mult of CS . K4((q3999 * y),p1) is set
((q3999 + r19) * p) + ((q3999 * y) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((q3999 + r19) * p),((q3999 * y) * p1)) is Element of the U1 of CS
K4(((q3999 + r19) * p),((q3999 * y) * p1)) is set
the U5 of CS . K4(((q3999 + r19) * p),((q3999 * y) * p1)) is set
r19 * z1 is V24() V25() Element of REAL
(r19 * z1) * r1 is Element of the U1 of CS
K138( the Mult of CS,(r19 * z1),r1) is set
K4((r19 * z1),r1) is set
the Mult of CS . K4((r19 * z1),r1) is set
(((q3999 + r19) * p) + ((q3999 * y) * p1)) + ((r19 * z1) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((q3999 + r19) * p) + ((q3999 * y) * p1)),((r19 * z1) * r1)) is Element of the U1 of CS
K4((((q3999 + r19) * p) + ((q3999 * y) * p1)),((r19 * z1) * r1)) is set
the U5 of CS . K4((((q3999 + r19) * p) + ((q3999 * y) * p1)),((r19 * z1) * r1)) is set
y * z1 is V24() V25() Element of REAL
y * z1 is V24() V25() Element of REAL
(y * z1) - (y * z1) is V24() V25() Element of REAL
z2 * z1 is V24() V25() Element of REAL
(y * z1) - (z2 * z1) is V24() V25() Element of REAL
((y * z1) - (z2 * z1)) " is V24() V25() Element of REAL
((y * z1) - (y * z1)) * (((y * z1) - (z2 * z1)) ") is V24() V25() Element of REAL
(((y * z1) - (y * z1)) * (((y * z1) - (z2 * z1)) ")) * p29999 is V24() V25() Element of REAL
(p + (y * p1)) + (z1 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + (y * p1)),(z1 * r1)) is Element of the U1 of CS
K4((p + (y * p1)),(z1 * r1)) is set
the U5 of CS . K4((p + (y * p1)),(z1 * r1)) is set
- (y * z1) is V24() V25() Element of REAL
(y * z1) - (z2 * z1) is V24() V25() Element of REAL
((y * z1) - (z2 * z1)) * p is Element of the U1 of CS
K138( the Mult of CS,((y * z1) - (z2 * z1)),p) is set
K4(((y * z1) - (z2 * z1)),p) is set
the Mult of CS . K4(((y * z1) - (z2 * z1)),p) is set
z2 * y is V24() V25() Element of REAL
z1 - z1 is V24() V25() Element of REAL
(z2 * y) * (z1 - z1) is V24() V25() Element of REAL
((z2 * y) * (z1 - z1)) * p1 is Element of the U1 of CS
K138( the Mult of CS,((z2 * y) * (z1 - z1)),p1) is set
K4(((z2 * y) * (z1 - z1)),p1) is set
the Mult of CS . K4(((z2 * y) * (z1 - z1)),p1) is set
(((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((y * z1) - (z2 * z1)) * p),(((z2 * y) * (z1 - z1)) * p1)) is Element of the U1 of CS
K4((((y * z1) - (z2 * z1)) * p),(((z2 * y) * (z1 - z1)) * p1)) is set
the U5 of CS . K4((((y * z1) - (z2 * z1)) * p),(((z2 * y) * (z1 - z1)) * p1)) is set
z1 * z1 is V24() V25() Element of REAL
y - z2 is V24() V25() Element of REAL
(z1 * z1) * (y - z2) is V24() V25() Element of REAL
((z1 * z1) * (y - z2)) * r1 is Element of the U1 of CS
K138( the Mult of CS,((z1 * z1) * (y - z2)),r1) is set
K4(((z1 * z1) * (y - z2)),r1) is set
the Mult of CS . K4(((z1 * z1) * (y - z2)),r1) is set
((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)),(((z1 * z1) * (y - z2)) * r1)) is Element of the U1 of CS
K4(((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)),(((z1 * z1) * (y - z2)) * r1)) is set
the U5 of CS . K4(((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)),(((z1 * z1) * (y - z2)) * r1)) is set
(p + (z2 * p1)) + (z1 * r1) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(p + (z2 * p1)),(z1 * r1)) is Element of the U1 of CS
K4((p + (z2 * p1)),(z1 * r1)) is set
the U5 of CS . K4((p + (z2 * p1)),(z1 * r1)) is set
(z2 * z1) * z1 is V24() V25() Element of REAL
(- (y * z1)) * z1 is V24() V25() Element of REAL
((z2 * z1) * z1) + ((- (y * z1)) * z1) is V24() V25() Element of REAL
z2 - y is V24() V25() Element of REAL
(z1 * z1) * (z2 - y) is V24() V25() Element of REAL
(z2 * z1) + (- (y * z1)) is V24() V25() Element of REAL
(z2 * z1) - (y * z1) is V24() V25() Element of REAL
(z2 * z1) * y is V24() V25() Element of REAL
(- (y * z1)) * z2 is V24() V25() Element of REAL
((z2 * z1) * y) + ((- (y * z1)) * z2) is V24() V25() Element of REAL
z1 - z1 is V24() V25() Element of REAL
(z2 * y) * (z1 - z1) is V24() V25() Element of REAL
1 * (((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1)) is Element of the U1 of CS
K138( the Mult of CS,1,(((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) is set
K4(1,(((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) is set
the Mult of CS . K4(1,(((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) is set
(z2 * z1) * ((p + (y * p1)) + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,(z2 * z1),((p + (y * p1)) + (z1 * r1))) is set
K4((z2 * z1),((p + (y * p1)) + (z1 * r1))) is set
the Mult of CS . K4((z2 * z1),((p + (y * p1)) + (z1 * r1))) is set
(1 * (((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) + ((z2 * z1) * ((p + (y * p1)) + (z1 * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(1 * (((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))),((z2 * z1) * ((p + (y * p1)) + (z1 * r1)))) is Element of the U1 of CS
K4((1 * (((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))),((z2 * z1) * ((p + (y * p1)) + (z1 * r1)))) is set
the U5 of CS . K4((1 * (((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))),((z2 * z1) * ((p + (y * p1)) + (z1 * r1)))) is set
(- (y * z1)) * ((p + (z2 * p1)) + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,(- (y * z1)),((p + (z2 * p1)) + (z1 * r1))) is set
K4((- (y * z1)),((p + (z2 * p1)) + (z1 * r1))) is set
the Mult of CS . K4((- (y * z1)),((p + (z2 * p1)) + (z1 * r1))) is set
((1 * (((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) + ((z2 * z1) * ((p + (y * p1)) + (z1 * r1)))) + ((- (y * z1)) * ((p + (z2 * p1)) + (z1 * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((1 * (((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) + ((z2 * z1) * ((p + (y * p1)) + (z1 * r1)))),((- (y * z1)) * ((p + (z2 * p1)) + (z1 * r1)))) is Element of the U1 of CS
K4(((1 * (((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) + ((z2 * z1) * ((p + (y * p1)) + (z1 * r1)))),((- (y * z1)) * ((p + (z2 * p1)) + (z1 * r1)))) is set
the U5 of CS . K4(((1 * (((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) + ((z2 * z1) * ((p + (y * p1)) + (z1 * r1)))),((- (y * z1)) * ((p + (z2 * p1)) + (z1 * r1)))) is set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
0 * (p + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,0,(p + (z1 * r1))) is set
K4(0,(p + (z1 * r1))) is set
the Mult of CS . K4(0,(p + (z1 * r1))) is set
(0. CS) + (0 * (p + (z1 * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0 * (p + (z1 * r1)))) is Element of the U1 of CS
K4((0. CS),(0 * (p + (z1 * r1)))) is set
the U5 of CS . K4((0. CS),(0 * (p + (z1 * r1)))) is set
(0. CS) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0. CS)) is Element of the U1 of CS
K4((0. CS),(0. CS)) is set
the U5 of CS . K4((0. CS),(0. CS)) is set
q399 * ((p + (y * p1)) + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,q399,((p + (y * p1)) + (z1 * r1))) is set
K4(q399,((p + (y * p1)) + (z1 * r1))) is set
the Mult of CS . K4(q399,((p + (y * p1)) + (z1 * r1))) is set
0 * (p + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,0,(p + (z1 * r1))) is set
K4(0,(p + (z1 * r1))) is set
the Mult of CS . K4(0,(p + (z1 * r1))) is set
(0. CS) + (0 * (p + (z1 * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0 * (p + (z1 * r1)))) is Element of the U1 of CS
K4((0. CS),(0 * (p + (z1 * r1)))) is set
the U5 of CS . K4((0. CS),(0 * (p + (z1 * r1)))) is set
(0. CS) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0. CS)) is Element of the U1 of CS
K4((0. CS),(0. CS)) is set
the U5 of CS . K4((0. CS),(0. CS)) is set
p2999 * ((p + (z2 * p1)) + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,p2999,((p + (z2 * p1)) + (z1 * r1))) is set
K4(p2999,((p + (z2 * p1)) + (z1 * r1))) is set
the Mult of CS . K4(p2999,((p + (z2 * p1)) + (z1 * r1))) is set
0 * (p + (z1 * r1)) is Element of the U1 of CS
K138( the Mult of CS,0,(p + (z1 * r1))) is set
K4(0,(p + (z1 * r1))) is set
the Mult of CS . K4(0,(p + (z1 * r1))) is set
(0. CS) + (0 * (p + (z1 * r1))) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0 * (p + (z1 * r1)))) is Element of the U1 of CS
K4((0. CS),(0 * (p + (z1 * r1)))) is set
the U5 of CS . K4((0. CS),(0 * (p + (z1 * r1)))) is set
(0. CS) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(0. CS),(0. CS)) is Element of the U1 of CS
K4((0. CS),(0. CS)) is set
the U5 of CS . K4((0. CS),(0. CS)) is set
p29999 * (((y * z1) - (z2 * z1)) ") is V24() V25() Element of REAL
(p29999 * (((y * z1) - (z2 * z1)) ")) * (((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1)) is Element of the U1 of CS
K138( the Mult of CS,(p29999 * (((y * z1) - (z2 * z1)) ")),(((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) is set
K4((p29999 * (((y * z1) - (z2 * z1)) ")),(((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) is set
the Mult of CS . K4((p29999 * (((y * z1) - (z2 * z1)) ")),(((((y * z1) - (z2 * z1)) * p) + (((z2 * y) * (z1 - z1)) * p1)) + (((z1 * z1) * (y - z2)) * r1))) is set
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
p is Element of CS
p1 is set
K33(CS,REAL) is non empty set
K32(K33(CS,REAL)) is non empty set
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of K32(K33(CS,REAL))
p2 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p2 . p is V24() V25() Element of REAL
r is set
p2 . r is set
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncZero CS is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K150(NAT,CS,0) is V7() V10(CS) V11( NAT ) Function-like quasi_total Element of K32(K33(CS,NAT))
K33(CS,NAT) is non empty set
K32(K33(CS,NAT)) is non empty set
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p2 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r is Element of CS
p . r is V24() V25() Element of REAL
r1 is Element of CS
p1 . r1 is V24() V25() Element of REAL
p is Element of CS
p2 . p is V24() V25() Element of REAL
p . r1 is V24() V25() Element of REAL
p2 . r1 is V24() V25() Element of REAL
q1 is V24() V25() Element of REAL
[q1,p] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [q1,p] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r is V24() V25() Element of REAL
[r,p1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [r,p1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1])) is set
(RealFuncAdd CS) . K4(((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1])) is set
y is V24() V25() Element of REAL
[y,p2] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [y,p2] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))),((RealFuncExtMult CS) . [y,p2])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))),((RealFuncExtMult CS) . [y,p2])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))),((RealFuncExtMult CS) . [y,p2])) is set
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))),((RealFuncExtMult CS) . [y,p2]))) . r1 is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))) . r1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p2]) . r1 is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))) . r1) + (((RealFuncExtMult CS) . [y,p2]) . r1) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [q1,p]) . r1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [r,p1]) . r1 is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q1,p]) . r1) + (((RealFuncExtMult CS) . [r,p1]) . r1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q1,p]) . r1) + (((RealFuncExtMult CS) . [r,p1]) . r1)) + (((RealFuncExtMult CS) . [y,p2]) . r1) is V24() V25() Element of REAL
y * (p2 . r1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q1,p]) . r1) + (((RealFuncExtMult CS) . [r,p1]) . r1)) + (y * (p2 . r1)) is V24() V25() Element of REAL
r * (p1 . r1) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q1,p]) . r1) + (r * (p1 . r1)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q1,p]) . r1) + (r * (p1 . r1))) + (y * (p2 . r1)) is V24() V25() Element of REAL
q1 * 0 is V24() V25() Element of REAL
r * 1 is V24() V25() Element of REAL
(q1 * 0) + (r * 1) is V24() V25() Element of REAL
y * 0 is V24() V25() Element of REAL
((q1 * 0) + (r * 1)) + (y * 0) is V24() V25() Element of REAL
p1 . r is V24() V25() Element of REAL
p2 . r is V24() V25() Element of REAL
p . p is V24() V25() Element of REAL
p1 . p is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))),((RealFuncExtMult CS) . [y,p2]))) . p is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))) . p is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p2]) . p is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))) . p) + (((RealFuncExtMult CS) . [y,p2]) . p) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [q1,p]) . p is V24() V25() Element of REAL
((RealFuncExtMult CS) . [r,p1]) . p is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q1,p]) . p) + (((RealFuncExtMult CS) . [r,p1]) . p) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q1,p]) . p) + (((RealFuncExtMult CS) . [r,p1]) . p)) + (((RealFuncExtMult CS) . [y,p2]) . p) is V24() V25() Element of REAL
y * (p2 . p) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q1,p]) . p) + (((RealFuncExtMult CS) . [r,p1]) . p)) + (y * (p2 . p)) is V24() V25() Element of REAL
r * (p1 . p) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q1,p]) . p) + (r * (p1 . p)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q1,p]) . p) + (r * (p1 . p))) + (y * (p2 . p)) is V24() V25() Element of REAL
r * 0 is V24() V25() Element of REAL
(q1 * 0) + (r * 0) is V24() V25() Element of REAL
y * 1 is V24() V25() Element of REAL
((q1 * 0) + (r * 0)) + (y * 1) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))),((RealFuncExtMult CS) . [y,p2]))) . r is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))) . r is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p2]) . r is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,p]),((RealFuncExtMult CS) . [r,p1]))) . r) + (((RealFuncExtMult CS) . [y,p2]) . r) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [q1,p]) . r is V24() V25() Element of REAL
((RealFuncExtMult CS) . [r,p1]) . r is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q1,p]) . r) + (((RealFuncExtMult CS) . [r,p1]) . r) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q1,p]) . r) + (((RealFuncExtMult CS) . [r,p1]) . r)) + (((RealFuncExtMult CS) . [y,p2]) . r) is V24() V25() Element of REAL
y * (p2 . r) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q1,p]) . r) + (((RealFuncExtMult CS) . [r,p1]) . r)) + (y * (p2 . r)) is V24() V25() Element of REAL
r * (p1 . r) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q1,p]) . r) + (r * (p1 . r)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q1,p]) . r) + (r * (p1 . r))) + (y * (p2 . r)) is V24() V25() Element of REAL
q1 * 1 is V24() V25() Element of REAL
(q1 * 1) + (r * 0) is V24() V25() Element of REAL
((q1 * 1) + (r * 0)) + (y * 0) is V24() V25() Element of REAL
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncZero CS is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K150(NAT,CS,0) is V7() V10(CS) V11( NAT ) Function-like quasi_total Element of K32(K33(CS,NAT))
K33(CS,NAT) is non empty set
K32(K33(CS,NAT)) is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
r is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r . p is V24() V25() Element of REAL
r1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r1 . p2 is V24() V25() Element of REAL
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p . p1 is V24() V25() Element of REAL
p1 is V24() V25() Element of REAL
[p1,r] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [p1,r] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
q is V24() V25() Element of REAL
[q,p] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [q,p] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p])) is set
(RealFuncAdd CS) . K4(((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p])) is set
q1 is V24() V25() Element of REAL
[q1,r1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [q1,r1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p]))),((RealFuncExtMult CS) . [q1,r1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p]))),((RealFuncExtMult CS) . [q1,r1])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p]))),((RealFuncExtMult CS) . [q1,r1])) is set
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p2 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r is Element of CS
p . r is V24() V25() Element of REAL
r1 is Element of CS
p1 . r1 is V24() V25() Element of REAL
p is Element of CS
{r,r1,p} is non empty Element of K32(CS)
K32(CS) is non empty set
p2 . p is V24() V25() Element of REAL
p1 . r is V24() V25() Element of REAL
p2 . r is V24() V25() Element of REAL
p . r1 is V24() V25() Element of REAL
p2 . r1 is V24() V25() Element of REAL
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 . r is V24() V25() Element of REAL
q is V24() V25() Element of REAL
[q,p] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [q,p] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 . r1 is V24() V25() Element of REAL
q1 is V24() V25() Element of REAL
[q1,p1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [q1,p1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1])) is set
(RealFuncAdd CS) . K4(((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1])) is set
p1 . p is V24() V25() Element of REAL
r is V24() V25() Element of REAL
[r,p2] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [r,p2] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))),((RealFuncExtMult CS) . [r,p2])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))),((RealFuncExtMult CS) . [r,p2])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))),((RealFuncExtMult CS) . [r,p2])) is set
p . p is V24() V25() Element of REAL
p1 . p is V24() V25() Element of REAL
y is Element of CS
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))),((RealFuncExtMult CS) . [r,p2]))) . r1 is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))) . r1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [r,p2]) . r1 is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))) . r1) + (((RealFuncExtMult CS) . [r,p2]) . r1) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [q,p]) . r1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [q1,p1]) . r1 is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q,p]) . r1) + (((RealFuncExtMult CS) . [q1,p1]) . r1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q,p]) . r1) + (((RealFuncExtMult CS) . [q1,p1]) . r1)) + (((RealFuncExtMult CS) . [r,p2]) . r1) is V24() V25() Element of REAL
r * (p2 . r1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q,p]) . r1) + (((RealFuncExtMult CS) . [q1,p1]) . r1)) + (r * (p2 . r1)) is V24() V25() Element of REAL
q1 * (p1 . r1) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q,p]) . r1) + (q1 * (p1 . r1)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q,p]) . r1) + (q1 * (p1 . r1))) + (r * (p2 . r1)) is V24() V25() Element of REAL
q * 0 is V24() V25() Element of REAL
q1 * 1 is V24() V25() Element of REAL
(q * 0) + (q1 * 1) is V24() V25() Element of REAL
r * 0 is V24() V25() Element of REAL
((q * 0) + (q1 * 1)) + (r * 0) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))),((RealFuncExtMult CS) . [r,p2]))) . p is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))) . p is V24() V25() Element of REAL
((RealFuncExtMult CS) . [r,p2]) . p is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))) . p) + (((RealFuncExtMult CS) . [r,p2]) . p) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [q,p]) . p is V24() V25() Element of REAL
((RealFuncExtMult CS) . [q1,p1]) . p is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q,p]) . p) + (((RealFuncExtMult CS) . [q1,p1]) . p) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q,p]) . p) + (((RealFuncExtMult CS) . [q1,p1]) . p)) + (((RealFuncExtMult CS) . [r,p2]) . p) is V24() V25() Element of REAL
r * (p2 . p) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q,p]) . p) + (((RealFuncExtMult CS) . [q1,p1]) . p)) + (r * (p2 . p)) is V24() V25() Element of REAL
q1 * (p1 . p) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q,p]) . p) + (q1 * (p1 . p)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q,p]) . p) + (q1 * (p1 . p))) + (r * (p2 . p)) is V24() V25() Element of REAL
q1 * 0 is V24() V25() Element of REAL
(q * 0) + (q1 * 0) is V24() V25() Element of REAL
r * 1 is V24() V25() Element of REAL
((q * 0) + (q1 * 0)) + (r * 1) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))),((RealFuncExtMult CS) . [r,p2]))) . r is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))) . r is V24() V25() Element of REAL
((RealFuncExtMult CS) . [r,p2]) . r is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))) . r) + (((RealFuncExtMult CS) . [r,p2]) . r) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [q,p]) . r is V24() V25() Element of REAL
((RealFuncExtMult CS) . [q1,p1]) . r is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q,p]) . r) + (((RealFuncExtMult CS) . [q1,p1]) . r) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q,p]) . r) + (((RealFuncExtMult CS) . [q1,p1]) . r)) + (((RealFuncExtMult CS) . [r,p2]) . r) is V24() V25() Element of REAL
r * (p2 . r) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q,p]) . r) + (((RealFuncExtMult CS) . [q1,p1]) . r)) + (r * (p2 . r)) is V24() V25() Element of REAL
q1 * (p1 . r) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [q,p]) . r) + (q1 * (p1 . r)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [q,p]) . r) + (q1 * (p1 . r))) + (r * (p2 . r)) is V24() V25() Element of REAL
q * 1 is V24() V25() Element of REAL
(q * 1) + (q1 * 0) is V24() V25() Element of REAL
((q * 1) + (q1 * 0)) + (r * 0) is V24() V25() Element of REAL
p1 . y is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q,p]),((RealFuncExtMult CS) . [q1,p1]))),((RealFuncExtMult CS) . [r,p2]))) . y is V24() V25() Element of REAL
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
{p,p1,p2} is non empty Element of K32(CS)
K32(CS) is non empty set
r is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r . p is V24() V25() Element of REAL
r1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r1 . p2 is V24() V25() Element of REAL
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p . p1 is V24() V25() Element of REAL
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncZero CS is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K150(NAT,CS,0) is V7() V10(CS) V11( NAT ) Function-like quasi_total Element of K32(K33(CS,NAT))
K33(CS,NAT) is non empty set
K32(K33(CS,NAT)) is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
{p,p1,p2} is non empty Element of K32(CS)
K32(CS) is non empty set
r is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r . p is V24() V25() Element of REAL
r1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r1 . p2 is V24() V25() Element of REAL
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p . p1 is V24() V25() Element of REAL
p1 is V24() V25() Element of REAL
[p1,r] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [p1,r] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
q is V24() V25() Element of REAL
[q,p] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [q,p] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p])) is set
(RealFuncAdd CS) . K4(((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p])) is set
q1 is V24() V25() Element of REAL
[q1,r1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [q1,r1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p]))),((RealFuncExtMult CS) . [q1,r1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p]))),((RealFuncExtMult CS) . [q1,r1])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [p1,r]),((RealFuncExtMult CS) . [q,p]))),((RealFuncExtMult CS) . [q1,r1])) is set
r is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
2 is non empty V17() V18() V19() V23() V24() V25() Element of NAT
{0,1,2} is non empty Element of K32(NAT)
CS is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
{p,p1,p2} is non empty Element of K32(CS)
K32(CS) is non empty set
CS is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
{p,p1,p2} is non empty Element of K32(CS)
K32(CS) is non empty set
CS is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
{p,p1,p2} is non empty Element of K32(CS)
K32(CS) is non empty set
RealVectSpace CS is non empty V70() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncZero CS is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K150(NAT,CS,0) is V7() V10(CS) V11( NAT ) Function-like quasi_total Element of K32(K33(CS,NAT))
K33(CS,NAT) is non empty set
K32(K33(CS,NAT)) is non empty set
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RLSStruct(# (Funcs (CS,REAL)),(RealFuncZero CS),(RealFuncAdd CS),(RealFuncExtMult CS) #) is strict RLSStruct
r1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
the U1 of (RealVectSpace CS) is non empty set
q is Element of the U1 of (RealVectSpace CS)
q1 is Element of the U1 of (RealVectSpace CS)
r is Element of the U1 of (RealVectSpace CS)
0. (RealVectSpace CS) is zero Element of the U1 of (RealVectSpace CS)
the U2 of (RealVectSpace CS) is Element of the U1 of (RealVectSpace CS)
y is V24() V25() Element of REAL
y * q is Element of the U1 of (RealVectSpace CS)
the Mult of (RealVectSpace CS) is V7() V10(K33(REAL, the U1 of (RealVectSpace CS))) V11( the U1 of (RealVectSpace CS)) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)))
K33(REAL, the U1 of (RealVectSpace CS)) is non empty set
K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)) is non empty set
K32(K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS))) is non empty set
K138( the Mult of (RealVectSpace CS),y,q) is set
K4(y,q) is set
the Mult of (RealVectSpace CS) . K4(y,q) is set
z2 is V24() V25() Element of REAL
z2 * q1 is Element of the U1 of (RealVectSpace CS)
K138( the Mult of (RealVectSpace CS),z2,q1) is set
K4(z2,q1) is set
the Mult of (RealVectSpace CS) . K4(z2,q1) is set
(y * q) + (z2 * q1) is Element of the U1 of (RealVectSpace CS)
the U5 of (RealVectSpace CS) is V7() V10(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS))) V11( the U1 of (RealVectSpace CS)) Function-like quasi_total Element of K32(K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)))
K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)) is non empty set
K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)) is non empty set
K32(K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS))) is non empty set
K142( the U1 of (RealVectSpace CS), the U5 of (RealVectSpace CS),(y * q),(z2 * q1)) is Element of the U1 of (RealVectSpace CS)
K4((y * q),(z2 * q1)) is set
the U5 of (RealVectSpace CS) . K4((y * q),(z2 * q1)) is set
z1 is V24() V25() Element of REAL
z1 * r is Element of the U1 of (RealVectSpace CS)
K138( the Mult of (RealVectSpace CS),z1,r) is set
K4(z1,r) is set
the Mult of (RealVectSpace CS) . K4(z1,r) is set
((y * q) + (z2 * q1)) + (z1 * r) is Element of the U1 of (RealVectSpace CS)
K142( the U1 of (RealVectSpace CS), the U5 of (RealVectSpace CS),((y * q) + (z2 * q1)),(z1 * r)) is Element of the U1 of (RealVectSpace CS)
K4(((y * q) + (z2 * q1)),(z1 * r)) is set
the U5 of (RealVectSpace CS) . K4(((y * q) + (z2 * q1)),(z1 * r)) is set
y is Element of the U1 of (RealVectSpace CS)
z2 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
z1 is V24() V25() Element of REAL
[z1,r1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [z1,r1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
x2 is V24() V25() Element of REAL
[x2,p] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [x2,p] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,r1]),((RealFuncExtMult CS) . [x2,p])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncExtMult CS) . [z1,r1]),((RealFuncExtMult CS) . [x2,p])) is set
(RealFuncAdd CS) . K4(((RealFuncExtMult CS) . [z1,r1]),((RealFuncExtMult CS) . [x2,p])) is set
z1 is V24() V25() Element of REAL
[z1,p1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [z1,p1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,r1]),((RealFuncExtMult CS) . [x2,p]))),((RealFuncExtMult CS) . [z1,p1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,r1]),((RealFuncExtMult CS) . [x2,p]))),((RealFuncExtMult CS) . [z1,p1])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,r1]),((RealFuncExtMult CS) . [x2,p]))),((RealFuncExtMult CS) . [z1,p1])) is set
z1 * q is Element of the U1 of (RealVectSpace CS)
the Mult of (RealVectSpace CS) is V7() V10(K33(REAL, the U1 of (RealVectSpace CS))) V11( the U1 of (RealVectSpace CS)) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)))
K33(REAL, the U1 of (RealVectSpace CS)) is non empty set
K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)) is non empty set
K32(K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS))) is non empty set
K138( the Mult of (RealVectSpace CS),z1,q) is set
K4(z1,q) is set
the Mult of (RealVectSpace CS) . K4(z1,q) is set
x2 * q1 is Element of the U1 of (RealVectSpace CS)
K138( the Mult of (RealVectSpace CS),x2,q1) is set
K4(x2,q1) is set
the Mult of (RealVectSpace CS) . K4(x2,q1) is set
(z1 * q) + (x2 * q1) is Element of the U1 of (RealVectSpace CS)
the U5 of (RealVectSpace CS) is V7() V10(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS))) V11( the U1 of (RealVectSpace CS)) Function-like quasi_total Element of K32(K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)))
K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)) is non empty set
K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)) is non empty set
K32(K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS))) is non empty set
K142( the U1 of (RealVectSpace CS), the U5 of (RealVectSpace CS),(z1 * q),(x2 * q1)) is Element of the U1 of (RealVectSpace CS)
K4((z1 * q),(x2 * q1)) is set
the U5 of (RealVectSpace CS) . K4((z1 * q),(x2 * q1)) is set
z1 * r is Element of the U1 of (RealVectSpace CS)
K138( the Mult of (RealVectSpace CS),z1,r) is set
K4(z1,r) is set
the Mult of (RealVectSpace CS) . K4(z1,r) is set
((z1 * q) + (x2 * q1)) + (z1 * r) is Element of the U1 of (RealVectSpace CS)
K142( the U1 of (RealVectSpace CS), the U5 of (RealVectSpace CS),((z1 * q) + (x2 * q1)),(z1 * r)) is Element of the U1 of (RealVectSpace CS)
K4(((z1 * q) + (x2 * q1)),(z1 * r)) is set
the U5 of (RealVectSpace CS) . K4(((z1 * q) + (x2 * q1)),(z1 * r)) is set
y is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of y is non empty non trivial set
0. y is zero Element of the U1 of y
the U2 of y is Element of the U1 of y
z2 is Element of the U1 of y
z1 is Element of the U1 of y
x2 is Element of the U1 of y
z1 is V24() V25() Element of REAL
z1 * z2 is Element of the U1 of y
the Mult of y is V7() V10(K33(REAL, the U1 of y)) V11( the U1 of y) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of y), the U1 of y))
K33(REAL, the U1 of y) is non empty set
K33(K33(REAL, the U1 of y), the U1 of y) is non empty set
K32(K33(K33(REAL, the U1 of y), the U1 of y)) is non empty set
K138( the Mult of y,z1,z2) is set
K4(z1,z2) is set
the Mult of y . K4(z1,z2) is set
z1 is V24() V25() Element of REAL
z1 * z1 is Element of the U1 of y
K138( the Mult of y,z1,z1) is set
K4(z1,z1) is set
the Mult of y . K4(z1,z1) is set
(z1 * z2) + (z1 * z1) is Element of the U1 of y
the U5 of y is V7() V10(K33( the U1 of y, the U1 of y)) V11( the U1 of y) Function-like quasi_total Element of K32(K33(K33( the U1 of y, the U1 of y), the U1 of y))
K33( the U1 of y, the U1 of y) is non empty set
K33(K33( the U1 of y, the U1 of y), the U1 of y) is non empty set
K32(K33(K33( the U1 of y, the U1 of y), the U1 of y)) is non empty set
K142( the U1 of y, the U5 of y,(z1 * z2),(z1 * z1)) is Element of the U1 of y
K4((z1 * z2),(z1 * z1)) is set
the U5 of y . K4((z1 * z2),(z1 * z1)) is set
z2 is V24() V25() Element of REAL
z2 * x2 is Element of the U1 of y
K138( the Mult of y,z2,x2) is set
K4(z2,x2) is set
the Mult of y . K4(z2,x2) is set
((z1 * z2) + (z1 * z1)) + (z2 * x2) is Element of the U1 of y
K142( the U1 of y, the U5 of y,((z1 * z2) + (z1 * z1)),(z2 * x2)) is Element of the U1 of y
K4(((z1 * z2) + (z1 * z1)),(z2 * x2)) is set
the U5 of y . K4(((z1 * z2) + (z1 * z1)),(z2 * x2)) is set
p199 is Element of the U1 of y
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncZero CS is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K150(NAT,CS,0) is V7() V10(CS) V11( NAT ) Function-like quasi_total Element of K32(K33(CS,NAT))
K33(CS,NAT) is non empty set
K32(K33(CS,NAT)) is non empty set
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p2 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r1 is Element of CS
p . r1 is V24() V25() Element of REAL
p is Element of CS
p1 . p is V24() V25() Element of REAL
p1 is Element of CS
p2 . p1 is V24() V25() Element of REAL
q is Element of CS
r . q is V24() V25() Element of REAL
p . p is V24() V25() Element of REAL
p2 . p is V24() V25() Element of REAL
p1 . r1 is V24() V25() Element of REAL
p2 . r1 is V24() V25() Element of REAL
r . r1 is V24() V25() Element of REAL
r . p is V24() V25() Element of REAL
y is V24() V25() Element of REAL
[y,p] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [y,p] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
z2 is V24() V25() Element of REAL
[z2,p1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [z2,p1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1])) is set
(RealFuncAdd CS) . K4(((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1])) is set
z1 is V24() V25() Element of REAL
[z1,p2] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [z1,p2] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2])) is set
x2 is V24() V25() Element of REAL
[x2,r] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [x2,r] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))),((RealFuncExtMult CS) . [x2,r])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))),((RealFuncExtMult CS) . [x2,r])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))),((RealFuncExtMult CS) . [x2,r])) is set
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))),((RealFuncExtMult CS) . [x2,r]))) . p is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))) . p is V24() V25() Element of REAL
((RealFuncExtMult CS) . [x2,r]) . p is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))) . p) + (((RealFuncExtMult CS) . [x2,r]) . p) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . p is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z1,p2]) . p is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . p) + (((RealFuncExtMult CS) . [z1,p2]) . p) is V24() V25() Element of REAL
((((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . p) + (((RealFuncExtMult CS) . [z1,p2]) . p)) + (((RealFuncExtMult CS) . [x2,r]) . p) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p]) . p is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z2,p1]) . p is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [y,p]) . p) + (((RealFuncExtMult CS) . [z2,p1]) . p) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . p) + (((RealFuncExtMult CS) . [z2,p1]) . p)) + (((RealFuncExtMult CS) . [z1,p2]) . p) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . p) + (((RealFuncExtMult CS) . [z2,p1]) . p)) + (((RealFuncExtMult CS) . [z1,p2]) . p)) + (((RealFuncExtMult CS) . [x2,r]) . p) is V24() V25() Element of REAL
x2 * (r . p) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . p) + (((RealFuncExtMult CS) . [z2,p1]) . p)) + (((RealFuncExtMult CS) . [z1,p2]) . p)) + (x2 * (r . p)) is V24() V25() Element of REAL
z1 * (p2 . p) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . p) + (((RealFuncExtMult CS) . [z2,p1]) . p)) + (z1 * (p2 . p)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . p) + (((RealFuncExtMult CS) . [z2,p1]) . p)) + (z1 * (p2 . p))) + (x2 * (r . p)) is V24() V25() Element of REAL
z2 * (p1 . p) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [y,p]) . p) + (z2 * (p1 . p)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . p) + (z2 * (p1 . p))) + (z1 * (p2 . p)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . p) + (z2 * (p1 . p))) + (z1 * (p2 . p))) + (x2 * (r . p)) is V24() V25() Element of REAL
y * 0 is V24() V25() Element of REAL
z2 * 1 is V24() V25() Element of REAL
(y * 0) + (z2 * 1) is V24() V25() Element of REAL
z1 * 0 is V24() V25() Element of REAL
((y * 0) + (z2 * 1)) + (z1 * 0) is V24() V25() Element of REAL
x2 * 0 is V24() V25() Element of REAL
(((y * 0) + (z2 * 1)) + (z1 * 0)) + (x2 * 0) is V24() V25() Element of REAL
p . q is V24() V25() Element of REAL
p1 . q is V24() V25() Element of REAL
p2 . q is V24() V25() Element of REAL
p . p1 is V24() V25() Element of REAL
p1 . p1 is V24() V25() Element of REAL
r . p1 is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))),((RealFuncExtMult CS) . [x2,r]))) . q is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))) . q is V24() V25() Element of REAL
((RealFuncExtMult CS) . [x2,r]) . q is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))) . q) + (((RealFuncExtMult CS) . [x2,r]) . q) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . q is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z1,p2]) . q is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . q) + (((RealFuncExtMult CS) . [z1,p2]) . q) is V24() V25() Element of REAL
((((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . q) + (((RealFuncExtMult CS) . [z1,p2]) . q)) + (((RealFuncExtMult CS) . [x2,r]) . q) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p]) . q is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z2,p1]) . q is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [y,p]) . q) + (((RealFuncExtMult CS) . [z2,p1]) . q) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . q) + (((RealFuncExtMult CS) . [z2,p1]) . q)) + (((RealFuncExtMult CS) . [z1,p2]) . q) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . q) + (((RealFuncExtMult CS) . [z2,p1]) . q)) + (((RealFuncExtMult CS) . [z1,p2]) . q)) + (((RealFuncExtMult CS) . [x2,r]) . q) is V24() V25() Element of REAL
x2 * (r . q) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . q) + (((RealFuncExtMult CS) . [z2,p1]) . q)) + (((RealFuncExtMult CS) . [z1,p2]) . q)) + (x2 * (r . q)) is V24() V25() Element of REAL
z1 * (p2 . q) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . q) + (((RealFuncExtMult CS) . [z2,p1]) . q)) + (z1 * (p2 . q)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . q) + (((RealFuncExtMult CS) . [z2,p1]) . q)) + (z1 * (p2 . q))) + (x2 * (r . q)) is V24() V25() Element of REAL
z2 * (p1 . q) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [y,p]) . q) + (z2 * (p1 . q)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . q) + (z2 * (p1 . q))) + (z1 * (p2 . q)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . q) + (z2 * (p1 . q))) + (z1 * (p2 . q))) + (x2 * (r . q)) is V24() V25() Element of REAL
z2 * 0 is V24() V25() Element of REAL
(y * 0) + (z2 * 0) is V24() V25() Element of REAL
((y * 0) + (z2 * 0)) + (z1 * 0) is V24() V25() Element of REAL
x2 * 1 is V24() V25() Element of REAL
(((y * 0) + (z2 * 0)) + (z1 * 0)) + (x2 * 1) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))),((RealFuncExtMult CS) . [x2,r]))) . p1 is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))) . p1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [x2,r]) . p1 is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))) . p1) + (((RealFuncExtMult CS) . [x2,r]) . p1) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . p1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z1,p2]) . p1 is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . p1) + (((RealFuncExtMult CS) . [z1,p2]) . p1) is V24() V25() Element of REAL
((((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . p1) + (((RealFuncExtMult CS) . [z1,p2]) . p1)) + (((RealFuncExtMult CS) . [x2,r]) . p1) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p]) . p1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z2,p1]) . p1 is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [y,p]) . p1) + (((RealFuncExtMult CS) . [z2,p1]) . p1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . p1) + (((RealFuncExtMult CS) . [z2,p1]) . p1)) + (((RealFuncExtMult CS) . [z1,p2]) . p1) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . p1) + (((RealFuncExtMult CS) . [z2,p1]) . p1)) + (((RealFuncExtMult CS) . [z1,p2]) . p1)) + (((RealFuncExtMult CS) . [x2,r]) . p1) is V24() V25() Element of REAL
x2 * (r . p1) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . p1) + (((RealFuncExtMult CS) . [z2,p1]) . p1)) + (((RealFuncExtMult CS) . [z1,p2]) . p1)) + (x2 * (r . p1)) is V24() V25() Element of REAL
z1 * (p2 . p1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . p1) + (((RealFuncExtMult CS) . [z2,p1]) . p1)) + (z1 * (p2 . p1)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . p1) + (((RealFuncExtMult CS) . [z2,p1]) . p1)) + (z1 * (p2 . p1))) + (x2 * (r . p1)) is V24() V25() Element of REAL
z2 * (p1 . p1) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [y,p]) . p1) + (z2 * (p1 . p1)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . p1) + (z2 * (p1 . p1))) + (z1 * (p2 . p1)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . p1) + (z2 * (p1 . p1))) + (z1 * (p2 . p1))) + (x2 * (r . p1)) is V24() V25() Element of REAL
z1 * 1 is V24() V25() Element of REAL
((y * 0) + (z2 * 0)) + (z1 * 1) is V24() V25() Element of REAL
(((y * 0) + (z2 * 0)) + (z1 * 1)) + (x2 * 0) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))),((RealFuncExtMult CS) . [x2,r]))) . r1 is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))) . r1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [x2,r]) . r1 is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [z1,p2]))) . r1) + (((RealFuncExtMult CS) . [x2,r]) . r1) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . r1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z1,p2]) . r1 is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . r1) + (((RealFuncExtMult CS) . [z1,p2]) . r1) is V24() V25() Element of REAL
((((RealFuncAdd CS) . (((RealFuncExtMult CS) . [y,p]),((RealFuncExtMult CS) . [z2,p1]))) . r1) + (((RealFuncExtMult CS) . [z1,p2]) . r1)) + (((RealFuncExtMult CS) . [x2,r]) . r1) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p]) . r1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z2,p1]) . r1 is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [y,p]) . r1) + (((RealFuncExtMult CS) . [z2,p1]) . r1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . r1) + (((RealFuncExtMult CS) . [z2,p1]) . r1)) + (((RealFuncExtMult CS) . [z1,p2]) . r1) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . r1) + (((RealFuncExtMult CS) . [z2,p1]) . r1)) + (((RealFuncExtMult CS) . [z1,p2]) . r1)) + (((RealFuncExtMult CS) . [x2,r]) . r1) is V24() V25() Element of REAL
x2 * (r . r1) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . r1) + (((RealFuncExtMult CS) . [z2,p1]) . r1)) + (((RealFuncExtMult CS) . [z1,p2]) . r1)) + (x2 * (r . r1)) is V24() V25() Element of REAL
z1 * (p2 . r1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . r1) + (((RealFuncExtMult CS) . [z2,p1]) . r1)) + (z1 * (p2 . r1)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . r1) + (((RealFuncExtMult CS) . [z2,p1]) . r1)) + (z1 * (p2 . r1))) + (x2 * (r . r1)) is V24() V25() Element of REAL
z2 * (p1 . r1) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [y,p]) . r1) + (z2 * (p1 . r1)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [y,p]) . r1) + (z2 * (p1 . r1))) + (z1 * (p2 . r1)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [y,p]) . r1) + (z2 * (p1 . r1))) + (z1 * (p2 . r1))) + (x2 * (r . r1)) is V24() V25() Element of REAL
y * 1 is V24() V25() Element of REAL
(y * 1) + (z2 * 0) is V24() V25() Element of REAL
((y * 1) + (z2 * 0)) + (z1 * 0) is V24() V25() Element of REAL
(((y * 1) + (z2 * 0)) + (z1 * 0)) + (x2 * 0) is V24() V25() Element of REAL
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncZero CS is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K150(NAT,CS,0) is V7() V10(CS) V11( NAT ) Function-like quasi_total Element of K32(K33(CS,NAT))
K33(CS,NAT) is non empty set
K32(K33(CS,NAT)) is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
r is Element of CS
r1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r1 . p is V24() V25() Element of REAL
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p . r is V24() V25() Element of REAL
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 . p2 is V24() V25() Element of REAL
q is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
q . p1 is V24() V25() Element of REAL
q1 is V24() V25() Element of REAL
[q1,r1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [q1,r1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r is V24() V25() Element of REAL
[r,q] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [r,q] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q])) is set
(RealFuncAdd CS) . K4(((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q])) is set
y is V24() V25() Element of REAL
[y,p1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [y,p1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1])) is set
z2 is V24() V25() Element of REAL
[z2,p] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [z2,p] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p])) is set
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p2 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r1 is Element of CS
p . r1 is V24() V25() Element of REAL
p is Element of CS
p1 . p is V24() V25() Element of REAL
p1 is Element of CS
p2 . p1 is V24() V25() Element of REAL
q is Element of CS
{r1,p,p1,q} is non empty Element of K32(CS)
K32(CS) is non empty set
r . q is V24() V25() Element of REAL
p . q is V24() V25() Element of REAL
p1 . q is V24() V25() Element of REAL
r . p1 is V24() V25() Element of REAL
r . p is V24() V25() Element of REAL
p . p is V24() V25() Element of REAL
p2 . p is V24() V25() Element of REAL
r . r1 is V24() V25() Element of REAL
p1 . r1 is V24() V25() Element of REAL
p2 . r1 is V24() V25() Element of REAL
p2 . q is V24() V25() Element of REAL
q1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
q1 . r1 is V24() V25() Element of REAL
r is V24() V25() Element of REAL
[r,p] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [r,p] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
q1 . p is V24() V25() Element of REAL
y is V24() V25() Element of REAL
[y,p1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [y,p1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1])) is set
(RealFuncAdd CS) . K4(((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1])) is set
q1 . p1 is V24() V25() Element of REAL
z2 is V24() V25() Element of REAL
[z2,p2] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [z2,p2] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2])) is set
q1 . q is V24() V25() Element of REAL
z1 is V24() V25() Element of REAL
[z1,r] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [z1,r] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))),((RealFuncExtMult CS) . [z1,r])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))),((RealFuncExtMult CS) . [z1,r])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))),((RealFuncExtMult CS) . [z1,r])) is set
p . p1 is V24() V25() Element of REAL
p1 . p1 is V24() V25() Element of REAL
x2 is Element of CS
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))),((RealFuncExtMult CS) . [z1,r]))) . p is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))) . p is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z1,r]) . p is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))) . p) + (((RealFuncExtMult CS) . [z1,r]) . p) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . p is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z2,p2]) . p is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . p) + (((RealFuncExtMult CS) . [z2,p2]) . p) is V24() V25() Element of REAL
((((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . p) + (((RealFuncExtMult CS) . [z2,p2]) . p)) + (((RealFuncExtMult CS) . [z1,r]) . p) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [r,p]) . p is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p1]) . p is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [r,p]) . p) + (((RealFuncExtMult CS) . [y,p1]) . p) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . p) + (((RealFuncExtMult CS) . [y,p1]) . p)) + (((RealFuncExtMult CS) . [z2,p2]) . p) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . p) + (((RealFuncExtMult CS) . [y,p1]) . p)) + (((RealFuncExtMult CS) . [z2,p2]) . p)) + (((RealFuncExtMult CS) . [z1,r]) . p) is V24() V25() Element of REAL
z1 * (r . p) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . p) + (((RealFuncExtMult CS) . [y,p1]) . p)) + (((RealFuncExtMult CS) . [z2,p2]) . p)) + (z1 * (r . p)) is V24() V25() Element of REAL
z2 * (p2 . p) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . p) + (((RealFuncExtMult CS) . [y,p1]) . p)) + (z2 * (p2 . p)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . p) + (((RealFuncExtMult CS) . [y,p1]) . p)) + (z2 * (p2 . p))) + (z1 * (r . p)) is V24() V25() Element of REAL
y * (p1 . p) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [r,p]) . p) + (y * (p1 . p)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . p) + (y * (p1 . p))) + (z2 * (p2 . p)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . p) + (y * (p1 . p))) + (z2 * (p2 . p))) + (z1 * (r . p)) is V24() V25() Element of REAL
r * 0 is V24() V25() Element of REAL
y * 1 is V24() V25() Element of REAL
(r * 0) + (y * 1) is V24() V25() Element of REAL
z2 * 0 is V24() V25() Element of REAL
((r * 0) + (y * 1)) + (z2 * 0) is V24() V25() Element of REAL
z1 * 0 is V24() V25() Element of REAL
(((r * 0) + (y * 1)) + (z2 * 0)) + (z1 * 0) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))),((RealFuncExtMult CS) . [z1,r]))) . q is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))) . q is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z1,r]) . q is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))) . q) + (((RealFuncExtMult CS) . [z1,r]) . q) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . q is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z2,p2]) . q is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . q) + (((RealFuncExtMult CS) . [z2,p2]) . q) is V24() V25() Element of REAL
((((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . q) + (((RealFuncExtMult CS) . [z2,p2]) . q)) + (((RealFuncExtMult CS) . [z1,r]) . q) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [r,p]) . q is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p1]) . q is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [r,p]) . q) + (((RealFuncExtMult CS) . [y,p1]) . q) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . q) + (((RealFuncExtMult CS) . [y,p1]) . q)) + (((RealFuncExtMult CS) . [z2,p2]) . q) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . q) + (((RealFuncExtMult CS) . [y,p1]) . q)) + (((RealFuncExtMult CS) . [z2,p2]) . q)) + (((RealFuncExtMult CS) . [z1,r]) . q) is V24() V25() Element of REAL
z1 * (r . q) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . q) + (((RealFuncExtMult CS) . [y,p1]) . q)) + (((RealFuncExtMult CS) . [z2,p2]) . q)) + (z1 * (r . q)) is V24() V25() Element of REAL
z2 * (p2 . q) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . q) + (((RealFuncExtMult CS) . [y,p1]) . q)) + (z2 * (p2 . q)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . q) + (((RealFuncExtMult CS) . [y,p1]) . q)) + (z2 * (p2 . q))) + (z1 * (r . q)) is V24() V25() Element of REAL
y * (p1 . q) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [r,p]) . q) + (y * (p1 . q)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . q) + (y * (p1 . q))) + (z2 * (p2 . q)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . q) + (y * (p1 . q))) + (z2 * (p2 . q))) + (z1 * (r . q)) is V24() V25() Element of REAL
y * 0 is V24() V25() Element of REAL
(r * 0) + (y * 0) is V24() V25() Element of REAL
((r * 0) + (y * 0)) + (z2 * 0) is V24() V25() Element of REAL
z1 * 1 is V24() V25() Element of REAL
(((r * 0) + (y * 0)) + (z2 * 0)) + (z1 * 1) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))),((RealFuncExtMult CS) . [z1,r]))) . p1 is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))) . p1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z1,r]) . p1 is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))) . p1) + (((RealFuncExtMult CS) . [z1,r]) . p1) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . p1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z2,p2]) . p1 is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . p1) + (((RealFuncExtMult CS) . [z2,p2]) . p1) is V24() V25() Element of REAL
((((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . p1) + (((RealFuncExtMult CS) . [z2,p2]) . p1)) + (((RealFuncExtMult CS) . [z1,r]) . p1) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [r,p]) . p1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p1]) . p1 is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [r,p]) . p1) + (((RealFuncExtMult CS) . [y,p1]) . p1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . p1) + (((RealFuncExtMult CS) . [y,p1]) . p1)) + (((RealFuncExtMult CS) . [z2,p2]) . p1) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . p1) + (((RealFuncExtMult CS) . [y,p1]) . p1)) + (((RealFuncExtMult CS) . [z2,p2]) . p1)) + (((RealFuncExtMult CS) . [z1,r]) . p1) is V24() V25() Element of REAL
z1 * (r . p1) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . p1) + (((RealFuncExtMult CS) . [y,p1]) . p1)) + (((RealFuncExtMult CS) . [z2,p2]) . p1)) + (z1 * (r . p1)) is V24() V25() Element of REAL
z2 * (p2 . p1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . p1) + (((RealFuncExtMult CS) . [y,p1]) . p1)) + (z2 * (p2 . p1)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . p1) + (((RealFuncExtMult CS) . [y,p1]) . p1)) + (z2 * (p2 . p1))) + (z1 * (r . p1)) is V24() V25() Element of REAL
y * (p1 . p1) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [r,p]) . p1) + (y * (p1 . p1)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . p1) + (y * (p1 . p1))) + (z2 * (p2 . p1)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . p1) + (y * (p1 . p1))) + (z2 * (p2 . p1))) + (z1 * (r . p1)) is V24() V25() Element of REAL
z2 * 1 is V24() V25() Element of REAL
((r * 0) + (y * 0)) + (z2 * 1) is V24() V25() Element of REAL
(((r * 0) + (y * 0)) + (z2 * 1)) + (z1 * 0) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))),((RealFuncExtMult CS) . [z1,r]))) . r1 is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))) . r1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z1,r]) . r1 is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))) . r1) + (((RealFuncExtMult CS) . [z1,r]) . r1) is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . r1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [z2,p2]) . r1 is V24() V25() Element of REAL
(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . r1) + (((RealFuncExtMult CS) . [z2,p2]) . r1) is V24() V25() Element of REAL
((((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))) . r1) + (((RealFuncExtMult CS) . [z2,p2]) . r1)) + (((RealFuncExtMult CS) . [z1,r]) . r1) is V24() V25() Element of REAL
((RealFuncExtMult CS) . [r,p]) . r1 is V24() V25() Element of REAL
((RealFuncExtMult CS) . [y,p1]) . r1 is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [r,p]) . r1) + (((RealFuncExtMult CS) . [y,p1]) . r1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . r1) + (((RealFuncExtMult CS) . [y,p1]) . r1)) + (((RealFuncExtMult CS) . [z2,p2]) . r1) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . r1) + (((RealFuncExtMult CS) . [y,p1]) . r1)) + (((RealFuncExtMult CS) . [z2,p2]) . r1)) + (((RealFuncExtMult CS) . [z1,r]) . r1) is V24() V25() Element of REAL
z1 * (r . r1) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . r1) + (((RealFuncExtMult CS) . [y,p1]) . r1)) + (((RealFuncExtMult CS) . [z2,p2]) . r1)) + (z1 * (r . r1)) is V24() V25() Element of REAL
z2 * (p2 . r1) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . r1) + (((RealFuncExtMult CS) . [y,p1]) . r1)) + (z2 * (p2 . r1)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . r1) + (((RealFuncExtMult CS) . [y,p1]) . r1)) + (z2 * (p2 . r1))) + (z1 * (r . r1)) is V24() V25() Element of REAL
y * (p1 . r1) is V24() V25() Element of REAL
(((RealFuncExtMult CS) . [r,p]) . r1) + (y * (p1 . r1)) is V24() V25() Element of REAL
((((RealFuncExtMult CS) . [r,p]) . r1) + (y * (p1 . r1))) + (z2 * (p2 . r1)) is V24() V25() Element of REAL
(((((RealFuncExtMult CS) . [r,p]) . r1) + (y * (p1 . r1))) + (z2 * (p2 . r1))) + (z1 * (r . r1)) is V24() V25() Element of REAL
r * 1 is V24() V25() Element of REAL
(r * 1) + (y * 0) is V24() V25() Element of REAL
((r * 1) + (y * 0)) + (z2 * 0) is V24() V25() Element of REAL
(((r * 1) + (y * 0)) + (z2 * 0)) + (z1 * 0) is V24() V25() Element of REAL
q1 . x2 is V24() V25() Element of REAL
((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [r,p]),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p2]))),((RealFuncExtMult CS) . [z1,r]))) . x2 is V24() V25() Element of REAL
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
r is Element of CS
{p,p1,p2,r} is non empty Element of K32(CS)
K32(CS) is non empty set
r1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r1 . p is V24() V25() Element of REAL
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p . r is V24() V25() Element of REAL
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 . p2 is V24() V25() Element of REAL
q is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
q . p1 is V24() V25() Element of REAL
q1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
CS is non empty set
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncZero CS is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K150(NAT,CS,0) is V7() V10(CS) V11( NAT ) Function-like quasi_total Element of K32(K33(CS,NAT))
K33(CS,NAT) is non empty set
K32(K33(CS,NAT)) is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
r is Element of CS
{p,p1,p2,r} is non empty Element of K32(CS)
K32(CS) is non empty set
r1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r1 . p is V24() V25() Element of REAL
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p . r is V24() V25() Element of REAL
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 . p2 is V24() V25() Element of REAL
q is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
q . p1 is V24() V25() Element of REAL
q1 is V24() V25() Element of REAL
[q1,r1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [q1,r1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
r is V24() V25() Element of REAL
[r,q] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [r,q] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q])) is set
(RealFuncAdd CS) . K4(((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q])) is set
y is V24() V25() Element of REAL
[y,p1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [y,p1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1])) is set
z2 is V24() V25() Element of REAL
[z2,p] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [z2,p] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [q1,r1]),((RealFuncExtMult CS) . [r,q]))),((RealFuncExtMult CS) . [y,p1]))),((RealFuncExtMult CS) . [z2,p])) is set
z1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
2 is non empty V17() V18() V19() V23() V24() V25() Element of NAT
3 is non empty V17() V18() V19() V23() V24() V25() Element of NAT
{0,1,2,3} is non empty Element of K32(NAT)
CS is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
r is Element of CS
{p,p1,p2,r} is non empty Element of K32(CS)
K32(CS) is non empty set
CS is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
r is Element of CS
{p,p1,p2,r} is non empty Element of K32(CS)
K32(CS) is non empty set
CS is non empty set
p is Element of CS
p1 is Element of CS
p2 is Element of CS
r is Element of CS
{p,p1,p2,r} is non empty Element of K32(CS)
K32(CS) is non empty set
RealVectSpace CS is non empty V70() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs (CS,REAL) is non empty FUNCTION_DOMAIN of CS, REAL
RealFuncZero CS is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K150(NAT,CS,0) is V7() V10(CS) V11( NAT ) Function-like quasi_total Element of K32(K33(CS,NAT))
K33(CS,NAT) is non empty set
K32(K33(CS,NAT)) is non empty set
RealFuncAdd CS is V7() V10(K33((Funcs (CS,REAL)),(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33((Funcs (CS,REAL)),(Funcs (CS,REAL))) is non empty set
K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33((Funcs (CS,REAL)),(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RealFuncExtMult CS is V7() V10(K33(REAL,(Funcs (CS,REAL)))) V11( Funcs (CS,REAL)) Function-like quasi_total Element of K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))))
K33(REAL,(Funcs (CS,REAL))) is non empty set
K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL))) is non empty set
K32(K33(K33(REAL,(Funcs (CS,REAL))),(Funcs (CS,REAL)))) is non empty set
RLSStruct(# (Funcs (CS,REAL)),(RealFuncZero CS),(RealFuncAdd CS),(RealFuncExtMult CS) #) is strict RLSStruct
p is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
p1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
q is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
q1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
the U1 of (RealVectSpace CS) is non empty set
r is Element of the U1 of (RealVectSpace CS)
y is Element of the U1 of (RealVectSpace CS)
z2 is Element of the U1 of (RealVectSpace CS)
z1 is Element of the U1 of (RealVectSpace CS)
0. (RealVectSpace CS) is zero Element of the U1 of (RealVectSpace CS)
the U2 of (RealVectSpace CS) is Element of the U1 of (RealVectSpace CS)
x2 is V24() V25() Element of REAL
x2 * r is Element of the U1 of (RealVectSpace CS)
the Mult of (RealVectSpace CS) is V7() V10(K33(REAL, the U1 of (RealVectSpace CS))) V11( the U1 of (RealVectSpace CS)) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)))
K33(REAL, the U1 of (RealVectSpace CS)) is non empty set
K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)) is non empty set
K32(K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS))) is non empty set
K138( the Mult of (RealVectSpace CS),x2,r) is set
K4(x2,r) is set
the Mult of (RealVectSpace CS) . K4(x2,r) is set
z1 is V24() V25() Element of REAL
z1 * y is Element of the U1 of (RealVectSpace CS)
K138( the Mult of (RealVectSpace CS),z1,y) is set
K4(z1,y) is set
the Mult of (RealVectSpace CS) . K4(z1,y) is set
(x2 * r) + (z1 * y) is Element of the U1 of (RealVectSpace CS)
the U5 of (RealVectSpace CS) is V7() V10(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS))) V11( the U1 of (RealVectSpace CS)) Function-like quasi_total Element of K32(K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)))
K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)) is non empty set
K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)) is non empty set
K32(K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS))) is non empty set
K142( the U1 of (RealVectSpace CS), the U5 of (RealVectSpace CS),(x2 * r),(z1 * y)) is Element of the U1 of (RealVectSpace CS)
K4((x2 * r),(z1 * y)) is set
the U5 of (RealVectSpace CS) . K4((x2 * r),(z1 * y)) is set
z1 is V24() V25() Element of REAL
z1 * z2 is Element of the U1 of (RealVectSpace CS)
K138( the Mult of (RealVectSpace CS),z1,z2) is set
K4(z1,z2) is set
the Mult of (RealVectSpace CS) . K4(z1,z2) is set
((x2 * r) + (z1 * y)) + (z1 * z2) is Element of the U1 of (RealVectSpace CS)
K142( the U1 of (RealVectSpace CS), the U5 of (RealVectSpace CS),((x2 * r) + (z1 * y)),(z1 * z2)) is Element of the U1 of (RealVectSpace CS)
K4(((x2 * r) + (z1 * y)),(z1 * z2)) is set
the U5 of (RealVectSpace CS) . K4(((x2 * r) + (z1 * y)),(z1 * z2)) is set
z2 is V24() V25() Element of REAL
z2 * z1 is Element of the U1 of (RealVectSpace CS)
K138( the Mult of (RealVectSpace CS),z2,z1) is set
K4(z2,z1) is set
the Mult of (RealVectSpace CS) . K4(z2,z1) is set
(((x2 * r) + (z1 * y)) + (z1 * z2)) + (z2 * z1) is Element of the U1 of (RealVectSpace CS)
K142( the U1 of (RealVectSpace CS), the U5 of (RealVectSpace CS),(((x2 * r) + (z1 * y)) + (z1 * z2)),(z2 * z1)) is Element of the U1 of (RealVectSpace CS)
K4((((x2 * r) + (z1 * y)) + (z1 * z2)),(z2 * z1)) is set
the U5 of (RealVectSpace CS) . K4((((x2 * r) + (z1 * y)) + (z1 * z2)),(z2 * z1)) is set
x2 is Element of the U1 of (RealVectSpace CS)
z1 is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
z1 is V24() V25() Element of REAL
[z1,p] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [z1,p] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
z2 is V24() V25() Element of REAL
[z2,p1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [z2,p1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,p]),((RealFuncExtMult CS) . [z2,p1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncExtMult CS) . [z1,p]),((RealFuncExtMult CS) . [z2,p1])) is set
(RealFuncAdd CS) . K4(((RealFuncExtMult CS) . [z1,p]),((RealFuncExtMult CS) . [z2,p1])) is set
p199 is V24() V25() Element of REAL
[p199,q] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [p199,q] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [p199,q])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [p199,q])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [p199,q])) is set
p39 is V24() V25() Element of REAL
[p39,q1] is Element of K33(REAL,(Funcs (CS,REAL)))
(RealFuncExtMult CS) . [p39,q1] is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
(RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [p199,q]))),((RealFuncExtMult CS) . [p39,q1])) is V7() V10(CS) V11( REAL ) Function-like quasi_total Element of Funcs (CS,REAL)
K4(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [p199,q]))),((RealFuncExtMult CS) . [p39,q1])) is set
(RealFuncAdd CS) . K4(((RealFuncAdd CS) . (((RealFuncAdd CS) . (((RealFuncExtMult CS) . [z1,p]),((RealFuncExtMult CS) . [z2,p1]))),((RealFuncExtMult CS) . [p199,q]))),((RealFuncExtMult CS) . [p39,q1])) is set
z1 * r is Element of the U1 of (RealVectSpace CS)
the Mult of (RealVectSpace CS) is V7() V10(K33(REAL, the U1 of (RealVectSpace CS))) V11( the U1 of (RealVectSpace CS)) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)))
K33(REAL, the U1 of (RealVectSpace CS)) is non empty set
K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)) is non empty set
K32(K33(K33(REAL, the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS))) is non empty set
K138( the Mult of (RealVectSpace CS),z1,r) is set
K4(z1,r) is set
the Mult of (RealVectSpace CS) . K4(z1,r) is set
z2 * y is Element of the U1 of (RealVectSpace CS)
K138( the Mult of (RealVectSpace CS),z2,y) is set
K4(z2,y) is set
the Mult of (RealVectSpace CS) . K4(z2,y) is set
(z1 * r) + (z2 * y) is Element of the U1 of (RealVectSpace CS)
the U5 of (RealVectSpace CS) is V7() V10(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS))) V11( the U1 of (RealVectSpace CS)) Function-like quasi_total Element of K32(K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)))
K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)) is non empty set
K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS)) is non empty set
K32(K33(K33( the U1 of (RealVectSpace CS), the U1 of (RealVectSpace CS)), the U1 of (RealVectSpace CS))) is non empty set
K142( the U1 of (RealVectSpace CS), the U5 of (RealVectSpace CS),(z1 * r),(z2 * y)) is Element of the U1 of (RealVectSpace CS)
K4((z1 * r),(z2 * y)) is set
the U5 of (RealVectSpace CS) . K4((z1 * r),(z2 * y)) is set
p199 * z2 is Element of the U1 of (RealVectSpace CS)
K138( the Mult of (RealVectSpace CS),p199,z2) is set
K4(p199,z2) is set
the Mult of (RealVectSpace CS) . K4(p199,z2) is set
((z1 * r) + (z2 * y)) + (p199 * z2) is Element of the U1 of (RealVectSpace CS)
K142( the U1 of (RealVectSpace CS), the U5 of (RealVectSpace CS),((z1 * r) + (z2 * y)),(p199 * z2)) is Element of the U1 of (RealVectSpace CS)
K4(((z1 * r) + (z2 * y)),(p199 * z2)) is set
the U5 of (RealVectSpace CS) . K4(((z1 * r) + (z2 * y)),(p199 * z2)) is set
p39 * z1 is Element of the U1 of (RealVectSpace CS)
K138( the Mult of (RealVectSpace CS),p39,z1) is set
K4(p39,z1) is set
the Mult of (RealVectSpace CS) . K4(p39,z1) is set
(((z1 * r) + (z2 * y)) + (p199 * z2)) + (p39 * z1) is Element of the U1 of (RealVectSpace CS)
K142( the U1 of (RealVectSpace CS), the U5 of (RealVectSpace CS),(((z1 * r) + (z2 * y)) + (p199 * z2)),(p39 * z1)) is Element of the U1 of (RealVectSpace CS)
K4((((z1 * r) + (z2 * y)) + (p199 * z2)),(p39 * z1)) is set
the U5 of (RealVectSpace CS) . K4((((z1 * r) + (z2 * y)) + (p199 * z2)),(p39 * z1)) is set
x2 is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of x2 is non empty non trivial set
0. x2 is zero Element of the U1 of x2
the U2 of x2 is Element of the U1 of x2
z1 is Element of the U1 of x2
z1 is Element of the U1 of x2
z2 is Element of the U1 of x2
p199 is Element of the U1 of x2
p39 is V24() V25() Element of REAL
p39 * z1 is Element of the U1 of x2
the Mult of x2 is V7() V10(K33(REAL, the U1 of x2)) V11( the U1 of x2) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of x2), the U1 of x2))
K33(REAL, the U1 of x2) is non empty set
K33(K33(REAL, the U1 of x2), the U1 of x2) is non empty set
K32(K33(K33(REAL, the U1 of x2), the U1 of x2)) is non empty set
K138( the Mult of x2,p39,z1) is set
K4(p39,z1) is set
the Mult of x2 . K4(p39,z1) is set
o9 is V24() V25() Element of REAL
o9 * z1 is Element of the U1 of x2
K138( the Mult of x2,o9,z1) is set
K4(o9,z1) is set
the Mult of x2 . K4(o9,z1) is set
(p39 * z1) + (o9 * z1) is Element of the U1 of x2
the U5 of x2 is V7() V10(K33( the U1 of x2, the U1 of x2)) V11( the U1 of x2) Function-like quasi_total Element of K32(K33(K33( the U1 of x2, the U1 of x2), the U1 of x2))
K33( the U1 of x2, the U1 of x2) is non empty set
K33(K33( the U1 of x2, the U1 of x2), the U1 of x2) is non empty set
K32(K33(K33( the U1 of x2, the U1 of x2), the U1 of x2)) is non empty set
K142( the U1 of x2, the U5 of x2,(p39 * z1),(o9 * z1)) is Element of the U1 of x2
K4((p39 * z1),(o9 * z1)) is set
the U5 of x2 . K4((p39 * z1),(o9 * z1)) is set
p19 is V24() V25() Element of REAL
p19 * z2 is Element of the U1 of x2
K138( the Mult of x2,p19,z2) is set
K4(p19,z2) is set
the Mult of x2 . K4(p19,z2) is set
((p39 * z1) + (o9 * z1)) + (p19 * z2) is Element of the U1 of x2
K142( the U1 of x2, the U5 of x2,((p39 * z1) + (o9 * z1)),(p19 * z2)) is Element of the U1 of x2
K4(((p39 * z1) + (o9 * z1)),(p19 * z2)) is set
the U5 of x2 . K4(((p39 * z1) + (o9 * z1)),(p19 * z2)) is set
p29 is V24() V25() Element of REAL
p29 * p199 is Element of the U1 of x2
K138( the Mult of x2,p29,p199) is set
K4(p29,p199) is set
the Mult of x2 . K4(p29,p199) is set
(((p39 * z1) + (o9 * z1)) + (p19 * z2)) + (p29 * p199) is Element of the U1 of x2
K142( the U1 of x2, the U5 of x2,(((p39 * z1) + (o9 * z1)) + (p19 * z2)),(p29 * p199)) is Element of the U1 of x2
K4((((p39 * z1) + (o9 * z1)) + (p19 * z2)),(p29 * p199)) is set
the U5 of x2 . K4((((p39 * z1) + (o9 * z1)) + (p19 * z2)),(p29 * p199)) is set
q1999 is Element of the U1 of x2
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
CS is non empty V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
1 * p2 is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,1,p2) is set
K4(1,p2) is set
the Mult of CS . K4(1,p2) is set
0 * p is Element of the U1 of CS
K138( the Mult of CS,0,p) is set
K4(0,p) is set
the Mult of CS . K4(0,p) is set
0 * p1 is Element of the U1 of CS
K138( the Mult of CS,0,p1) is set
K4(0,p1) is set
the Mult of CS . K4(0,p1) is set
(0 * p) + (0 * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(0 * p),(0 * p1)) is Element of the U1 of CS
K4((0 * p),(0 * p1)) is set
the U5 of CS . K4((0 * p),(0 * p1)) is set
((0 * p) + (0 * p1)) + (1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((0 * p) + (0 * p1)),(1 * p2)) is Element of the U1 of CS
K4(((0 * p) + (0 * p1)),(1 * p2)) is set
the U5 of CS . K4(((0 * p) + (0 * p1)),(1 * p2)) is set
CS is non empty CollStr
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
[p,p1,p] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
K34( the U1 of CS, the U1 of CS, the U1 of CS) is non empty set
the Collinearity of CS is Relation3 of the U1 of CS
[p,p,p1] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
[p,p1,p1] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
[p,p1,p2] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
[p,p1,r1] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
K34( the U1 of CS, the U1 of CS, the U1 of CS) is non empty set
the Collinearity of CS is Relation3 of the U1 of CS
[p,p1,p2] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
[p,p1,r] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
[p2,r,r1] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
[p,p1,p2] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
r is Element of the U1 of CS
[p,p1,r] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
r1 is Element of the U1 of CS
[p,p1,r1] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
[p2,r,r1] is Element of K34( the U1 of CS, the U1 of CS, the U1 of CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
the U1 of CS is non empty non trivial set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
[p,p1,p2] is Element of K34( the U1 of (ProjectiveSpace CS), the U1 of (ProjectiveSpace CS), the U1 of (ProjectiveSpace CS))
K34( the U1 of (ProjectiveSpace CS), the U1 of (ProjectiveSpace CS), the U1 of (ProjectiveSpace CS)) is non empty set
the Collinearity of (ProjectiveSpace CS) is Relation3 of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of CS
Dir r is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
r1 is Element of the U1 of CS
Dir r1 is Element of K32(K175(CS))
p is Element of the U1 of CS
Dir p is Element of K32(K175(CS))
p1 is Element of the U1 of CS
Dir p1 is Element of K32(K175(CS))
q is Element of the U1 of CS
Dir q is Element of K32(K175(CS))
q1 is Element of the U1 of CS
Dir q1 is Element of K32(K175(CS))
r is Element of the U1 of CS
Dir r is Element of K32(K175(CS))
r1 is Element of the U1 of CS
Dir r1 is Element of K32(K175(CS))
p is Element of the U1 of CS
Dir p is Element of K32(K175(CS))
r is Element of the U1 of CS
Dir r is Element of K32(K175(CS))
r1 is Element of the U1 of CS
Dir r1 is Element of K32(K175(CS))
p is Element of the U1 of CS
Dir p is Element of K32(K175(CS))
p1 is Element of the U1 of CS
Dir p1 is Element of K32(K175(CS))
q is Element of the U1 of CS
Dir q is Element of K32(K175(CS))
q1 is Element of the U1 of CS
Dir q1 is Element of K32(K175(CS))
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
the U1 of CS is non empty non trivial set
p2 is Element of the U1 of CS
Dir p2 is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
r is Element of the U1 of CS
Dir r is Element of K32(K175(CS))
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
the U1 of CS is non empty non trivial set
p is Element of the U1 of CS
Dir p is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
p1 is Element of the U1 of CS
Dir p1 is Element of K32(K175(CS))
q is Element of the U1 of CS
Dir q is Element of K32(K175(CS))
q1 is Element of the U1 of CS
Dir q1 is Element of K32(K175(CS))
r is Element of the U1 of CS
Dir r is Element of K32(K175(CS))
y is Element of the U1 of CS
Dir y is Element of K32(K175(CS))
z2 is Element of the U1 of CS
Dir z2 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
x2 is Element of the U1 of CS
Dir x2 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
the U1 of CS is non empty non trivial set
r is Element of the U1 of CS
Dir r is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
r1 is Element of the U1 of CS
Dir r1 is Element of K32(K175(CS))
p is Element of the U1 of CS
Dir p is Element of K32(K175(CS))
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
the U1 of CS is non empty non trivial set
p is Element of the U1 of CS
Dir p is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
p1 is Element of the U1 of CS
Dir p1 is Element of K32(K175(CS))
q is Element of the U1 of CS
Dir q is Element of K32(K175(CS))
q1 is Element of the U1 of CS
Dir q1 is Element of K32(K175(CS))
r is Element of the U1 of CS
Dir r is Element of K32(K175(CS))
y is Element of the U1 of CS
Dir y is Element of K32(K175(CS))
z2 is Element of the U1 of CS
Dir z2 is Element of K32(K175(CS))
z1 is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
the U1 of (ProjectiveSpace CS) is non empty set
Dir p is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
Dir p1 is Element of K32(K175(CS))
Dir p2 is Element of K32(K175(CS))
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
[(Dir p),(Dir p1),(Dir p2)] is Element of K34(K32(K175(CS)),K32(K175(CS)),K32(K175(CS)))
K34(K32(K175(CS)),K32(K175(CS)),K32(K175(CS))) is non empty set
the Collinearity of (ProjectiveSpace CS) is Relation3 of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
p is Element of the U1 of CS
p1 is Element of the U1 of CS
the U1 of (ProjectiveSpace CS) is non empty set
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of CS
Dir r1 is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
p is Element of the U1 of CS
Dir p is Element of K32(K175(CS))
p1 is Element of the U1 of CS
Dir p1 is Element of K32(K175(CS))
q is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is V24() V25() Element of REAL
r * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,r,p) is set
K4(r,p) is set
the Mult of CS . K4(r,p) is set
r1 is V24() V25() Element of REAL
r1 * p1 is Element of the U1 of CS
K138( the Mult of CS,r1,p1) is set
K4(r1,p1) is set
the Mult of CS . K4(r1,p1) is set
(r * p) + (r1 * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(r * p),(r1 * p1)) is Element of the U1 of CS
K4((r * p),(r1 * p1)) is set
the U5 of CS . K4((r * p),(r1 * p1)) is set
((r * p) + (r1 * p1)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (r1 * p1)),(0. CS)) is Element of the U1 of CS
K4(((r * p) + (r1 * p1)),(0. CS)) is set
the U5 of CS . K4(((r * p) + (r1 * p1)),(0. CS)) is set
0 * p2 is Element of the U1 of CS
K138( the Mult of CS,0,p2) is set
K4(0,p2) is set
the Mult of CS . K4(0,p2) is set
((r * p) + (r1 * p1)) + (0 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r * p) + (r1 * p1)),(0 * p2)) is Element of the U1 of CS
K4(((r * p) + (r1 * p1)),(0 * p2)) is set
the U5 of CS . K4(((r * p) + (r1 * p1)),(0 * p2)) is set
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive proper () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
ProjectiveSpace the non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct is non empty strict reflexive transitive proper () () CollStr
ProjectivePoints the non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct is non empty set
ProjectiveCollinearity the non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct is Relation3 of ProjectivePoints the non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
CollStr(# (ProjectivePoints the non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct ),(ProjectiveCollinearity the non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct ) #) is strict CollStr
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
the U1 of CS is non empty non trivial set
q is Element of the U1 of CS
Dir q is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
q1 is Element of the U1 of CS
Dir q1 is Element of K32(K175(CS))
r is Element of the U1 of CS
Dir r is Element of K32(K175(CS))
y is Element of the U1 of CS
Dir y is Element of K32(K175(CS))
z2 is Element of the U1 of CS
Dir z2 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
x2 is Element of the U1 of CS
Dir x2 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
z2 is Element of the U1 of CS
Dir z2 is Element of K32(K175(CS))
p199 is Element of the U1 of CS
Dir p199 is Element of K32(K175(CS))
p39 is Element of the U1 of CS
Dir p39 is Element of K32(K175(CS))
o9 is Element of the U1 of CS
Dir o9 is Element of K32(K175(CS))
p19 is Element of the U1 of CS
Dir p19 is Element of K32(K175(CS))
p29 is Element of the U1 of CS
Dir p29 is Element of K32(K175(CS))
q1999 is Element of the U1 of CS
Dir q1999 is Element of K32(K175(CS))
p2999 is Element of the U1 of CS
Dir p2999 is Element of K32(K175(CS))
r399 is Element of the U1 of CS
Dir r399 is Element of K32(K175(CS))
p29999 is Element of the U1 of CS
Dir p29999 is Element of K32(K175(CS))
q3999 is Element of the U1 of CS
Dir q3999 is Element of K32(K175(CS))
r19 is Element of the U1 of CS
Dir r19 is Element of K32(K175(CS))
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive proper () () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive proper () () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
the U1 of CS is non empty non trivial set
y is Element of the U1 of CS
Dir y is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
z2 is Element of the U1 of CS
Dir z2 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
x2 is Element of the U1 of CS
Dir x2 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
z2 is Element of the U1 of CS
Dir z2 is Element of K32(K175(CS))
p199 is Element of the U1 of CS
Dir p199 is Element of K32(K175(CS))
p39 is Element of the U1 of CS
Dir p39 is Element of K32(K175(CS))
o9 is Element of the U1 of CS
Dir o9 is Element of K32(K175(CS))
p19 is Element of the U1 of CS
Dir p19 is Element of K32(K175(CS))
p29 is Element of the U1 of CS
Dir p29 is Element of K32(K175(CS))
q1999 is Element of the U1 of CS
Dir q1999 is Element of K32(K175(CS))
p2999 is Element of the U1 of CS
Dir p2999 is Element of K32(K175(CS))
r399 is Element of the U1 of CS
Dir r399 is Element of K32(K175(CS))
p29999 is Element of the U1 of CS
Dir p29999 is Element of K32(K175(CS))
q3999 is Element of the U1 of CS
Dir q3999 is Element of K32(K175(CS))
r19 is Element of the U1 of CS
Dir r19 is Element of K32(K175(CS))
p19999 is Element of the U1 of CS
Dir p19999 is Element of K32(K175(CS))
q399 is Element of the U1 of CS
Dir q399 is Element of K32(K175(CS))
r29 is Element of the U1 of CS
Dir r29 is Element of K32(K175(CS))
p3999 is Element of the U1 of CS
Dir p3999 is Element of K32(K175(CS))
q29999 is Element of the U1 of CS
Dir q29999 is Element of K32(K175(CS))
r199 is Element of the U1 of CS
Dir r199 is Element of K32(K175(CS))
p399 is Element of the U1 of CS
Dir p399 is Element of K32(K175(CS))
q1999 is Element of the U1 of CS
Dir q1999 is Element of K32(K175(CS))
r299 is Element of the U1 of CS
Dir r299 is Element of K32(K175(CS))
p1999 is Element of the U1 of CS
Dir p1999 is Element of K32(K175(CS))
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive proper () () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
the U1 of CS is non empty non trivial set
y is Element of the U1 of CS
Dir y is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
z2 is Element of the U1 of CS
Dir z2 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
x2 is Element of the U1 of CS
Dir x2 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
z1 is Element of the U1 of CS
Dir z1 is Element of K32(K175(CS))
z2 is Element of the U1 of CS
Dir z2 is Element of K32(K175(CS))
p199 is Element of the U1 of CS
Dir p199 is Element of K32(K175(CS))
p39 is Element of the U1 of CS
Dir p39 is Element of K32(K175(CS))
o9 is Element of the U1 of CS
Dir o9 is Element of K32(K175(CS))
p19 is Element of the U1 of CS
Dir p19 is Element of K32(K175(CS))
p29 is Element of the U1 of CS
Dir p29 is Element of K32(K175(CS))
q1999 is Element of the U1 of CS
Dir q1999 is Element of K32(K175(CS))
p2999 is Element of the U1 of CS
Dir p2999 is Element of K32(K175(CS))
r399 is Element of the U1 of CS
Dir r399 is Element of K32(K175(CS))
p29999 is Element of the U1 of CS
Dir p29999 is Element of K32(K175(CS))
q3999 is Element of the U1 of CS
Dir q3999 is Element of K32(K175(CS))
r19 is Element of the U1 of CS
Dir r19 is Element of K32(K175(CS))
p19999 is Element of the U1 of CS
Dir p19999 is Element of K32(K175(CS))
q399 is Element of the U1 of CS
Dir q399 is Element of K32(K175(CS))
r29 is Element of the U1 of CS
Dir r29 is Element of K32(K175(CS))
p3999 is Element of the U1 of CS
Dir p3999 is Element of K32(K175(CS))
q29999 is Element of the U1 of CS
Dir q29999 is Element of K32(K175(CS))
r199 is Element of the U1 of CS
Dir r199 is Element of K32(K175(CS))
p399 is Element of the U1 of CS
Dir p399 is Element of K32(K175(CS))
q1999 is Element of the U1 of CS
Dir q1999 is Element of K32(K175(CS))
r299 is Element of the U1 of CS
Dir r299 is Element of K32(K175(CS))
p1999 is Element of the U1 of CS
Dir p1999 is Element of K32(K175(CS))
q2999 is Element of the U1 of CS
Dir q2999 is Element of K32(K175(CS))
r39 is Element of the U1 of CS
Dir r39 is Element of K32(K175(CS))
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive proper () () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
Dir p is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
Dir p1 is Element of K32(K175(CS))
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of CS
Dir q is Element of K32(K175(CS))
q1 is Element of the U1 of CS
Dir q1 is Element of K32(K175(CS))
r is Element of the U1 of CS
Dir r is Element of K32(K175(CS))
y is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
y is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
x2 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
p199 is Element of the U1 of (ProjectiveSpace CS)
o9 is Element of the U1 of (ProjectiveSpace CS)
p29 is Element of the U1 of (ProjectiveSpace CS)
p2999 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
p199 is Element of the U1 of (ProjectiveSpace CS)
o9 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
p199 is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
ProjectiveSpace r is non empty strict reflexive transitive proper () () () () () CollStr
ProjectivePoints r is non empty set
ProjectiveCollinearity r is Relation3 of ProjectivePoints r
CollStr(# (ProjectivePoints r),(ProjectiveCollinearity r) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is V24() V25() Element of REAL
r1 * p is Element of the U1 of CS
the Mult of CS is V7() V10(K33(REAL, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33(REAL, the U1 of CS), the U1 of CS))
K33(REAL, the U1 of CS) is non empty set
K33(K33(REAL, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33(REAL, the U1 of CS), the U1 of CS)) is non empty set
K138( the Mult of CS,r1,p) is set
K4(r1,p) is set
the Mult of CS . K4(r1,p) is set
p is V24() V25() Element of REAL
p * p1 is Element of the U1 of CS
K138( the Mult of CS,p,p1) is set
K4(p,p1) is set
the Mult of CS . K4(p,p1) is set
(r1 * p) + (p * p1) is Element of the U1 of CS
the U5 of CS is V7() V10(K33( the U1 of CS, the U1 of CS)) V11( the U1 of CS) Function-like quasi_total Element of K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS))
K33( the U1 of CS, the U1 of CS) is non empty set
K33(K33( the U1 of CS, the U1 of CS), the U1 of CS) is non empty set
K32(K33(K33( the U1 of CS, the U1 of CS), the U1 of CS)) is non empty set
K142( the U1 of CS, the U5 of CS,(r1 * p),(p * p1)) is Element of the U1 of CS
K4((r1 * p),(p * p1)) is set
the U5 of CS . K4((r1 * p),(p * p1)) is set
p1 is V24() V25() Element of REAL
p1 * p2 is Element of the U1 of CS
K138( the Mult of CS,p1,p2) is set
K4(p1,p2) is set
the Mult of CS . K4(p1,p2) is set
((r1 * p) + (p * p1)) + (p1 * p2) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,((r1 * p) + (p * p1)),(p1 * p2)) is Element of the U1 of CS
K4(((r1 * p) + (p * p1)),(p1 * p2)) is set
the U5 of CS . K4(((r1 * p) + (p * p1)),(p1 * p2)) is set
(((r1 * p) + (p * p1)) + (p1 * p2)) + (0. CS) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r1 * p) + (p * p1)) + (p1 * p2)),(0. CS)) is Element of the U1 of CS
K4((((r1 * p) + (p * p1)) + (p1 * p2)),(0. CS)) is set
the U5 of CS . K4((((r1 * p) + (p * p1)) + (p1 * p2)),(0. CS)) is set
0 * r is Element of the U1 of CS
K138( the Mult of CS,0,r) is set
K4(0,r) is set
the Mult of CS . K4(0,r) is set
(((r1 * p) + (p * p1)) + (p1 * p2)) + (0 * r) is Element of the U1 of CS
K142( the U1 of CS, the U5 of CS,(((r1 * p) + (p * p1)) + (p1 * p2)),(0 * r)) is Element of the U1 of CS
K4((((r1 * p) + (p * p1)) + (p1 * p2)),(0 * r)) is set
the U5 of CS . K4((((r1 * p) + (p * p1)) + (p1 * p2)),(0 * r)) is set
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
Dir p is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
Dir p1 is Element of K32(K175(CS))
Dir p2 is Element of K32(K175(CS))
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
[r1,p,p1] is Element of K34( the U1 of (ProjectiveSpace CS), the U1 of (ProjectiveSpace CS), the U1 of (ProjectiveSpace CS))
K34( the U1 of (ProjectiveSpace CS), the U1 of (ProjectiveSpace CS), the U1 of (ProjectiveSpace CS)) is non empty set
the Collinearity of (ProjectiveSpace CS) is Relation3 of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of CS
Dir r is Element of K32(K175(CS))
y is Element of the U1 of CS
Dir y is Element of K32(K175(CS))
z1 is Element of the U1 of CS
z2 is Element of the U1 of CS
Dir z2 is Element of K32(K175(CS))
Dir z1 is Element of K32(K175(CS))
x2 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
the U1 of (ProjectiveSpace CS) is non empty set
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
y is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
x2 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
p199 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
y is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
p2 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
p is non empty reflexive transitive proper () () CollStr
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
y is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
x2 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
x2 is Element of the U1 of (ProjectiveSpace CS)
z2 is Element of the U1 of (ProjectiveSpace CS)
z1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
y is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
y is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
y is Element of the U1 of (ProjectiveSpace CS)
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
q is Element of the U1 of (ProjectiveSpace CS)
q1 is Element of the U1 of (ProjectiveSpace CS)
y is Element of the U1 of (ProjectiveSpace CS)
r is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
the U1 of (ProjectiveSpace CS) is non empty set
r1 is Element of the U1 of (ProjectiveSpace CS)
p is Element of the U1 of (ProjectiveSpace CS)
p1 is Element of the U1 of (ProjectiveSpace CS)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is non empty reflexive transitive proper () () CollStr
the U1 of r1 is non empty set
Dir p is Element of K32(K175(CS))
K175(CS) is non empty Element of K32( the U1 of CS)
K32( the U1 of CS) is non empty set
[#] CS is non empty non proper Element of K32( the U1 of CS)
K1((0. CS)) is non empty set
([#] CS) \ K1((0. CS)) is Element of K32( the U1 of CS)
K32(K175(CS)) is non empty set
Dir p1 is Element of K32(K175(CS))
Dir p2 is Element of K32(K175(CS))
Dir r is Element of K32(K175(CS))
p is Element of the U1 of r1
p1 is Element of the U1 of r1
q is Element of the U1 of r1
q1 is Element of the U1 of r1
r is Element of the U1 of r1
r is Element of the U1 of r1
y is Element of the U1 of CS
Dir y is Element of K32(K175(CS))
[q,q1,r] is Element of K34( the U1 of r1, the U1 of r1, the U1 of r1)
K34( the U1 of r1, the U1 of r1, the U1 of r1) is non empty set
the Collinearity of (ProjectiveSpace CS) is Relation3 of the U1 of (ProjectiveSpace CS)
the U1 of (ProjectiveSpace CS) is non empty set
[p,p1,r] is Element of K34( the U1 of r1, the U1 of r1, the U1 of r1)
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
ProjectiveSpace CS is non empty strict reflexive transitive () CollStr
ProjectivePoints CS is non empty set
ProjectiveCollinearity CS is Relation3 of ProjectivePoints CS
CollStr(# (ProjectivePoints CS),(ProjectiveCollinearity CS) #) is strict CollStr
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
p is non empty reflexive transitive proper () () CollStr
p1 is non empty reflexive transitive proper () () CollStr
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
p is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
ProjectiveSpace p is non empty strict reflexive transitive proper () () () () () CollStr
ProjectivePoints p is non empty set
ProjectiveCollinearity p is Relation3 of ProjectivePoints p
CollStr(# (ProjectivePoints p),(ProjectiveCollinearity p) #) is strict CollStr
p1 is non empty strict reflexive transitive proper () () () () () CollStr
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p2 is non empty reflexive transitive proper () () CollStr
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
CS is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the U1 of CS is non empty non trivial set
0. CS is zero Element of the U1 of CS
the U2 of CS is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is non empty non trivial V70() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () RLSStruct
ProjectiveSpace p is non empty strict reflexive transitive proper () () () () () CollStr
ProjectivePoints p is non empty set
ProjectiveCollinearity p is Relation3 of ProjectivePoints p
CollStr(# (ProjectivePoints p),(ProjectiveCollinearity p) #) is strict CollStr
p1 is non empty strict reflexive transitive proper () () () () () CollStr
p2 is Element of the U1 of CS
r is Element of the U1 of CS
r1 is Element of the U1 of CS
p is Element of the U1 of CS
p2 is non empty reflexive transitive proper () () CollStr
CS is non empty CollStr
the U1 of CS is non empty set
p is Element of the U1 of CS
p1 is Element of the U1 of CS
p2 is Element of the U1 of CS
r is Element of the U1 of CS
p is Element of the U1 of CS
p1 is Element of the U1 of CS
r is Element of the U1 of CS
p2 is Element of the U1 of CS
r1 is Element of the U1 of CS