:: WEDDWITT semantic presentation

REAL is non empty non trivial non finite set
NAT is V6() V7() V8() non empty non trivial non finite cardinal limit_cardinal Element of bool REAL
bool REAL is non empty non trivial non finite set
F_Complex is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of F_Complex is non empty non trivial set
COMPLEX is non empty non trivial non finite set
NAT is V6() V7() V8() non empty non trivial non finite cardinal limit_cardinal set
bool NAT is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
[:NAT,REAL:] is non empty non trivial non finite set
bool [:NAT,REAL:] is non empty non trivial non finite set
RAT is non empty non trivial non finite set
INT is non empty non trivial non finite set
[:REAL,REAL:] is non empty non trivial non finite set
bool [:REAL,REAL:] is non empty non trivial non finite set
{} is V6() V7() V8() V10() V11() V12() Function-like functional empty V31() V32() integer finite V39() cardinal {} -element FinSequence-membered ext-real non positive non negative set
1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
{{},1} is non empty finite V39() set
K397() is set
bool K397() is non empty set
K398() is Element of bool K397()
2 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
[:2,2:] is non empty finite set
[:[:2,2:],2:] is non empty finite set
bool [:[:2,2:],2:] is non empty finite V39() set
K548() is non empty strict multMagma
the carrier of K548() is non empty set
K553() is non empty strict unital Group-like associative commutative V190() V191() V192() V193() V194() V195() multMagma
K554() is non empty strict associative commutative V193() V194() V195() M35(K553())
K555() is non empty strict unital associative commutative V193() V194() V195() V196() M38(K553(),K554())
K557() is non empty strict unital associative commutative multMagma
K558() is non empty strict unital associative commutative V196() M35(K557())
1 -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
bool the carrier of F_Complex is non empty set
[:NAT, the carrier of F_Complex:] is non empty non trivial non finite set
bool [:NAT, the carrier of F_Complex:] is non empty non trivial non finite set
[:COMPLEX,COMPLEX:] is non empty non trivial non finite set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial non finite set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial non finite set
[:[:REAL,REAL:],REAL:] is non empty non trivial non finite set
bool [:[:REAL,REAL:],REAL:] is non empty non trivial non finite set
[:RAT,RAT:] is non empty non trivial non finite set
bool [:RAT,RAT:] is non empty non trivial non finite set
[:[:RAT,RAT:],RAT:] is non empty non trivial non finite set
bool [:[:RAT,RAT:],RAT:] is non empty non trivial non finite set
[:INT,INT:] is non empty non trivial non finite set
bool [:INT,INT:] is non empty non trivial non finite set
[:[:INT,INT:],INT:] is non empty non trivial non finite set
bool [:[:INT,INT:],INT:] is non empty non trivial non finite set
[:NAT,NAT:] is non empty non trivial non finite set
[:[:NAT,NAT:],NAT:] is non empty non trivial non finite set
bool [:[:NAT,NAT:],NAT:] is non empty non trivial non finite set
3 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
0 is V6() V7() V8() V10() V11() V12() Function-like functional empty V31() V32() integer finite V39() cardinal {} -element FinSequence-membered ext-real non positive non negative Element of NAT
card {} is V6() V7() V8() V10() V11() V12() Function-like functional empty V31() V32() integer finite V39() cardinal {} -element FinSequence-membered ext-real non positive non negative set
Seg 1 is non empty trivial finite 1 -element Element of bool NAT
K692() is Relation-like [:COMPLEX,COMPLEX:] -defined COMPLEX -valued Function-like quasi_total V62() Element of bool [:[:COMPLEX,COMPLEX:],COMPLEX:]
K694() is Relation-like [:COMPLEX,COMPLEX:] -defined COMPLEX -valued Function-like quasi_total V62() Element of bool [:[:COMPLEX,COMPLEX:],COMPLEX:]
K122() is Element of COMPLEX
K121() is V6() V7() V8() V10() V11() V12() Function-like functional empty V31() V32() integer finite V39() cardinal {} -element FinSequence-membered ext-real non positive non negative Element of COMPLEX
<*> REAL is Relation-like NAT -defined REAL -valued V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty proper V31() V32() integer finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V62() V63() V64() V65() Function-yielding V84() FinSequence of REAL
Sum (<*> REAL) is V31() V32() ext-real Element of REAL
{{}} is non empty trivial finite V39() 1 -element set
R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Z is V31() V32() ext-real Element of REAL
Z |^ R is V31() V32() ext-real Element of REAL
1 + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
0 + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
Z #Z R is V31() V32() ext-real Element of REAL
Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
R * Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
(R * Z) + cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
Z -' 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R * (Z -' 1) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(R * (Z -' 1)) + cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
q is V31() V32() ext-real Element of REAL
q |^ ((R * Z) + cZ) is V31() V32() ext-real Element of REAL
q |^ R is V31() V32() ext-real Element of REAL
q |^ ((R * (Z -' 1)) + cZ) is V31() V32() ext-real Element of REAL
(q |^ R) * (q |^ ((R * (Z -' 1)) + cZ)) is V31() V32() ext-real set
0 + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(Z -' 1) + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
R + ((R * (Z -' 1)) + cZ) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
q #Z (R + ((R * (Z -' 1)) + cZ)) is V31() V32() ext-real Element of REAL
q #Z R is V31() V32() ext-real Element of REAL
q #Z ((R * (Z -' 1)) + cZ) is V31() V32() ext-real Element of REAL
(q #Z R) * (q #Z ((R * (Z -' 1)) + cZ)) is V31() V32() ext-real set
(q |^ R) * (q #Z ((R * (Z -' 1)) + cZ)) is V31() V32() ext-real set
Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R |^ Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(R |^ Z) -' 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R |^ cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(R |^ cZ) -' 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cZ mod Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R |^ (cZ mod Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cZ div Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Z * (cZ div Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(Z * (cZ div Z)) + (cZ mod Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Rs is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
Z * Rs is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(Z * Rs) + (cZ mod Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R |^ ((Z * Rs) + (cZ mod Z)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(R |^ ((Z * Rs) + (cZ mod Z))) -' 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(R |^ (cZ mod Z)) -' 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
(cZ mod Z) + cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R |^ ((cZ mod Z) + cR) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R #Z ((cZ mod Z) + cR) is V31() V32() ext-real Element of REAL
R #Z (cZ mod Z) is V31() V32() ext-real Element of REAL
R #Z cR is V31() V32() ext-real Element of REAL
(R #Z (cZ mod Z)) * (R #Z cR) is V31() V32() ext-real set
R |^ cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
0 + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(R |^ Z) - 1 is V31() V32() integer ext-real set
- 1 is V31() V32() integer ext-real non positive set
(R |^ Z) + (- 1) is V31() V32() integer ext-real set
(R |^ (cZ mod Z)) - 1 is V31() V32() integer ext-real set
(R |^ (cZ mod Z)) + (- 1) is V31() V32() integer ext-real set
((R |^ (cZ mod Z)) - 1) + 1 is V31() V32() integer ext-real set
cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
cR + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
Rs - 1 is V31() V32() integer ext-real set
0 + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
Rs -' 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Z * cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(Z * cR) + (cZ mod Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R |^ ((Z * cR) + (cZ mod Z)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Z * (Rs -' 1) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(Z * (Rs -' 1)) + (cZ mod Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R |^ ((Z * (Rs -' 1)) + (cZ mod Z)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(R |^ ((Z * cR) + (cZ mod Z))) -' 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
- ((R |^ Z) -' 1) is V31() V32() integer ext-real non positive set
((R |^ ((Z * Rs) + (cZ mod Z))) -' 1) + (- ((R |^ Z) -' 1)) is V31() V32() integer ext-real set
(R |^ ((Z * Rs) + (cZ mod Z))) - 1 is V31() V32() integer ext-real set
(R |^ Z) - 1 is V31() V32() integer ext-real set
((R |^ ((Z * Rs) + (cZ mod Z))) - 1) - ((R |^ Z) - 1) is V31() V32() integer ext-real set
(R |^ ((Z * Rs) + (cZ mod Z))) - (R |^ Z) is V31() V32() integer ext-real set
(R |^ Z) * (R |^ ((Z * (Rs -' 1)) + (cZ mod Z))) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(R |^ Z) * 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
((R |^ Z) * (R |^ ((Z * (Rs -' 1)) + (cZ mod Z)))) - ((R |^ Z) * 1) is V31() V32() integer ext-real set
((R |^ ((Z * Rs) + (cZ mod Z))) -' 1) - ((R |^ Z) -' 1) is V31() V32() integer ext-real set
(R |^ ((Z * (Rs -' 1)) + (cZ mod Z))) - 1 is V31() V32() integer ext-real set
(R |^ Z) * ((R |^ ((Z * (Rs -' 1)) + (cZ mod Z))) - 1) is V31() V32() integer ext-real set
(R |^ ((Z * (Rs -' 1)) + (cZ mod Z))) -' 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(R |^ Z) * ((R |^ ((Z * (Rs -' 1)) + (cZ mod Z))) -' 1) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
((R |^ Z) -' 1) + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
Funcs (R,Z) is set
card (Funcs (R,Z)) is V6() V7() V8() cardinal set
Z |^ R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Funcs ({},cZ) is set
Funcs (0,cZ) is set
card (Funcs (0,cZ)) is V6() V7() V8() cardinal set
cZ #Z 0 is V31() V32() ext-real Element of REAL
cZ |^ 0 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cZ |^ 0 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
Funcs (q,cZ) is set
card (Funcs (q,cZ)) is V6() V7() V8() cardinal set
cZ |^ q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
q + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
Funcs ((q + 1),cZ) is set
card (Funcs ((q + 1),cZ)) is V6() V7() V8() cardinal set
cZ |^ (q + 1) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
vR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
vR + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
[:(vR + 1),cZ:] is finite set
bool [:(vR + 1),cZ:] is non empty finite V39() set
n is non empty set
Funcs ((vR + 1),n) is non empty FUNCTION_DOMAIN of vR + 1,n
Funcs (vR,n) is non empty FUNCTION_DOMAIN of vR,n
Rs is set
cR is Relation-like Function-like set
dom cR is set
rng cR is set
[:(vR + 1),n:] is non empty set
bool [:(vR + 1),n:] is non empty set
{vR} is non empty trivial finite V39() 1 -element set
(vR + 1) /\ vR is finite set
vR \/ {vR} is non empty finite set
(vR \/ {vR}) /\ vR is finite set
vR /\ vR is finite set
{vR} /\ vR is finite set
(vR /\ vR) \/ ({vR} /\ vR) is finite set
vR \/ {} is finite set
cRs is Relation-like vR + 1 -defined n -valued Function-like quasi_total finite Element of bool [:(vR + 1),n:]
cRs | vR is Relation-like vR + 1 -defined n -valued Function-like finite Element of bool [:(vR + 1),n:]
dom (cRs | vR) is finite Element of bool (vR + 1)
bool (vR + 1) is non empty finite V39() set
rng (cRs | vR) is finite Element of bool n
bool n is non empty set
[:(Funcs ((vR + 1),n)),(Funcs (vR,n)):] is non empty set
bool [:(Funcs ((vR + 1),n)),(Funcs (vR,n)):] is non empty set
Rs is Relation-like Funcs ((vR + 1),n) -defined Funcs (vR,n) -valued Function-like quasi_total Element of bool [:(Funcs ((vR + 1),n)),(Funcs (vR,n)):]
rng Rs is Element of bool (Funcs (vR,n))
bool (Funcs (vR,n)) is non empty set
cR is set
cRs is set
cZs is Relation-like vR -defined n -valued Function-like quasi_total Element of Funcs (vR,n)
vR .--> cRs is Relation-like NAT -defined {vR} -defined Function-like one-to-one finite set
{vR} is non empty trivial finite V39() 1 -element set
{vR} --> cRs is Relation-like {vR} -defined {cRs} -valued Function-like constant non empty total quasi_total finite Element of bool [:{vR},{cRs}:]
{cRs} is non empty trivial finite 1 -element set
[:{vR},{cRs}:] is non empty finite set
bool [:{vR},{cRs}:] is non empty finite V39() set
cZs +* (vR .--> cRs) is Relation-like Function-like set
{cZs} is functional non empty trivial finite 1 -element set
Rs " {cZs} is Element of bool (Funcs ((vR + 1),n))
bool (Funcs ((vR + 1),n)) is non empty set
A is set
vR .--> A is Relation-like NAT -defined {vR} -defined Function-like one-to-one finite set
{vR} --> A is Relation-like {vR} -defined {A} -valued Function-like constant non empty total quasi_total finite Element of bool [:{vR},{A}:]
{A} is non empty trivial finite 1 -element set
[:{vR},{A}:] is non empty finite set
bool [:{vR},{A}:] is non empty finite V39() set
cZs +* (vR .--> A) is Relation-like Function-like set
B is Relation-like Function-like set
dom cZs is finite Element of bool vR
bool vR is non empty finite V39() set
dom (vR .--> A) is trivial finite V39() Element of bool {vR}
bool {vR} is non empty finite V39() set
dom B is set
vR \/ {vR} is non empty finite set
rng (vR .--> A) is finite set
rng B is set
rng cZs is Element of bool n
bool n is non empty set
(rng cZs) \/ {A} is non empty set
Funcs ((vR + 1),cZ) is set
f is Relation-like vR + 1 -defined cZ -valued Function-like quasi_total finite Element of bool [:(vR + 1),cZ:]
f | vR is Relation-like vR + 1 -defined cZ -valued Function-like finite Element of bool [:(vR + 1),cZ:]
Rs . f is set
{cR} is non empty trivial finite 1 -element set
f1 is Relation-like vR + 1 -defined cZ -valued Function-like quasi_total finite Element of bool [:(vR + 1),cZ:]
f1 | vR is Relation-like vR + 1 -defined cZ -valued Function-like finite Element of bool [:(vR + 1),cZ:]
dom Rs is Element of bool (Funcs ((vR + 1),n))
A is set
[(cZs +* (vR .--> cRs)),A] is set
{(cZs +* (vR .--> cRs)),A} is non empty finite set
{(cZs +* (vR .--> cRs))} is functional non empty trivial finite 1 -element set
{{(cZs +* (vR .--> cRs)),A},{(cZs +* (vR .--> cRs))}} is non empty finite V39() set
dom Rs is Element of bool (Funcs ((vR + 1),n))
Rs . (cZs +* (vR .--> cRs)) is set
(cZs +* (vR .--> cRs)) | vR is Relation-like Function-like finite set
B is Relation-like vR + 1 -defined cZ -valued Function-like quasi_total finite Element of bool [:(vR + 1),cZ:]
B | vR is Relation-like vR + 1 -defined cZ -valued Function-like finite Element of bool [:(vR + 1),cZ:]
dom cZs is finite Element of bool vR
bool vR is non empty finite V39() set
dom (vR .--> cRs) is trivial finite V39() Element of bool {vR}
bool {vR} is non empty finite V39() set
cR is Relation-like vR -defined n -valued Function-like quasi_total Element of Funcs (vR,n)
{cR} is functional non empty trivial finite 1 -element set
Rs " {cR} is Element of bool (Funcs ((vR + 1),n))
bool (Funcs ((vR + 1),n)) is non empty set
card (Rs " {cR}) is V6() V7() V8() cardinal set
cRs is set
vR .--> cRs is Relation-like NAT -defined {vR} -defined Function-like one-to-one finite set
{vR} is non empty trivial finite V39() 1 -element set
{vR} --> cRs is Relation-like {vR} -defined {cRs} -valued Function-like constant non empty total quasi_total finite Element of bool [:{vR},{cRs}:]
{cRs} is non empty trivial finite 1 -element set
[:{vR},{cRs}:] is non empty finite set
bool [:{vR},{cRs}:] is non empty finite V39() set
cR +* (vR .--> cRs) is Relation-like Function-like set
cZs is Relation-like Function-like set
dom cR is finite Element of bool vR
bool vR is non empty finite V39() set
dom (vR .--> cRs) is trivial finite V39() Element of bool {vR}
bool {vR} is non empty finite V39() set
dom cZs is set
vR \/ {vR} is non empty finite set
rng (vR .--> cRs) is finite set
rng cZs is set
rng cR is Element of bool n
bool n is non empty set
(rng cR) \/ {cRs} is non empty set
Funcs ((vR + 1),cZ) is set
natq1 is Relation-like vR + 1 -defined cZ -valued Function-like quasi_total finite Element of bool [:(vR + 1),cZ:]
natq1 | vR is Relation-like vR + 1 -defined cZ -valued Function-like finite Element of bool [:(vR + 1),cZ:]
Rs . natq1 is set
A is Relation-like vR + 1 -defined cZ -valued Function-like quasi_total finite Element of bool [:(vR + 1),cZ:]
A | vR is Relation-like vR + 1 -defined cZ -valued Function-like finite Element of bool [:(vR + 1),cZ:]
dom Rs is Element of bool (Funcs ((vR + 1),n))
[:cZ,(Rs " {cR}):] is set
bool [:cZ,(Rs " {cR}):] is non empty set
cRs is Relation-like cZ -defined Rs " {cR} -valued Function-like quasi_total finite Element of bool [:cZ,(Rs " {cR}):]
cZs is set
[:(vR + 1),n:] is non empty set
bool [:(vR + 1),n:] is non empty set
Rs . cZs is set
natq1 is Relation-like vR + 1 -defined n -valued Function-like quasi_total finite Element of bool [:(vR + 1),n:]
natq1 | vR is Relation-like vR + 1 -defined n -valued Function-like finite Element of bool [:(vR + 1),n:]
natq1 . vR is set
A is set
cRs . A is set
{vR} is non empty trivial finite V39() 1 -element set
vR \/ {vR} is non empty finite set
dom natq1 is finite Element of bool (vR + 1)
bool (vR + 1) is non empty finite V39() set
vR .--> (natq1 . vR) is Relation-like NAT -defined {vR} -defined Function-like one-to-one finite set
{vR} --> (natq1 . vR) is Relation-like {vR} -defined {(natq1 . vR)} -valued Function-like constant non empty total quasi_total finite Element of bool [:{vR},{(natq1 . vR)}:]
{(natq1 . vR)} is non empty trivial finite 1 -element set
[:{vR},{(natq1 . vR)}:] is non empty finite set
bool [:{vR},{(natq1 . vR)}:] is non empty finite V39() set
(natq1 | vR) +* (vR .--> (natq1 . vR)) is Relation-like Function-like finite set
rng cRs is finite Element of bool (Rs " {cR})
bool (Rs " {cR}) is non empty set
dom cRs is finite Element of bool cZ
bool cZ is non empty finite V39() set
cZs is set
natq1 is set
cRs . cZs is set
cRs . natq1 is set
vR .--> natq1 is Relation-like NAT -defined {vR} -defined Function-like one-to-one finite set
{vR} is non empty trivial finite V39() 1 -element set
{vR} --> natq1 is Relation-like {vR} -defined {natq1} -valued Function-like constant non empty total quasi_total finite Element of bool [:{vR},{natq1}:]
{natq1} is non empty trivial finite 1 -element set
[:{vR},{natq1}:] is non empty finite set
bool [:{vR},{natq1}:] is non empty finite V39() set
cR +* (vR .--> natq1) is Relation-like Function-like set
vR .--> cZs is Relation-like NAT -defined {vR} -defined Function-like one-to-one finite set
{vR} --> cZs is Relation-like {vR} -defined {cZs} -valued Function-like constant non empty total quasi_total finite Element of bool [:{vR},{cZs}:]
{cZs} is non empty trivial finite 1 -element set
[:{vR},{cZs}:] is non empty finite set
bool [:{vR},{cZs}:] is non empty finite V39() set
dom (vR .--> cZs) is trivial finite V39() Element of bool {vR}
bool {vR} is non empty finite V39() set
dom (vR .--> natq1) is trivial finite V39() Element of bool {vR}
cR +* (vR .--> cZs) is Relation-like Function-like set
(vR .--> cZs) . vR is set
(vR .--> natq1) . vR is set
(cR +* (vR .--> cZs)) . vR is set
cRs .: cZ is finite Element of bool (Rs " {cR})
cR is set
cRs is set
{cR} is non empty trivial finite 1 -element set
Rs " {cR} is Element of bool (Funcs ((vR + 1),n))
bool (Funcs ((vR + 1),n)) is non empty set
{cRs} is non empty trivial finite 1 -element set
Rs " {cRs} is Element of bool (Funcs ((vR + 1),n))
(Rs " {cR}) /\ (Rs " {cRs}) is Element of bool (Funcs ((vR + 1),n))
cZs is set
Rs . cZs is set
natq1 is Relation-like vR + 1 -defined cZ -valued Function-like quasi_total finite Element of bool [:(vR + 1),cZ:]
Funcs ((vR + 1),cZ) is set
Rs . natq1 is set
natq1 | vR is Relation-like vR + 1 -defined cZ -valued Function-like finite Element of bool [:(vR + 1),cZ:]
A is Relation-like vR + 1 -defined cZ -valued Function-like quasi_total finite Element of bool [:(vR + 1),cZ:]
A | vR is Relation-like vR + 1 -defined cZ -valued Function-like finite Element of bool [:(vR + 1),cZ:]
A is Relation-like vR + 1 -defined cZ -valued Function-like quasi_total finite Element of bool [:(vR + 1),cZ:]
A | vR is Relation-like vR + 1 -defined cZ -valued Function-like finite Element of bool [:(vR + 1),cZ:]
{ (Rs " {b₁}) where b₁ is Relation-like vR -defined n -valued Function-like quasi_total Element of Funcs (vR,n) : verum } is set
cR is set
union cR is set
Funcs ((vR + 1),cZ) is set
cRs is set
cZs is set
Funcs (vR,cZ) is set
natq1 is Element of Funcs (vR,cZ)
{natq1} is non empty trivial finite 1 -element set
Rs " {natq1} is Element of bool (Funcs ((vR + 1),n))
bool (Funcs ((vR + 1),n)) is non empty set
cRs is set
Rs . cRs is set
cZs is Relation-like vR + 1 -defined cZ -valued Function-like quasi_total finite Element of bool [:(vR + 1),cZ:]
cZs | vR is Relation-like vR + 1 -defined cZ -valued Function-like finite Element of bool [:(vR + 1),cZ:]
dom Rs is Element of bool (Funcs ((vR + 1),n))
bool (Funcs ((vR + 1),n)) is non empty set
Rs . cZs is set
{(cZs | vR)} is functional non empty trivial finite V39() 1 -element set
Rs " {(cZs | vR)} is Element of bool (Funcs ((vR + 1),n))
natq1 is set
A is Relation-like vR + 1 -defined cZ -valued Function-like quasi_total finite Element of bool [:(vR + 1),cZ:]
A | vR is Relation-like vR + 1 -defined cZ -valued Function-like finite Element of bool [:(vR + 1),cZ:]
cRs is finite set
card cRs is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cZ |^ vR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
bool (Funcs ((vR + 1),n)) is non empty set
Funcs (vR,cZ) is set
cZs is set
{cZs} is non empty trivial finite 1 -element set
Rs " {cZs} is Element of bool (Funcs ((vR + 1),n))
[:(Funcs (vR,cZ)),cRs:] is set
bool [:(Funcs (vR,cZ)),cRs:] is non empty set
cZs is Relation-like Funcs (vR,cZ) -defined cRs -valued Function-like quasi_total Element of bool [:(Funcs (vR,cZ)),cRs:]
natq1 is set
A is Element of Funcs (vR,cZ)
{A} is non empty trivial finite 1 -element set
Rs " {A} is Element of bool (Funcs ((vR + 1),n))
cZs . A is set
the Relation-like vR -defined n -valued Function-like quasi_total Element of Funcs (vR,n) is Relation-like vR -defined n -valued Function-like quasi_total Element of Funcs (vR,n)
{ the Relation-like vR -defined n -valued Function-like quasi_total Element of Funcs (vR,n)} is functional non empty trivial finite 1 -element set
Rs " { the Relation-like vR -defined n -valued Function-like quasi_total Element of Funcs (vR,n)} is Element of bool (Funcs ((vR + 1),n))
rng cZs is finite Element of bool cRs
bool cRs is non empty finite V39() set
dom cZs is Element of bool (Funcs (vR,cZ))
bool (Funcs (vR,cZ)) is non empty set
A is set
B is set
cZs . A is set
cZs . B is set
{A} is non empty trivial finite 1 -element set
Rs " {A} is Element of bool (Funcs ((vR + 1),n))
{B} is non empty trivial finite 1 -element set
Rs " {B} is Element of bool (Funcs ((vR + 1),n))
(Rs " {A}) /\ (Rs " {A}) is Element of bool (Funcs ((vR + 1),n))
cZs .: (Funcs (vR,cZ)) is finite Element of bool cRs
cZs is set
natq1 is Relation-like vR -defined n -valued Function-like quasi_total Element of Funcs (vR,n)
{natq1} is functional non empty trivial finite 1 -element set
Rs " {natq1} is Element of bool (Funcs ((vR + 1),n))
bool (Funcs ((vR + 1),n)) is non empty set
card cZs is V6() V7() V8() cardinal set
A is set
B is Relation-like vR -defined n -valued Function-like quasi_total Element of Funcs (vR,n)
{B} is functional non empty trivial finite 1 -element set
Rs " {B} is Element of bool (Funcs ((vR + 1),n))
card A is V6() V7() V8() cardinal set
union cRs is set
cZ * (card cRs) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cZs is finite set
card cZs is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom R is finite Element of bool NAT
Sum R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
<*> NAT is Relation-like NAT -defined NAT -valued V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty proper V31() V32() integer finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V62() V63() V64() V65() Function-yielding V84() FinSequence of NAT
Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
Z is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom Z is finite Element of bool NAT
Sum Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
vR is set
<*vR*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
q ^ <*vR*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
n is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Rs is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len Rs is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(len n) + (len Rs) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(len n) + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
dom n is finite Element of bool NAT
cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
n /. cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Z /. cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Z . cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
n . cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
Sum n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
rng Rs is finite V72() V73() V74() V77() Element of bool REAL
{vR} is non empty trivial finite 1 -element set
Z . (len Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Seg (len Z) is finite len Z -element Element of bool NAT
Z /. (len Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(Sum n) + cR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
dom R is finite Element of bool NAT
Sum R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
len R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is finite set
card R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Z is finite V39() V50() a_partition of R
card Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cZ is Relation-like NAT -defined Z -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of Z
rng cZ is finite V39() Element of bool Z
bool Z is non empty finite V39() set
len cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom q is finite Element of bool NAT
Sum q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
Z is finite set
card Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cZ is finite V39() V50() a_partition of Z
card cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
q is Relation-like NAT -defined cZ -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of cZ
rng q is finite V39() Element of bool cZ
bool cZ is non empty finite V39() set
len q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
vR is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len vR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom vR is finite Element of bool NAT
Sum vR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
n is non empty set
Rs is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of n
Seg R is finite R -element Element of bool NAT
Rs | (Seg R) is Relation-like NAT -defined n -valued Function-like finite FinSubsequence-like Element of bool [:NAT,n:]
[:NAT,n:] is non empty non trivial non finite set
bool [:NAT,n:] is non empty non trivial non finite set
cRs is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of n
len cRs is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Rs . (R + 1) is set
<*(Rs . (R + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
cRs ^ <*(Rs . (R + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
rng cRs is finite Element of bool n
bool n is non empty set
cZs is finite set
natq1 is Relation-like NAT -defined cZs -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of cZs
card cZs is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
union cZs is set
A is finite set
bool A is non empty finite V39() set
B is finite Element of bool A
f is finite Element of bool A
f is finite Element of bool A
bool (union cZs) is non empty set
vR | (Seg R) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite FinSubsequence-like V62() V63() V64() V65() Element of bool [:NAT,NAT:]
bool [:NAT,NAT:] is non empty non trivial non finite set
B is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len B is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
len natq1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom B is finite Element of bool NAT
f is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
B . f is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
natq1 . f is set
card (natq1 . f) is V6() V7() V8() cardinal set
dom natq1 is finite Element of bool NAT
vR . f is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
Rs . f is set
card (Rs . f) is V6() V7() V8() cardinal set
card A is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Sum B is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
f is set
f1 is set
dom Rs is finite Element of bool NAT
len Rs is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Seg (len Rs) is finite len Rs -element Element of bool NAT
rng Rs is finite Element of bool n
dom natq1 is finite Element of bool NAT
f2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
natq1 . f2 is set
Seg (R + 1) is non empty finite R + 1 -element Element of bool NAT
Rs . f2 is set
dom Rs is finite Element of bool NAT
len Rs is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Seg (len Rs) is finite len Rs -element Element of bool NAT
rng Rs is finite Element of bool n
rng natq1 is finite Element of bool cZs
bool cZs is non empty finite V39() set
f1 is finite set
<*f1*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
rng <*f1*> is trivial finite set
(rng natq1) \/ (rng <*f1*>) is finite set
{f1} is non empty trivial finite V39() 1 -element set
cZs \/ {f1} is non empty finite set
cR is non empty finite set
union n is set
union {f1} is finite set
(union cZs) \/ (union {f1}) is set
A \/ f1 is finite set
Seg (R + 1) is non empty finite R + 1 -element Element of bool NAT
rng B is finite V72() V73() V74() V77() Element of bool REAL
card cR is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
card f1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(Sum B) + (card f1) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
vR . (R + 1) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
(Sum B) + (vR . (R + 1)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() FinSequence of REAL
<*(vR . (R + 1))*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V62() V63() V64() V66() V67() V68() V69() FinSequence of REAL
f2 ^ <*(vR . (R + 1))*> is Relation-like NAT -defined REAL -valued Function-like non empty finite FinSequence-like FinSubsequence-like V62() V63() V64() FinSequence of REAL
Sum (f2 ^ <*(vR . (R + 1))*>) is V31() V32() ext-real Element of REAL
R is finite set
card R is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Z is finite V39() V50() a_partition of R
card Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
cZ is Relation-like NAT -defined Z -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of Z
rng cZ is finite V39() Element of bool Z
bool Z is non empty finite V39() set
q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
len cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom q is finite Element of bool NAT
Sum q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is non empty finite unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
center R is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
R is non empty unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty set
Z is Element of the carrier of R
{ b₁ where b₁ is Element of the carrier of R : Z * b₁ = b₁ * Z } is set
1_ R is Element of the carrier of R
Z * (1_ R) is Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (Z,(1_ R)) is Element of the carrier of R
[Z,(1_ R)] is set
{Z,(1_ R)} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,(1_ R)},{Z}} is non empty finite V39() set
the multF of R . [Z,(1_ R)] is set
(1_ R) * Z is Element of the carrier of R
the multF of R . ((1_ R),Z) is Element of the carrier of R
[(1_ R),Z] is set
{(1_ R),Z} is non empty finite set
{(1_ R)} is non empty trivial finite 1 -element set
{{(1_ R),Z},{(1_ R)}} is non empty finite V39() set
the multF of R . [(1_ R),Z] is set
q is set
vR is Element of the carrier of R
Z * vR is Element of the carrier of R
the multF of R . (Z,vR) is Element of the carrier of R
[Z,vR] is set
{Z,vR} is non empty finite set
{{Z,vR},{Z}} is non empty finite V39() set
the multF of R . [Z,vR] is set
vR * Z is Element of the carrier of R
the multF of R . (vR,Z) is Element of the carrier of R
[vR,Z] is set
{vR,Z} is non empty finite set
{vR} is non empty trivial finite 1 -element set
{{vR,Z},{vR}} is non empty finite V39() set
the multF of R . [vR,Z] is set
bool the carrier of R is non empty set
q is Element of the carrier of R
vR is Element of the carrier of R
q * vR is Element of the carrier of R
the multF of R . (q,vR) is Element of the carrier of R
[q,vR] is set
{q,vR} is non empty finite set
{q} is non empty trivial finite 1 -element set
{{q,vR},{q}} is non empty finite V39() set
the multF of R . [q,vR] is set
Z * (q * vR) is Element of the carrier of R
the multF of R . (Z,(q * vR)) is Element of the carrier of R
[Z,(q * vR)] is set
{Z,(q * vR)} is non empty finite set
{{Z,(q * vR)},{Z}} is non empty finite V39() set
the multF of R . [Z,(q * vR)] is set
q * Z is Element of the carrier of R
the multF of R . (q,Z) is Element of the carrier of R
[q,Z] is set
{q,Z} is non empty finite set
{{q,Z},{q}} is non empty finite V39() set
the multF of R . [q,Z] is set
(q * Z) * vR is Element of the carrier of R
the multF of R . ((q * Z),vR) is Element of the carrier of R
[(q * Z),vR] is set
{(q * Z),vR} is non empty finite set
{(q * Z)} is non empty trivial finite 1 -element set
{{(q * Z),vR},{(q * Z)}} is non empty finite V39() set
the multF of R . [(q * Z),vR] is set
vR * Z is Element of the carrier of R
the multF of R . (vR,Z) is Element of the carrier of R
[vR,Z] is set
{vR,Z} is non empty finite set
{vR} is non empty trivial finite 1 -element set
{{vR,Z},{vR}} is non empty finite V39() set
the multF of R . [vR,Z] is set
q * (vR * Z) is Element of the carrier of R
the multF of R . (q,(vR * Z)) is Element of the carrier of R
[q,(vR * Z)] is set
{q,(vR * Z)} is non empty finite set
{{q,(vR * Z)},{q}} is non empty finite V39() set
the multF of R . [q,(vR * Z)] is set
(q * vR) * Z is Element of the carrier of R
the multF of R . ((q * vR),Z) is Element of the carrier of R
[(q * vR),Z] is set
{(q * vR),Z} is non empty finite set
{(q * vR)} is non empty trivial finite 1 -element set
{{(q * vR),Z},{(q * vR)}} is non empty finite V39() set
the multF of R . [(q * vR),Z] is set
n is Element of the carrier of R
n * Z is Element of the carrier of R
the multF of R . (n,Z) is Element of the carrier of R
[n,Z] is set
{n,Z} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,Z},{n}} is non empty finite V39() set
the multF of R . [n,Z] is set
Z * n is Element of the carrier of R
the multF of R . (Z,n) is Element of the carrier of R
[Z,n] is set
{Z,n} is non empty finite set
{{Z,n},{Z}} is non empty finite V39() set
the multF of R . [Z,n] is set
n is Element of the carrier of R
n * Z is Element of the carrier of R
the multF of R . (n,Z) is Element of the carrier of R
[n,Z] is set
{n,Z} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,Z},{n}} is non empty finite V39() set
the multF of R . [n,Z] is set
Z * n is Element of the carrier of R
the multF of R . (Z,n) is Element of the carrier of R
[Z,n] is set
{Z,n} is non empty finite set
{{Z,n},{Z}} is non empty finite V39() set
the multF of R . [Z,n] is set
q is Element of the carrier of R
q " is Element of the carrier of R
q * Z is Element of the carrier of R
the multF of R . (q,Z) is Element of the carrier of R
[q,Z] is set
{q,Z} is non empty finite set
{q} is non empty trivial finite 1 -element set
{{q,Z},{q}} is non empty finite V39() set
the multF of R . [q,Z] is set
(q ") * (q * Z) is Element of the carrier of R
the multF of R . ((q "),(q * Z)) is Element of the carrier of R
[(q "),(q * Z)] is set
{(q "),(q * Z)} is non empty finite set
{(q ")} is non empty trivial finite 1 -element set
{{(q "),(q * Z)},{(q ")}} is non empty finite V39() set
the multF of R . [(q "),(q * Z)] is set
Z * q is Element of the carrier of R
the multF of R . (Z,q) is Element of the carrier of R
[Z,q] is set
{Z,q} is non empty finite set
{{Z,q},{Z}} is non empty finite V39() set
the multF of R . [Z,q] is set
(Z * q) * (q ") is Element of the carrier of R
the multF of R . ((Z * q),(q ")) is Element of the carrier of R
[(Z * q),(q ")] is set
{(Z * q),(q ")} is non empty finite set
{(Z * q)} is non empty trivial finite 1 -element set
{{(Z * q),(q ")},{(Z * q)}} is non empty finite V39() set
the multF of R . [(Z * q),(q ")] is set
(q ") * ((Z * q) * (q ")) is Element of the carrier of R
the multF of R . ((q "),((Z * q) * (q "))) is Element of the carrier of R
[(q "),((Z * q) * (q "))] is set
{(q "),((Z * q) * (q "))} is non empty finite set
{{(q "),((Z * q) * (q "))},{(q ")}} is non empty finite V39() set
the multF of R . [(q "),((Z * q) * (q "))] is set
Z * (q ") is Element of the carrier of R
the multF of R . (Z,(q ")) is Element of the carrier of R
[Z,(q ")] is set
{Z,(q ")} is non empty finite set
{{Z,(q ")},{Z}} is non empty finite V39() set
the multF of R . [Z,(q ")] is set
vR is Element of the carrier of R
vR * Z is Element of the carrier of R
the multF of R . (vR,Z) is Element of the carrier of R
[vR,Z] is set
{vR,Z} is non empty finite set
{vR} is non empty trivial finite 1 -element set
{{vR,Z},{vR}} is non empty finite V39() set
the multF of R . [vR,Z] is set
Z * vR is Element of the carrier of R
the multF of R . (Z,vR) is Element of the carrier of R
[Z,vR] is set
{Z,vR} is non empty finite set
{{Z,vR},{Z}} is non empty finite V39() set
the multF of R . [Z,vR] is set
(q ") * Z is Element of the carrier of R
the multF of R . ((q "),Z) is Element of the carrier of R
[(q "),Z] is set
{(q "),Z} is non empty finite set
{{(q "),Z},{(q ")}} is non empty finite V39() set
the multF of R . [(q "),Z] is set
cZ is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the carrier of cZ is non empty set
q is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the carrier of q is non empty set
vR is Element of the carrier of R
R is non empty finite unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty finite set
Z is Element of the carrier of R
(R,Z) is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
R is non empty unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty set
Z is Element of the carrier of R
(R,Z) is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
cZ is set
the carrier of (R,Z) is non empty set
{ b₁ where b₁ is Element of the carrier of R : Z * b₁ = b₁ * Z } is set
q is Element of the carrier of R
Z * q is Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (Z,q) is Element of the carrier of R
[Z,q] is set
{Z,q} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,q},{Z}} is non empty finite V39() set
the multF of R . [Z,q] is set
q * Z is Element of the carrier of R
the multF of R . (q,Z) is Element of the carrier of R
[q,Z] is set
{q,Z} is non empty finite set
{q} is non empty trivial finite 1 -element set
{{q,Z},{q}} is non empty finite V39() set
the multF of R . [q,Z] is set
R is non empty unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty set
Z is Element of the carrier of R
cZ is Element of the carrier of R
Z * cZ is Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (Z,cZ) is Element of the carrier of R
[Z,cZ] is set
{Z,cZ} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,cZ},{Z}} is non empty finite V39() set
the multF of R . [Z,cZ] is set
cZ * Z is Element of the carrier of R
the multF of R . (cZ,Z) is Element of the carrier of R
[cZ,Z] is set
{cZ,Z} is non empty finite set
{cZ} is non empty trivial finite 1 -element set
{{cZ,Z},{cZ}} is non empty finite V39() set
the multF of R . [cZ,Z] is set
(R,Z) is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the carrier of (R,Z) is non empty set
{ b₁ where b₁ is Element of the carrier of R : Z * b₁ = b₁ * Z } is set
q is Element of the carrier of R
Z * q is Element of the carrier of R
the multF of R . (Z,q) is Element of the carrier of R
[Z,q] is set
{Z,q} is non empty finite set
{{Z,q},{Z}} is non empty finite V39() set
the multF of R . [Z,q] is set
q * Z is Element of the carrier of R
the multF of R . (q,Z) is Element of the carrier of R
[q,Z] is set
{q,Z} is non empty finite set
{q} is non empty trivial finite 1 -element set
{{q,Z},{q}} is non empty finite V39() set
the multF of R . [q,Z] is set
R is non empty unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty set
Z is Element of the carrier of R
con_class Z is Element of bool the carrier of R
bool the carrier of R is non empty set
(Omega). R is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
multMagma(# the carrier of R, the multF of R #) is non empty strict multMagma
carr ((Omega). R) is Element of bool the carrier of R
the carrier of ((Omega). R) is non empty set
Z |^ (carr ((Omega). R)) is Element of bool the carrier of R
K462( the carrier of R,Z) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,Z) |^ (carr ((Omega). R)) is Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,Z) & b₂ in carr ((Omega). R) ) } is set
R is non empty unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty set
Z is Element of the carrier of R
con_class Z is non empty Element of bool the carrier of R
bool the carrier of R is non empty set
(Omega). R is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
multMagma(# the carrier of R, the multF of R #) is non empty strict multMagma
carr ((Omega). R) is Element of bool the carrier of R
the carrier of ((Omega). R) is non empty set
Z |^ (carr ((Omega). R)) is Element of bool the carrier of R
K462( the carrier of R,Z) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,Z) |^ (carr ((Omega). R)) is Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,Z) & b₂ in carr ((Omega). R) ) } is set
[: the carrier of R,(con_class Z):] is non empty set
bool [: the carrier of R,(con_class Z):] is non empty set
cZ is Element of the carrier of R
Z |^ cZ is Element of the carrier of R
cZ " is Element of the carrier of R
(cZ ") * Z is Element of the carrier of R
the multF of R . ((cZ "),Z) is Element of the carrier of R
[(cZ "),Z] is set
{(cZ "),Z} is non empty finite set
{(cZ ")} is non empty trivial finite 1 -element set
{{(cZ "),Z},{(cZ ")}} is non empty finite V39() set
the multF of R . [(cZ "),Z] is set
((cZ ") * Z) * cZ is Element of the carrier of R
the multF of R . (((cZ ") * Z),cZ) is Element of the carrier of R
[((cZ ") * Z),cZ] is set
{((cZ ") * Z),cZ} is non empty finite set
{((cZ ") * Z)} is non empty trivial finite 1 -element set
{{((cZ ") * Z),cZ},{((cZ ") * Z)}} is non empty finite V39() set
the multF of R . [((cZ ") * Z),cZ] is set
cZ is Relation-like the carrier of R -defined con_class Z -valued Function-like quasi_total Element of bool [: the carrier of R,(con_class Z):]
cZ is Relation-like the carrier of R -defined con_class Z -valued Function-like quasi_total Element of bool [: the carrier of R,(con_class Z):]
q is Relation-like the carrier of R -defined con_class Z -valued Function-like quasi_total Element of bool [: the carrier of R,(con_class Z):]
dom cZ is Element of bool the carrier of R
dom q is Element of bool the carrier of R
vR is set
cZ . vR is set
q . vR is set
n is Element of the carrier of R
cZ . n is Element of con_class Z
Z |^ n is Element of the carrier of R
n " is Element of the carrier of R
(n ") * Z is Element of the carrier of R
the multF of R . ((n "),Z) is Element of the carrier of R
[(n "),Z] is set
{(n "),Z} is non empty finite set
{(n ")} is non empty trivial finite 1 -element set
{{(n "),Z},{(n ")}} is non empty finite V39() set
the multF of R . [(n "),Z] is set
((n ") * Z) * n is Element of the carrier of R
the multF of R . (((n ") * Z),n) is Element of the carrier of R
[((n ") * Z),n] is set
{((n ") * Z),n} is non empty finite set
{((n ") * Z)} is non empty trivial finite 1 -element set
{{((n ") * Z),n},{((n ") * Z)}} is non empty finite V39() set
the multF of R . [((n ") * Z),n] is set
R is non empty finite unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty finite set
Z is Element of the carrier of R
con_class Z is non empty finite Element of bool the carrier of R
bool the carrier of R is non empty finite V39() set
(Omega). R is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total finite Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty finite set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite V39() set
multMagma(# the carrier of R, the multF of R #) is non empty strict multMagma
carr ((Omega). R) is finite Element of bool the carrier of R
the carrier of ((Omega). R) is non empty finite set
Z |^ (carr ((Omega). R)) is finite Element of bool the carrier of R
K462( the carrier of R,Z) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,Z) |^ (carr ((Omega). R)) is finite Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,Z) & b₂ in carr ((Omega). R) ) } is set
(R,Z) is Relation-like the carrier of R -defined con_class Z -valued Function-like quasi_total finite Element of bool [: the carrier of R,(con_class Z):]
[: the carrier of R,(con_class Z):] is non empty finite set
bool [: the carrier of R,(con_class Z):] is non empty finite V39() set
(R,Z) is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
card (R,Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
the carrier of (R,Z) is non empty finite set
card the carrier of (R,Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
cZ is Element of con_class Z
{cZ} is non empty trivial finite 1 -element set
(R,Z) " {cZ} is finite Element of bool the carrier of R
card ((R,Z) " {cZ}) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
q is Element of the carrier of R
q is Element of the carrier of R
Z |^ q is Element of the carrier of R
q " is Element of the carrier of R
(q ") * Z is Element of the carrier of R
the multF of R . ((q "),Z) is Element of the carrier of R
[(q "),Z] is set
{(q "),Z} is non empty finite set
{(q ")} is non empty trivial finite 1 -element set
{{(q "),Z},{(q ")}} is non empty finite V39() set
the multF of R . [(q "),Z] is set
((q ") * Z) * q is Element of the carrier of R
the multF of R . (((q ") * Z),q) is Element of the carrier of R
[((q ") * Z),q] is set
{((q ") * Z),q} is non empty finite set
{((q ") * Z)} is non empty trivial finite 1 -element set
{{((q ") * Z),q},{((q ") * Z)}} is non empty finite V39() set
the multF of R . [((q ") * Z),q] is set
(R,Z) * q is finite Element of bool the carrier of R
carr (R,Z) is finite Element of bool the carrier of R
(carr (R,Z)) * q is finite Element of bool the carrier of R
K462( the carrier of R,q) is non empty trivial finite 1 -element Element of bool the carrier of R
(carr (R,Z)) * K462( the carrier of R,q) is finite Element of bool the carrier of R
{ (b₁ * b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in carr (R,Z) & b₂ in K462( the carrier of R,q) ) } is set
q * (R,Z) is finite Element of bool the carrier of R
q * (carr (R,Z)) is finite Element of bool the carrier of R
K462( the carrier of R,q) * (carr (R,Z)) is finite Element of bool the carrier of R
{ (b₁ * b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,q) & b₂ in carr (R,Z) ) } is set
vR is finite Element of bool the carrier of R
n is set
(R,Z) . n is set
Rs is Element of the carrier of R
Z |^ Rs is Element of the carrier of R
Rs " is Element of the carrier of R
(Rs ") * Z is Element of the carrier of R
the multF of R . ((Rs "),Z) is Element of the carrier of R
[(Rs "),Z] is set
{(Rs "),Z} is non empty finite set
{(Rs ")} is non empty trivial finite 1 -element set
{{(Rs "),Z},{(Rs ")}} is non empty finite V39() set
the multF of R . [(Rs "),Z] is set
((Rs ") * Z) * Rs is Element of the carrier of R
the multF of R . (((Rs ") * Z),Rs) is Element of the carrier of R
[((Rs ") * Z),Rs] is set
{((Rs ") * Z),Rs} is non empty finite set
{((Rs ") * Z)} is non empty trivial finite 1 -element set
{{((Rs ") * Z),Rs},{((Rs ") * Z)}} is non empty finite V39() set
the multF of R . [((Rs ") * Z),Rs] is set
Rs * (((q ") * Z) * q) is Element of the carrier of R
the multF of R . (Rs,(((q ") * Z) * q)) is Element of the carrier of R
[Rs,(((q ") * Z) * q)] is set
{Rs,(((q ") * Z) * q)} is non empty finite set
{Rs} is non empty trivial finite 1 -element set
{{Rs,(((q ") * Z) * q)},{Rs}} is non empty finite V39() set
the multF of R . [Rs,(((q ") * Z) * q)] is set
Rs * ((q ") * Z) is Element of the carrier of R
the multF of R . (Rs,((q ") * Z)) is Element of the carrier of R
[Rs,((q ") * Z)] is set
{Rs,((q ") * Z)} is non empty finite set
{{Rs,((q ") * Z)},{Rs}} is non empty finite V39() set
the multF of R . [Rs,((q ") * Z)] is set
(Rs * ((q ") * Z)) * q is Element of the carrier of R
the multF of R . ((Rs * ((q ") * Z)),q) is Element of the carrier of R
[(Rs * ((q ") * Z)),q] is set
{(Rs * ((q ") * Z)),q} is non empty finite set
{(Rs * ((q ") * Z))} is non empty trivial finite 1 -element set
{{(Rs * ((q ") * Z)),q},{(Rs * ((q ") * Z))}} is non empty finite V39() set
the multF of R . [(Rs * ((q ") * Z)),q] is set
Rs * (q ") is Element of the carrier of R
the multF of R . (Rs,(q ")) is Element of the carrier of R
[Rs,(q ")] is set
{Rs,(q ")} is non empty finite set
{{Rs,(q ")},{Rs}} is non empty finite V39() set
the multF of R . [Rs,(q ")] is set
(Rs * (q ")) * Z is Element of the carrier of R
the multF of R . ((Rs * (q ")),Z) is Element of the carrier of R
[(Rs * (q ")),Z] is set
{(Rs * (q ")),Z} is non empty finite set
{(Rs * (q "))} is non empty trivial finite 1 -element set
{{(Rs * (q ")),Z},{(Rs * (q "))}} is non empty finite V39() set
the multF of R . [(Rs * (q ")),Z] is set
((Rs * (q ")) * Z) * q is Element of the carrier of R
the multF of R . (((Rs * (q ")) * Z),q) is Element of the carrier of R
[((Rs * (q ")) * Z),q] is set
{((Rs * (q ")) * Z),q} is non empty finite set
{((Rs * (q ")) * Z)} is non empty trivial finite 1 -element set
{{((Rs * (q ")) * Z),q},{((Rs * (q ")) * Z)}} is non empty finite V39() set
the multF of R . [((Rs * (q ")) * Z),q] is set
Rs * (((Rs ") * Z) * Rs) is Element of the carrier of R
the multF of R . (Rs,(((Rs ") * Z) * Rs)) is Element of the carrier of R
[Rs,(((Rs ") * Z) * Rs)] is set
{Rs,(((Rs ") * Z) * Rs)} is non empty finite set
{{Rs,(((Rs ") * Z) * Rs)},{Rs}} is non empty finite V39() set
the multF of R . [Rs,(((Rs ") * Z) * Rs)] is set
Rs * ((Rs ") * Z) is Element of the carrier of R
the multF of R . (Rs,((Rs ") * Z)) is Element of the carrier of R
[Rs,((Rs ") * Z)] is set
{Rs,((Rs ") * Z)} is non empty finite set
{{Rs,((Rs ") * Z)},{Rs}} is non empty finite V39() set
the multF of R . [Rs,((Rs ") * Z)] is set
(Rs * ((Rs ") * Z)) * Rs is Element of the carrier of R
the multF of R . ((Rs * ((Rs ") * Z)),Rs) is Element of the carrier of R
[(Rs * ((Rs ") * Z)),Rs] is set
{(Rs * ((Rs ") * Z)),Rs} is non empty finite set
{(Rs * ((Rs ") * Z))} is non empty trivial finite 1 -element set
{{(Rs * ((Rs ") * Z)),Rs},{(Rs * ((Rs ") * Z))}} is non empty finite V39() set
the multF of R . [(Rs * ((Rs ") * Z)),Rs] is set
Z * Rs is Element of the carrier of R
the multF of R . (Z,Rs) is Element of the carrier of R
[Z,Rs] is set
{Z,Rs} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,Rs},{Z}} is non empty finite V39() set
the multF of R . [Z,Rs] is set
(((Rs * (q ")) * Z) * q) * (q ") is Element of the carrier of R
the multF of R . ((((Rs * (q ")) * Z) * q),(q ")) is Element of the carrier of R
[(((Rs * (q ")) * Z) * q),(q ")] is set
{(((Rs * (q ")) * Z) * q),(q ")} is non empty finite set
{(((Rs * (q ")) * Z) * q)} is non empty trivial finite 1 -element set
{{(((Rs * (q ")) * Z) * q),(q ")},{(((Rs * (q ")) * Z) * q)}} is non empty finite V39() set
the multF of R . [(((Rs * (q ")) * Z) * q),(q ")] is set
Z * (Rs * (q ")) is Element of the carrier of R
the multF of R . (Z,(Rs * (q "))) is Element of the carrier of R
[Z,(Rs * (q "))] is set
{Z,(Rs * (q "))} is non empty finite set
{{Z,(Rs * (q "))},{Z}} is non empty finite V39() set
the multF of R . [Z,(Rs * (q "))] is set
cR is Element of the carrier of R
cRs is Element of the carrier of R
cRs * q is Element of the carrier of R
the multF of R . (cRs,q) is Element of the carrier of R
[cRs,q] is set
{cRs,q} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,q},{cRs}} is non empty finite V39() set
the multF of R . [cRs,q] is set
Rs is Element of the carrier of R
Rs * q is Element of the carrier of R
the multF of R . (Rs,q) is Element of the carrier of R
[Rs,q] is set
{Rs,q} is non empty finite set
{Rs} is non empty trivial finite 1 -element set
{{Rs,q},{Rs}} is non empty finite V39() set
the multF of R . [Rs,q] is set
cR is Element of the carrier of R
cR * (q ") is Element of the carrier of R
the multF of R . (cR,(q ")) is Element of the carrier of R
[cR,(q ")] is set
{cR,(q ")} is non empty finite set
{cR} is non empty trivial finite 1 -element set
{{cR,(q ")},{cR}} is non empty finite V39() set
the multF of R . [cR,(q ")] is set
(cR * (q ")) * Z is Element of the carrier of R
the multF of R . ((cR * (q ")),Z) is Element of the carrier of R
[(cR * (q ")),Z] is set
{(cR * (q ")),Z} is non empty finite set
{(cR * (q "))} is non empty trivial finite 1 -element set
{{(cR * (q ")),Z},{(cR * (q "))}} is non empty finite V39() set
the multF of R . [(cR * (q ")),Z] is set
Z * (cR * (q ")) is Element of the carrier of R
the multF of R . (Z,(cR * (q "))) is Element of the carrier of R
[Z,(cR * (q "))] is set
{Z,(cR * (q "))} is non empty finite set
{{Z,(cR * (q "))},{Z}} is non empty finite V39() set
the multF of R . [Z,(cR * (q "))] is set
((cR * (q ")) * Z) * q is Element of the carrier of R
the multF of R . (((cR * (q ")) * Z),q) is Element of the carrier of R
[((cR * (q ")) * Z),q] is set
{((cR * (q ")) * Z),q} is non empty finite set
{((cR * (q ")) * Z)} is non empty trivial finite 1 -element set
{{((cR * (q ")) * Z),q},{((cR * (q ")) * Z)}} is non empty finite V39() set
the multF of R . [((cR * (q ")) * Z),q] is set
(cR * (q ")) * q is Element of the carrier of R
the multF of R . ((cR * (q ")),q) is Element of the carrier of R
[(cR * (q ")),q] is set
{(cR * (q ")),q} is non empty finite set
{{(cR * (q ")),q},{(cR * (q "))}} is non empty finite V39() set
the multF of R . [(cR * (q ")),q] is set
Z * ((cR * (q ")) * q) is Element of the carrier of R
the multF of R . (Z,((cR * (q ")) * q)) is Element of the carrier of R
[Z,((cR * (q ")) * q)] is set
{Z,((cR * (q ")) * q)} is non empty finite set
{{Z,((cR * (q ")) * q)},{Z}} is non empty finite V39() set
the multF of R . [Z,((cR * (q ")) * q)] is set
Z * cR is Element of the carrier of R
the multF of R . (Z,cR) is Element of the carrier of R
[Z,cR] is set
{Z,cR} is non empty finite set
{{Z,cR},{Z}} is non empty finite V39() set
the multF of R . [Z,cR] is set
Z * q is Element of the carrier of R
the multF of R . (Z,q) is Element of the carrier of R
[Z,q] is set
{Z,q} is non empty finite set
{{Z,q},{Z}} is non empty finite V39() set
the multF of R . [Z,q] is set
(cR * (q ")) * (Z * q) is Element of the carrier of R
the multF of R . ((cR * (q ")),(Z * q)) is Element of the carrier of R
[(cR * (q ")),(Z * q)] is set
{(cR * (q ")),(Z * q)} is non empty finite set
{{(cR * (q ")),(Z * q)},{(cR * (q "))}} is non empty finite V39() set
the multF of R . [(cR * (q ")),(Z * q)] is set
cR " is Element of the carrier of R
(cR ") * ((cR * (q ")) * (Z * q)) is Element of the carrier of R
the multF of R . ((cR "),((cR * (q ")) * (Z * q))) is Element of the carrier of R
[(cR "),((cR * (q ")) * (Z * q))] is set
{(cR "),((cR * (q ")) * (Z * q))} is non empty finite set
{(cR ")} is non empty trivial finite 1 -element set
{{(cR "),((cR * (q ")) * (Z * q))},{(cR ")}} is non empty finite V39() set
the multF of R . [(cR "),((cR * (q ")) * (Z * q))] is set
(cR ") * Z is Element of the carrier of R
the multF of R . ((cR "),Z) is Element of the carrier of R
[(cR "),Z] is set
{(cR "),Z} is non empty finite set
{{(cR "),Z},{(cR ")}} is non empty finite V39() set
the multF of R . [(cR "),Z] is set
((cR ") * Z) * cR is Element of the carrier of R
the multF of R . (((cR ") * Z),cR) is Element of the carrier of R
[((cR ") * Z),cR] is set
{((cR ") * Z),cR} is non empty finite set
{((cR ") * Z)} is non empty trivial finite 1 -element set
{{((cR ") * Z),cR},{((cR ") * Z)}} is non empty finite V39() set
the multF of R . [((cR ") * Z),cR] is set
(cR ") * (cR * (q ")) is Element of the carrier of R
the multF of R . ((cR "),(cR * (q "))) is Element of the carrier of R
[(cR "),(cR * (q "))] is set
{(cR "),(cR * (q "))} is non empty finite set
{{(cR "),(cR * (q "))},{(cR ")}} is non empty finite V39() set
the multF of R . [(cR "),(cR * (q "))] is set
((cR ") * (cR * (q "))) * (Z * q) is Element of the carrier of R
the multF of R . (((cR ") * (cR * (q "))),(Z * q)) is Element of the carrier of R
[((cR ") * (cR * (q "))),(Z * q)] is set
{((cR ") * (cR * (q "))),(Z * q)} is non empty finite set
{((cR ") * (cR * (q ")))} is non empty trivial finite 1 -element set
{{((cR ") * (cR * (q "))),(Z * q)},{((cR ") * (cR * (q ")))}} is non empty finite V39() set
the multF of R . [((cR ") * (cR * (q "))),(Z * q)] is set
(q ") * (Z * q) is Element of the carrier of R
the multF of R . ((q "),(Z * q)) is Element of the carrier of R
[(q "),(Z * q)] is set
{(q "),(Z * q)} is non empty finite set
{{(q "),(Z * q)},{(q ")}} is non empty finite V39() set
the multF of R . [(q "),(Z * q)] is set
Z |^ cR is Element of the carrier of R
(R,Z) . cR is Element of con_class Z
dom (R,Z) is finite Element of bool the carrier of R
n is finite set
Rs is finite set
card n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
card Rs is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is non empty unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty set
Z is Element of the carrier of R
con_class Z is non empty Element of bool the carrier of R
bool the carrier of R is non empty set
(Omega). R is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
multMagma(# the carrier of R, the multF of R #) is non empty strict multMagma
carr ((Omega). R) is Element of bool the carrier of R
the carrier of ((Omega). R) is non empty set
Z |^ (carr ((Omega). R)) is Element of bool the carrier of R
K462( the carrier of R,Z) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,Z) |^ (carr ((Omega). R)) is Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,Z) & b₂ in carr ((Omega). R) ) } is set
(R,Z) is Relation-like the carrier of R -defined con_class Z -valued Function-like quasi_total Element of bool [: the carrier of R,(con_class Z):]
[: the carrier of R,(con_class Z):] is non empty set
bool [: the carrier of R,(con_class Z):] is non empty set
cZ is Element of con_class Z
q is Element of con_class Z
{cZ} is non empty trivial finite 1 -element set
(R,Z) " {cZ} is Element of bool the carrier of R
{q} is non empty trivial finite 1 -element set
(R,Z) " {q} is Element of bool the carrier of R
((R,Z) " {cZ}) /\ ((R,Z) " {q}) is Element of bool the carrier of R
vR is set
vR is set
(R,Z) . vR is set
R is non empty unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty set
Z is Element of the carrier of R
con_class Z is non empty Element of bool the carrier of R
bool the carrier of R is non empty set
(Omega). R is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
multMagma(# the carrier of R, the multF of R #) is non empty strict multMagma
carr ((Omega). R) is Element of bool the carrier of R
the carrier of ((Omega). R) is non empty set
Z |^ (carr ((Omega). R)) is Element of bool the carrier of R
K462( the carrier of R,Z) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,Z) |^ (carr ((Omega). R)) is Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,Z) & b₂ in carr ((Omega). R) ) } is set
(R,Z) is Relation-like the carrier of R -defined con_class Z -valued Function-like quasi_total Element of bool [: the carrier of R,(con_class Z):]
[: the carrier of R,(con_class Z):] is non empty set
bool [: the carrier of R,(con_class Z):] is non empty set
{ ((R,Z) " {b₁}) where b₁ is Element of con_class Z : verum } is set
cZ is set
union cZ is set
q is set
vR is set
n is Element of con_class Z
{n} is non empty trivial finite 1 -element set
(R,Z) " {n} is Element of bool the carrier of R
q is set
vR is Element of the carrier of R
Z |^ vR is Element of the carrier of R
vR " is Element of the carrier of R
(vR ") * Z is Element of the carrier of R
the multF of R . ((vR "),Z) is Element of the carrier of R
[(vR "),Z] is set
{(vR "),Z} is non empty finite set
{(vR ")} is non empty trivial finite 1 -element set
{{(vR "),Z},{(vR ")}} is non empty finite V39() set
the multF of R . [(vR "),Z] is set
((vR ") * Z) * vR is Element of the carrier of R
the multF of R . (((vR ") * Z),vR) is Element of the carrier of R
[((vR ") * Z),vR] is set
{((vR ") * Z),vR} is non empty finite set
{((vR ") * Z)} is non empty trivial finite 1 -element set
{{((vR ") * Z),vR},{((vR ") * Z)}} is non empty finite V39() set
the multF of R . [((vR ") * Z),vR] is set
n is Element of the carrier of R
(R,Z) . vR is Element of con_class Z
{n} is non empty trivial finite 1 -element set
dom (R,Z) is Element of bool the carrier of R
(R,Z) " {n} is Element of bool the carrier of R
q is Element of bool the carrier of R
vR is Element of con_class Z
{vR} is non empty trivial finite 1 -element set
(R,Z) " {vR} is Element of bool the carrier of R
n is Element of the carrier of R
Z |^ n is Element of the carrier of R
n " is Element of the carrier of R
(n ") * Z is Element of the carrier of R
the multF of R . ((n "),Z) is Element of the carrier of R
[(n "),Z] is set
{(n "),Z} is non empty finite set
{(n ")} is non empty trivial finite 1 -element set
{{(n "),Z},{(n ")}} is non empty finite V39() set
the multF of R . [(n "),Z] is set
((n ") * Z) * n is Element of the carrier of R
the multF of R . (((n ") * Z),n) is Element of the carrier of R
[((n ") * Z),n] is set
{((n ") * Z),n} is non empty finite set
{((n ") * Z)} is non empty trivial finite 1 -element set
{{((n ") * Z),n},{((n ") * Z)}} is non empty finite V39() set
the multF of R . [((n ") * Z),n] is set
(R,Z) . n is Element of con_class Z
dom (R,Z) is Element of bool the carrier of R
Rs is Element of bool the carrier of R
cR is Element of con_class Z
{cR} is non empty trivial finite 1 -element set
(R,Z) " {cR} is Element of bool the carrier of R
Rs is Element of bool the carrier of R
bool (union cZ) is non empty set
R is non empty finite unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty finite set
Z is Element of the carrier of R
con_class Z is non empty finite Element of bool the carrier of R
bool the carrier of R is non empty finite V39() set
(Omega). R is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total finite Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty finite set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite V39() set
multMagma(# the carrier of R, the multF of R #) is non empty strict multMagma
carr ((Omega). R) is finite Element of bool the carrier of R
the carrier of ((Omega). R) is non empty finite set
Z |^ (carr ((Omega). R)) is finite Element of bool the carrier of R
K462( the carrier of R,Z) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,Z) |^ (carr ((Omega). R)) is finite Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,Z) & b₂ in carr ((Omega). R) ) } is set
(R,Z) is Relation-like the carrier of R -defined con_class Z -valued Function-like quasi_total finite Element of bool [: the carrier of R,(con_class Z):]
[: the carrier of R,(con_class Z):] is non empty finite set
bool [: the carrier of R,(con_class Z):] is non empty finite V39() set
{ ((R,Z) " {b₁}) where b₁ is Element of con_class Z : verum } is set
card { ((R,Z) " {b₁}) where b₁ is Element of con_class Z : verum } is V6() V7() V8() cardinal set
card (con_class Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
cZ is non empty finite V39() V50() a_partition of the carrier of R
q is set
{q} is non empty trivial finite 1 -element set
(R,Z) " {q} is finite Element of bool the carrier of R
[:(con_class Z),cZ:] is non empty finite set
bool [:(con_class Z),cZ:] is non empty finite V39() set
q is Relation-like con_class Z -defined cZ -valued Function-like quasi_total finite Element of bool [:(con_class Z),cZ:]
vR is set
n is finite Element of bool the carrier of R
Rs is Element of con_class Z
{Rs} is non empty trivial finite 1 -element set
(R,Z) " {Rs} is finite Element of bool the carrier of R
q . Rs is finite Element of cZ
rng q is finite V39() Element of bool cZ
bool cZ is non empty finite V39() set
dom q is finite Element of bool (con_class Z)
bool (con_class Z) is non empty finite V39() set
vR is set
n is set
q . vR is set
q . n is set
Rs is Element of con_class Z
{Rs} is non empty trivial finite 1 -element set
(R,Z) " {Rs} is finite Element of bool the carrier of R
q . Rs is finite Element of cZ
cR is Element of con_class Z
{cR} is non empty trivial finite 1 -element set
(R,Z) " {cR} is finite Element of bool the carrier of R
q . cR is finite Element of cZ
((R,Z) " {Rs}) /\ ((R,Z) " {cR}) is finite Element of bool the carrier of R
cRs is Element of the carrier of R
cZs is Element of the carrier of R
Z |^ cZs is Element of the carrier of R
cZs " is Element of the carrier of R
(cZs ") * Z is Element of the carrier of R
the multF of R . ((cZs "),Z) is Element of the carrier of R
[(cZs "),Z] is set
{(cZs "),Z} is non empty finite set
{(cZs ")} is non empty trivial finite 1 -element set
{{(cZs "),Z},{(cZs ")}} is non empty finite V39() set
the multF of R . [(cZs "),Z] is set
((cZs ") * Z) * cZs is Element of the carrier of R
the multF of R . (((cZs ") * Z),cZs) is Element of the carrier of R
[((cZs ") * Z),cZs] is set
{((cZs ") * Z),cZs} is non empty finite set
{((cZs ") * Z)} is non empty trivial finite 1 -element set
{{((cZs ") * Z),cZs},{((cZs ") * Z)}} is non empty finite V39() set
the multF of R . [((cZs ") * Z),cZs] is set
(R,Z) . cZs is Element of con_class Z
dom (R,Z) is finite Element of bool the carrier of R
q .: (con_class Z) is finite V39() Element of bool cZ
R is non empty finite unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty finite set
card R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
card the carrier of R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
Z is Element of the carrier of R
con_class Z is non empty finite Element of bool the carrier of R
bool the carrier of R is non empty finite V39() set
(Omega). R is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total finite Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty finite set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite V39() set
multMagma(# the carrier of R, the multF of R #) is non empty strict multMagma
carr ((Omega). R) is finite Element of bool the carrier of R
the carrier of ((Omega). R) is non empty finite set
Z |^ (carr ((Omega). R)) is finite Element of bool the carrier of R
K462( the carrier of R,Z) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,Z) |^ (carr ((Omega). R)) is finite Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,Z) & b₂ in carr ((Omega). R) ) } is set
card (con_class Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(R,Z) is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
card (R,Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
the carrier of (R,Z) is non empty finite set
card the carrier of (R,Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
(card (con_class Z)) * (card (R,Z)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(R,Z) is Relation-like the carrier of R -defined con_class Z -valued Function-like quasi_total finite Element of bool [: the carrier of R,(con_class Z):]
[: the carrier of R,(con_class Z):] is non empty finite set
bool [: the carrier of R,(con_class Z):] is non empty finite V39() set
{ ((R,Z) " {b₁}) where b₁ is Element of con_class Z : verum } is set
cZ is non empty finite V39() V50() a_partition of the carrier of R
q is set
card q is V6() V7() V8() cardinal set
vR is finite Element of bool the carrier of R
n is set
Rs is Element of con_class Z
{Rs} is non empty trivial finite 1 -element set
(R,Z) " {Rs} is finite Element of bool the carrier of R
q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
vR is set
n is finite set
card n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Rs is set
card Rs is V6() V7() V8() cardinal set
union cZ is finite set
card cZ is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(card cZ) * q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
vR is finite set
card vR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is non empty unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty set
{ (con_class b₁) where b₁ is Element of the carrier of R : verum } is set
bool the carrier of R is non empty set
q is set
vR is Element of the carrier of R
con_class vR is non empty Element of bool the carrier of R
(Omega). R is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
multMagma(# the carrier of R, the multF of R #) is non empty strict multMagma
carr ((Omega). R) is Element of bool the carrier of R
the carrier of ((Omega). R) is non empty set
vR |^ (carr ((Omega). R)) is Element of bool the carrier of R
K462( the carrier of R,vR) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,vR) |^ (carr ((Omega). R)) is Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,vR) & b₂ in carr ((Omega). R) ) } is set
q is set
union { (con_class b₁) where b₁ is Element of the carrier of R : verum } is set
vR is set
n is Element of the carrier of R
con_class n is non empty Element of bool the carrier of R
(Omega). R is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
multMagma(# the carrier of R, the multF of R #) is non empty strict multMagma
carr ((Omega). R) is Element of bool the carrier of R
the carrier of ((Omega). R) is non empty set
n |^ (carr ((Omega). R)) is Element of bool the carrier of R
K462( the carrier of R,n) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,n) |^ (carr ((Omega). R)) is Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,n) & b₂ in carr ((Omega). R) ) } is set
vR is Element of the carrier of R
con_class vR is non empty Element of bool the carrier of R
(Omega). R is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
multMagma(# the carrier of R, the multF of R #) is non empty strict multMagma
carr ((Omega). R) is Element of bool the carrier of R
the carrier of ((Omega). R) is non empty set
vR |^ (carr ((Omega). R)) is Element of bool the carrier of R
K462( the carrier of R,vR) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,vR) |^ (carr ((Omega). R)) is Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,vR) & b₂ in carr ((Omega). R) ) } is set
n is Element of bool the carrier of R
q is Element of bool the carrier of R
vR is Element of the carrier of R
con_class vR is non empty Element of bool the carrier of R
vR |^ (carr ((Omega). R)) is Element of bool the carrier of R
K462( the carrier of R,vR) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,vR) |^ (carr ((Omega). R)) is Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,vR) & b₂ in carr ((Omega). R) ) } is set
n is Element of the carrier of R
con_class n is non empty Element of bool the carrier of R
n |^ (carr ((Omega). R)) is Element of bool the carrier of R
K462( the carrier of R,n) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,n) |^ (carr ((Omega). R)) is Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,n) & b₂ in carr ((Omega). R) ) } is set
n is Element of bool the carrier of R
Rs is Element of the carrier of R
con_class Rs is non empty Element of bool the carrier of R
Rs |^ (carr ((Omega). R)) is Element of bool the carrier of R
K462( the carrier of R,Rs) is non empty trivial finite 1 -element Element of bool the carrier of R
K462( the carrier of R,Rs) |^ (carr ((Omega). R)) is Element of bool the carrier of R
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of R : ( b₁ in K462( the carrier of R,Rs) & b₂ in carr ((Omega). R) ) } is set
cR is set
cRs is Element of the carrier of R
cZs is set
natq1 is Element of the carrier of R
natq1 is Element of the carrier of R
R is non empty finite unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
(R) is non empty finite V39() V50() a_partition of the carrier of R
the carrier of R is non empty finite set
{ (con_class b₁) where b₁ is Element of the carrier of R : verum } is set
Z is Relation-like NAT -defined (R) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (R)
rng Z is finite V39() Element of bool (R)
bool (R) is non empty finite V39() set
cZ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
len Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom cZ is finite Element of bool NAT
card R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
card the carrier of R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
Sum cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial finite set
card the carrier of R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
Z is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over R
dim Z is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
the carrier of Z is non empty set
card the carrier of Z is V6() V7() V8() non empty cardinal set
cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
q |^ cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
bool the carrier of Z is non empty set
vR is finite Element of bool the carrier of Z
Lin vR is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of Z
the addF of Z is Relation-like [: the carrier of Z, the carrier of Z:] -defined the carrier of Z -valued Function-like quasi_total Element of bool [:[: the carrier of Z, the carrier of Z:], the carrier of Z:]
[: the carrier of Z, the carrier of Z:] is non empty set
[:[: the carrier of Z, the carrier of Z:], the carrier of Z:] is non empty set
bool [:[: the carrier of Z, the carrier of Z:], the carrier of Z:] is non empty set
the ZeroF of Z is right_complementable Element of the carrier of Z
the lmult of Z is Relation-like [: the carrier of R, the carrier of Z:] -defined the carrier of Z -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of Z:], the carrier of Z:]
[: the carrier of R, the carrier of Z:] is non empty set
[:[: the carrier of R, the carrier of Z:], the carrier of Z:] is non empty set
bool [:[: the carrier of R, the carrier of Z:], the carrier of Z:] is non empty set
VectSpStr(# the carrier of Z, the addF of Z, the ZeroF of Z, the lmult of Z #) is non empty strict VectSpStr over R
card vR is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(Omega). Z is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of Z
(0). Z is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of Z
0. Z is V104(Z) right_complementable Element of the carrier of Z
{(0. Z)} is non empty trivial finite 1 -element set
q #Z 0 is set
q |^ 0 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng n is finite set
len n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Seg cZ is finite cZ -element Element of bool NAT
dom n is finite Element of bool NAT
the carrier of (Lin vR) is non empty set
cZ -tuples_on the carrier of R is functional non empty FinSequence-membered FinSequenceSet of the carrier of R
Rs is Relation-like NAT -defined the carrier of Z -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of Z
cZs is Relation-like NAT -defined the carrier of R -valued Function-like finite cZ -element FinSequence-like FinSubsequence-like Element of cZ -tuples_on the carrier of R
dom cZs is finite cZ -element set
dom cZs is finite cZ -element Element of bool NAT
natq1 is set
{natq1} is non empty trivial finite 1 -element set
Rs " {natq1} is finite Element of bool NAT
union (Rs " {natq1}) is set
cZs . (union (Rs " {natq1})) is set
A is set
{A} is non empty trivial finite 1 -element set
dom Rs is finite Element of bool NAT
cZs . A is set
rng cZs is finite Element of bool the carrier of R
bool the carrier of R is non empty finite V39() set
[:vR, the carrier of R:] is finite set
bool [:vR, the carrier of R:] is non empty finite V39() set
natq1 is Relation-like vR -defined the carrier of R -valued Function-like quasi_total finite Element of bool [:vR, the carrier of R:]
the carrier of Z \ vR is Element of bool the carrier of Z
0. R is V104(R) right_complementable Element of the carrier of R
the ZeroF of R is right_complementable Element of the carrier of R
( the carrier of Z \ vR) --> (0. R) is Relation-like the carrier of Z \ vR -defined the carrier of R -valued Function-like constant total quasi_total Element of bool [:( the carrier of Z \ vR), the carrier of R:]
[:( the carrier of Z \ vR), the carrier of R:] is set
bool [:( the carrier of Z \ vR), the carrier of R:] is non empty set
{(0. R)} is non empty trivial finite 1 -element set
[:( the carrier of Z \ vR),{(0. R)}:] is set
natq1 +* (( the carrier of Z \ vR) --> (0. R)) is Relation-like Function-like set
dom (( the carrier of Z \ vR) --> (0. R)) is Element of bool ( the carrier of Z \ vR)
bool ( the carrier of Z \ vR) is non empty set
dom (natq1 +* (( the carrier of Z \ vR) --> (0. R))) is set
dom natq1 is finite Element of bool vR
bool vR is non empty finite V39() set
(dom natq1) \/ ( the carrier of Z \ vR) is set
vR \/ ( the carrier of Z \ vR) is Element of bool the carrier of Z
vR \/ the carrier of Z is non empty set
rng (natq1 +* (( the carrier of Z \ vR) --> (0. R))) is set
rng natq1 is finite Element of bool the carrier of R
bool the carrier of R is non empty finite V39() set
rng (( the carrier of Z \ vR) --> (0. R)) is trivial finite Element of bool the carrier of R
(rng natq1) \/ (rng (( the carrier of Z \ vR) --> (0. R))) is finite Element of bool the carrier of R
[: the carrier of Z, the carrier of R:] is non empty set
bool [: the carrier of Z, the carrier of R:] is non empty set
Funcs ( the carrier of Z, the carrier of R) is non empty FUNCTION_DOMAIN of the carrier of Z, the carrier of R
B is set
Rs . B is set
(natq1 +* (( the carrier of Z \ vR) --> (0. R))) . (Rs . B) is set
cZs . B is set
dom Rs is finite Element of bool NAT
f is Element of vR
{f} is non empty trivial finite 1 -element set
Rs " {f} is finite Element of bool NAT
f1 is set
{f1} is non empty trivial finite 1 -element set
{B} is non empty trivial finite 1 -element set
(natq1 +* (( the carrier of Z \ vR) --> (0. R))) . f is set
natq1 . f is set
union (Rs " {f}) is set
cZs . (union (Rs " {f})) is set
B is right_complementable Element of the carrier of Z
(natq1 +* (( the carrier of Z \ vR) --> (0. R))) . B is set
(( the carrier of Z \ vR) --> (0. R)) . B is set
B is Relation-like the carrier of Z -defined the carrier of R -valued Function-like quasi_total Linear_Combination of Z
Carrier B is finite Element of bool the carrier of Z
f is right_complementable Element of the carrier of Z
(natq1 +* (( the carrier of Z \ vR) --> (0. R))) . f is set
natq1 is Relation-like the carrier of Z -defined the carrier of R -valued Function-like quasi_total Linear_Combination of vR
natq1 is Relation-like the carrier of Z -defined the carrier of R -valued Function-like quasi_total Linear_Combination of vR
natq1 (#) Rs is Relation-like NAT -defined the carrier of Z -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of Z
Sum (natq1 (#) Rs) is right_complementable Element of the carrier of Z
A is right_complementable Element of the carrier of Z
[:(cZ -tuples_on the carrier of R), the carrier of (Lin vR):] is non empty set
bool [:(cZ -tuples_on the carrier of R), the carrier of (Lin vR):] is non empty set
cZs is Relation-like cZ -tuples_on the carrier of R -defined the carrier of (Lin vR) -valued Function-like quasi_total Element of bool [:(cZ -tuples_on the carrier of R), the carrier of (Lin vR):]
dom cZs is functional FinSequence-membered Element of bool (cZ -tuples_on the carrier of R)
bool (cZ -tuples_on the carrier of R) is non empty set
natq1 is Relation-like the carrier of Z -defined the carrier of R -valued Function-like quasi_total Linear_Combination of vR
A is set
Rs . A is set
natq1 . (Rs . A) is set
rng Rs is finite Element of bool the carrier of Z
B is right_complementable Element of the carrier of Z
natq1 . B is right_complementable Element of the carrier of R
[:(Seg cZ), the carrier of R:] is finite set
bool [:(Seg cZ), the carrier of R:] is non empty finite V39() set
A is Relation-like Seg cZ -defined the carrier of R -valued Function-like quasi_total finite Element of bool [:(Seg cZ), the carrier of R:]
dom A is finite Element of bool (Seg cZ)
bool (Seg cZ) is non empty finite V39() set
rng A is finite Element of bool the carrier of R
bool the carrier of R is non empty finite V39() set
B is Relation-like NAT -defined the carrier of R -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of R
len B is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
natq1 is set
A is Relation-like the carrier of Z -defined the carrier of R -valued Function-like quasi_total Linear_Combination of vR
Sum A is right_complementable Element of the carrier of Z
Carrier A is finite Element of bool the carrier of Z
rng Rs is finite Element of bool the carrier of Z
A (#) Rs is Relation-like NAT -defined the carrier of Z -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of Z
Sum (A (#) Rs) is right_complementable Element of the carrier of Z
B is Relation-like NAT -defined the carrier of R -valued Function-like finite cZ -element FinSequence-like FinSubsequence-like Element of cZ -tuples_on the carrier of R
dom B is finite cZ -element Element of bool NAT
cZs . B is right_complementable Element of the carrier of (Lin vR)
f is Relation-like the carrier of Z -defined the carrier of R -valued Function-like quasi_total Linear_Combination of vR
f (#) Rs is Relation-like NAT -defined the carrier of Z -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of Z
Sum (f (#) Rs) is right_complementable Element of the carrier of Z
f1 is right_complementable Element of the carrier of Z
A . f1 is right_complementable Element of the carrier of R
f . f1 is right_complementable Element of the carrier of R
f2 is set
[f2,f1] is set
{f2,f1} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,f1},{f2}} is non empty finite V39() set
dom Rs is finite Element of bool NAT
Rs . f2 is set
A . (Rs . f2) is set
B . f2 is set
0. R is V104(R) right_complementable Element of the carrier of R
the ZeroF of R is right_complementable Element of the carrier of R
Carrier f is finite Element of bool the carrier of Z
rng cZs is Element of bool the carrier of (Lin vR)
bool the carrier of (Lin vR) is non empty set
natq1 is set
A is set
cZs . natq1 is set
cZs . A is set
B is Relation-like NAT -defined the carrier of R -valued Function-like finite cZ -element FinSequence-like FinSubsequence-like Element of cZ -tuples_on the carrier of R
dom B is finite cZ -element Element of bool NAT
cZs . B is right_complementable Element of the carrier of (Lin vR)
f1 is Relation-like the carrier of Z -defined the carrier of R -valued Function-like quasi_total Linear_Combination of vR
f1 (#) Rs is Relation-like NAT -defined the carrier of Z -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of Z
Sum (f1 (#) Rs) is right_complementable Element of the carrier of Z
f is Relation-like NAT -defined the carrier of R -valued Function-like finite cZ -element FinSequence-like FinSubsequence-like Element of cZ -tuples_on the carrier of R
dom f is finite cZ -element Element of bool NAT
cZs . f is right_complementable Element of the carrier of (Lin vR)
f2 is Relation-like the carrier of Z -defined the carrier of R -valued Function-like quasi_total Linear_Combination of vR
f2 (#) Rs is Relation-like NAT -defined the carrier of Z -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of Z
Sum (f2 (#) Rs) is right_complementable Element of the carrier of Z
Carrier f1 is finite Element of bool the carrier of Z
rng Rs is finite Element of bool the carrier of Z
Sum f1 is right_complementable Element of the carrier of Z
Carrier f2 is finite Element of bool the carrier of Z
Sum f2 is right_complementable Element of the carrier of Z
(Sum f1) - (Sum f2) is right_complementable Element of the carrier of Z
- (Sum f2) is right_complementable Element of the carrier of Z
(Sum f1) + (- (Sum f2)) is right_complementable Element of the carrier of Z
the addF of Z . ((Sum f1),(- (Sum f2))) is right_complementable Element of the carrier of Z
[(Sum f1),(- (Sum f2))] is set
{(Sum f1),(- (Sum f2))} is non empty finite set
{(Sum f1)} is non empty trivial finite 1 -element set
{{(Sum f1),(- (Sum f2))},{(Sum f1)}} is non empty finite V39() set
the addF of Z . [(Sum f1),(- (Sum f2))] is set
0. Z is V104(Z) right_complementable Element of the carrier of Z
f1 - f2 is Relation-like the carrier of Z -defined the carrier of R -valued Function-like quasi_total Linear_Combination of Z
Sum (f1 - f2) is right_complementable Element of the carrier of Z
Carrier (f1 - f2) is finite Element of bool the carrier of Z
f is right_complementable Element of the carrier of Z
f1 . f is right_complementable Element of the carrier of R
f2 . f is right_complementable Element of the carrier of R
p1 is Relation-like the carrier of Z -defined the carrier of R -valued Function-like quasi_total Linear_Combination of vR
p1 . f is right_complementable Element of the carrier of R
0. R is V104(R) right_complementable Element of the carrier of R
the ZeroF of R is right_complementable Element of the carrier of R
(f1 . f) - (f2 . f) is right_complementable Element of the carrier of R
- (f2 . f) is right_complementable Element of the carrier of R
(f1 . f) + (- (f2 . f)) is right_complementable Element of the carrier of R
the addF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total finite Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty finite set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite V39() set
the addF of R . ((f1 . f),(- (f2 . f))) is right_complementable Element of the carrier of R
[(f1 . f),(- (f2 . f))] is set
{(f1 . f),(- (f2 . f))} is non empty finite set
{(f1 . f)} is non empty trivial finite 1 -element set
{{(f1 . f),(- (f2 . f))},{(f1 . f)}} is non empty finite V39() set
the addF of R . [(f1 . f),(- (f2 . f))] is set
f is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
B . f is set
f . f is set
Rs . f is set
f1 . (Rs . f) is set
cZs .: (cZ -tuples_on the carrier of R) is Element of bool the carrier of (Lin vR)
card (Seg cZ) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
card cZ is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
card q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
card (cZ -tuples_on the carrier of R) is V6() V7() V8() non empty cardinal set
Funcs ((Seg cZ), the carrier of R) is non empty FUNCTION_DOMAIN of Seg cZ, the carrier of R
card (Funcs ((Seg cZ), the carrier of R)) is V6() V7() V8() non empty cardinal set
Funcs (cZ,q) is set
card (Funcs (cZ,q)) is V6() V7() V8() cardinal set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
{ b₁ where b₁ is right_complementable Element of the carrier of R : for b₂ being right_complementable Element of the carrier of R holds b₁ * b₂ = b₂ * b₁ } is set
the addF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
0. R is V104(R) right_complementable Element of the carrier of R
the ZeroF of R is right_complementable Element of the carrier of R
1. R is V104(R) right_complementable Element of the carrier of R
the OneF of R is right_complementable Element of the carrier of R
q is right_complementable Element of the carrier of R
(0. R) * q is right_complementable Element of the carrier of R
the multF of R . ((0. R),q) is right_complementable Element of the carrier of R
[(0. R),q] is set
{(0. R),q} is non empty finite set
{(0. R)} is non empty trivial finite 1 -element set
{{(0. R),q},{(0. R)}} is non empty finite V39() set
the multF of R . [(0. R),q] is set
q * (0. R) is right_complementable Element of the carrier of R
the multF of R . (q,(0. R)) is right_complementable Element of the carrier of R
[q,(0. R)] is set
{q,(0. R)} is non empty finite set
{q} is non empty trivial finite 1 -element set
{{q,(0. R)},{q}} is non empty finite V39() set
the multF of R . [q,(0. R)] is set
q is non empty set
vR is set
n is right_complementable Element of the carrier of R
the addF of R || q is set
[:q,q:] is non empty set
the addF of R | [:q,q:] is Relation-like Function-like set
the multF of R || q is set
the multF of R | [:q,q:] is Relation-like Function-like set
1_ R is right_complementable Element of the carrier of R
cRs is set
cZs is set
natq1 is set
[cZs,natq1] is set
{cZs,natq1} is non empty finite set
{cZs} is non empty trivial finite 1 -element set
{{cZs,natq1},{cZs}} is non empty finite V39() set
[:[:q,q:], the carrier of R:] is non empty set
bool [:[:q,q:], the carrier of R:] is non empty set
cRs is Relation-like [:q,q:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[:q,q:], the carrier of R:]
rng cRs is Element of bool the carrier of R
bool the carrier of R is non empty set
cZs is set
dom cRs is Relation-like q -defined q -valued Element of bool [:q,q:]
bool [:q,q:] is non empty set
natq1 is set
cRs . natq1 is set
A is set
B is set
[A,B] is set
{A,B} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,B},{A}} is non empty finite V39() set
f is right_complementable Element of the carrier of R
f1 is right_complementable Element of the carrier of R
[f,f1] is set
{f,f1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,f1},{f}} is non empty finite V39() set
f + f1 is right_complementable Element of the carrier of R
the addF of R . (f,f1) is right_complementable Element of the carrier of R
the addF of R . [f,f1] is set
f2 is right_complementable Element of the carrier of R
(f + f1) * f2 is right_complementable Element of the carrier of R
the multF of R . ((f + f1),f2) is right_complementable Element of the carrier of R
[(f + f1),f2] is set
{(f + f1),f2} is non empty finite set
{(f + f1)} is non empty trivial finite 1 -element set
{{(f + f1),f2},{(f + f1)}} is non empty finite V39() set
the multF of R . [(f + f1),f2] is set
f * f2 is right_complementable Element of the carrier of R
the multF of R . (f,f2) is right_complementable Element of the carrier of R
[f,f2] is set
{f,f2} is non empty finite set
{{f,f2},{f}} is non empty finite V39() set
the multF of R . [f,f2] is set
f1 * f2 is right_complementable Element of the carrier of R
the multF of R . (f1,f2) is right_complementable Element of the carrier of R
[f1,f2] is set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V39() set
the multF of R . [f1,f2] is set
(f * f2) + (f1 * f2) is right_complementable Element of the carrier of R
the addF of R . ((f * f2),(f1 * f2)) is right_complementable Element of the carrier of R
[(f * f2),(f1 * f2)] is set
{(f * f2),(f1 * f2)} is non empty finite set
{(f * f2)} is non empty trivial finite 1 -element set
{{(f * f2),(f1 * f2)},{(f * f2)}} is non empty finite V39() set
the addF of R . [(f * f2),(f1 * f2)] is set
f2 * f is right_complementable Element of the carrier of R
the multF of R . (f2,f) is right_complementable Element of the carrier of R
[f2,f] is set
{f2,f} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,f},{f2}} is non empty finite V39() set
the multF of R . [f2,f] is set
(f2 * f) + (f1 * f2) is right_complementable Element of the carrier of R
the addF of R . ((f2 * f),(f1 * f2)) is right_complementable Element of the carrier of R
[(f2 * f),(f1 * f2)] is set
{(f2 * f),(f1 * f2)} is non empty finite set
{(f2 * f)} is non empty trivial finite 1 -element set
{{(f2 * f),(f1 * f2)},{(f2 * f)}} is non empty finite V39() set
the addF of R . [(f2 * f),(f1 * f2)] is set
f2 * f1 is right_complementable Element of the carrier of R
the multF of R . (f2,f1) is right_complementable Element of the carrier of R
[f2,f1] is set
{f2,f1} is non empty finite set
{{f2,f1},{f2}} is non empty finite V39() set
the multF of R . [f2,f1] is set
(f2 * f) + (f2 * f1) is right_complementable Element of the carrier of R
the addF of R . ((f2 * f),(f2 * f1)) is right_complementable Element of the carrier of R
[(f2 * f),(f2 * f1)] is set
{(f2 * f),(f2 * f1)} is non empty finite set
{{(f2 * f),(f2 * f1)},{(f2 * f)}} is non empty finite V39() set
the addF of R . [(f2 * f),(f2 * f1)] is set
f2 * (f + f1) is right_complementable Element of the carrier of R
the multF of R . (f2,(f + f1)) is right_complementable Element of the carrier of R
[f2,(f + f1)] is set
{f2,(f + f1)} is non empty finite set
{{f2,(f + f1)},{f2}} is non empty finite V39() set
the multF of R . [f2,(f + f1)] is set
f is right_complementable Element of the carrier of R
f is right_complementable Element of the carrier of R
[:[:q,q:],q:] is non empty set
bool [:[:q,q:],q:] is non empty set
natq1 is Relation-like [:q,q:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[:q,q:], the carrier of R:]
rng natq1 is Element of bool the carrier of R
A is set
dom natq1 is Relation-like q -defined q -valued Element of bool [:q,q:]
bool [:q,q:] is non empty set
B is set
natq1 . B is set
f is set
f1 is set
[f,f1] is set
{f,f1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,f1},{f}} is non empty finite V39() set
f2 is right_complementable Element of the carrier of R
f is right_complementable Element of the carrier of R
[f2,f] is set
{f2,f} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,f},{f2}} is non empty finite V39() set
f2 * f is right_complementable Element of the carrier of R
the multF of R . (f2,f) is right_complementable Element of the carrier of R
the multF of R . [f2,f] is set
p1 is right_complementable Element of the carrier of R
(f2 * f) * p1 is right_complementable Element of the carrier of R
the multF of R . ((f2 * f),p1) is right_complementable Element of the carrier of R
[(f2 * f),p1] is set
{(f2 * f),p1} is non empty finite set
{(f2 * f)} is non empty trivial finite 1 -element set
{{(f2 * f),p1},{(f2 * f)}} is non empty finite V39() set
the multF of R . [(f2 * f),p1] is set
f * p1 is right_complementable Element of the carrier of R
the multF of R . (f,p1) is right_complementable Element of the carrier of R
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
the multF of R . [f,p1] is set
f2 * (f * p1) is right_complementable Element of the carrier of R
the multF of R . (f2,(f * p1)) is right_complementable Element of the carrier of R
[f2,(f * p1)] is set
{f2,(f * p1)} is non empty finite set
{{f2,(f * p1)},{f2}} is non empty finite V39() set
the multF of R . [f2,(f * p1)] is set
p1 * f is right_complementable Element of the carrier of R
the multF of R . (p1,f) is right_complementable Element of the carrier of R
[p1,f] is set
{p1,f} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,f},{p1}} is non empty finite V39() set
the multF of R . [p1,f] is set
f2 * (p1 * f) is right_complementable Element of the carrier of R
the multF of R . (f2,(p1 * f)) is right_complementable Element of the carrier of R
[f2,(p1 * f)] is set
{f2,(p1 * f)} is non empty finite set
{{f2,(p1 * f)},{f2}} is non empty finite V39() set
the multF of R . [f2,(p1 * f)] is set
f2 * p1 is right_complementable Element of the carrier of R
the multF of R . (f2,p1) is right_complementable Element of the carrier of R
[f2,p1] is set
{f2,p1} is non empty finite set
{{f2,p1},{f2}} is non empty finite V39() set
the multF of R . [f2,p1] is set
(f2 * p1) * f is right_complementable Element of the carrier of R
the multF of R . ((f2 * p1),f) is right_complementable Element of the carrier of R
[(f2 * p1),f] is set
{(f2 * p1),f} is non empty finite set
{(f2 * p1)} is non empty trivial finite 1 -element set
{{(f2 * p1),f},{(f2 * p1)}} is non empty finite V39() set
the multF of R . [(f2 * p1),f] is set
p1 * f2 is right_complementable Element of the carrier of R
the multF of R . (p1,f2) is right_complementable Element of the carrier of R
[p1,f2] is set
{p1,f2} is non empty finite set
{{p1,f2},{p1}} is non empty finite V39() set
the multF of R . [p1,f2] is set
(p1 * f2) * f is right_complementable Element of the carrier of R
the multF of R . ((p1 * f2),f) is right_complementable Element of the carrier of R
[(p1 * f2),f] is set
{(p1 * f2),f} is non empty finite set
{(p1 * f2)} is non empty trivial finite 1 -element set
{{(p1 * f2),f},{(p1 * f2)}} is non empty finite V39() set
the multF of R . [(p1 * f2),f] is set
p1 * (f2 * f) is right_complementable Element of the carrier of R
the multF of R . (p1,(f2 * f)) is right_complementable Element of the carrier of R
[p1,(f2 * f)] is set
{p1,(f2 * f)} is non empty finite set
{{p1,(f2 * f)},{p1}} is non empty finite V39() set
the multF of R . [p1,(f2 * f)] is set
c1 is right_complementable Element of the carrier of R
c1 is right_complementable Element of the carrier of R
f is right_complementable Element of the carrier of R
(1_ R) * f is right_complementable Element of the carrier of R
the multF of R . ((1_ R),f) is right_complementable Element of the carrier of R
[(1_ R),f] is set
{(1_ R),f} is non empty finite set
{(1_ R)} is non empty trivial finite 1 -element set
{{(1_ R),f},{(1_ R)}} is non empty finite V39() set
the multF of R . [(1_ R),f] is set
f * (1_ R) is right_complementable Element of the carrier of R
the multF of R . (f,(1_ R)) is right_complementable Element of the carrier of R
[f,(1_ R)] is set
{f,(1_ R)} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,(1_ R)},{f}} is non empty finite V39() set
the multF of R . [f,(1_ R)] is set
cZs is Relation-like [:q,q:] -defined q -valued Function-like quasi_total Element of bool [:[:q,q:],q:]
A is Relation-like [:q,q:] -defined q -valued Function-like quasi_total Element of bool [:[:q,q:],q:]
f is Element of q
B is Element of q
doubleLoopStr(# q,cZs,A,f,B #) is non empty strict doubleLoopStr
f1 is non empty doubleLoopStr
0. f1 is V104(f1) Element of the carrier of f1
the carrier of f1 is non empty set
the ZeroF of f1 is Element of the carrier of f1
f is right_complementable Element of the carrier of R
p1 is right_complementable Element of the carrier of R
f * p1 is right_complementable Element of the carrier of R
the multF of R . (f,p1) is right_complementable Element of the carrier of R
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
the multF of R . [f,p1] is set
p1 * f is right_complementable Element of the carrier of R
the multF of R . (p1,f) is right_complementable Element of the carrier of R
[p1,f] is set
{p1,f} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,f},{p1}} is non empty finite V39() set
the multF of R . [p1,f] is set
c1 is right_complementable Element of the carrier of R
f is right_complementable Element of the carrier of R
c1 is Element of the carrier of f1
p1 is right_complementable Element of the carrier of R
p2 is Element of the carrier of f1
[c1,p2] is set
{c1,p2} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p2},{c1}} is non empty finite V39() set
f * p1 is right_complementable Element of the carrier of R
the multF of R . (f,p1) is right_complementable Element of the carrier of R
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
the multF of R . [f,p1] is set
c1 * p2 is Element of the carrier of f1
the multF of f1 is Relation-like [: the carrier of f1, the carrier of f1:] -defined the carrier of f1 -valued Function-like quasi_total Element of bool [:[: the carrier of f1, the carrier of f1:], the carrier of f1:]
[: the carrier of f1, the carrier of f1:] is non empty set
[:[: the carrier of f1, the carrier of f1:], the carrier of f1:] is non empty set
bool [:[: the carrier of f1, the carrier of f1:], the carrier of f1:] is non empty set
the multF of f1 . (c1,p2) is Element of the carrier of f1
the multF of f1 . [c1,p2] is set
f is right_complementable Element of the carrier of R
p1 is right_complementable Element of the carrier of R
f + p1 is right_complementable Element of the carrier of R
the addF of R . (f,p1) is right_complementable Element of the carrier of R
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
the addF of R . [f,p1] is set
c1 is Element of the carrier of f1
p2 is Element of the carrier of f1
c1 + p2 is Element of the carrier of f1
the addF of f1 is Relation-like [: the carrier of f1, the carrier of f1:] -defined the carrier of f1 -valued Function-like quasi_total Element of bool [:[: the carrier of f1, the carrier of f1:], the carrier of f1:]
the addF of f1 . (c1,p2) is Element of the carrier of f1
[c1,p2] is set
{c1,p2} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p2},{c1}} is non empty finite V39() set
the addF of f1 . [c1,p2] is set
f is Element of the carrier of f1
p1 is Element of the carrier of f1
f + p1 is Element of the carrier of f1
the addF of f1 is Relation-like [: the carrier of f1, the carrier of f1:] -defined the carrier of f1 -valued Function-like quasi_total Element of bool [:[: the carrier of f1, the carrier of f1:], the carrier of f1:]
the addF of f1 . (f,p1) is Element of the carrier of f1
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
the addF of f1 . [f,p1] is set
p1 + f is Element of the carrier of f1
the addF of f1 . (p1,f) is Element of the carrier of f1
[p1,f] is set
{p1,f} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,f},{p1}} is non empty finite V39() set
the addF of f1 . [p1,f] is set
p2 is right_complementable Element of the carrier of R
c1 is right_complementable Element of the carrier of R
p2 + c1 is right_complementable Element of the carrier of R
the addF of R . (p2,c1) is right_complementable Element of the carrier of R
[p2,c1] is set
{p2,c1} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,c1},{p2}} is non empty finite V39() set
the addF of R . [p2,c1] is set
f is Element of the carrier of f1
p1 is Element of the carrier of f1
f + p1 is Element of the carrier of f1
the addF of f1 is Relation-like [: the carrier of f1, the carrier of f1:] -defined the carrier of f1 -valued Function-like quasi_total Element of bool [:[: the carrier of f1, the carrier of f1:], the carrier of f1:]
the addF of f1 . (f,p1) is Element of the carrier of f1
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
the addF of f1 . [f,p1] is set
c1 is Element of the carrier of f1
(f + p1) + c1 is Element of the carrier of f1
the addF of f1 . ((f + p1),c1) is Element of the carrier of f1
[(f + p1),c1] is set
{(f + p1),c1} is non empty finite set
{(f + p1)} is non empty trivial finite 1 -element set
{{(f + p1),c1},{(f + p1)}} is non empty finite V39() set
the addF of f1 . [(f + p1),c1] is set
p1 + c1 is Element of the carrier of f1
the addF of f1 . (p1,c1) is Element of the carrier of f1
[p1,c1] is set
{p1,c1} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c1},{p1}} is non empty finite V39() set
the addF of f1 . [p1,c1] is set
f + (p1 + c1) is Element of the carrier of f1
the addF of f1 . (f,(p1 + c1)) is Element of the carrier of f1
[f,(p1 + c1)] is set
{f,(p1 + c1)} is non empty finite set
{{f,(p1 + c1)},{f}} is non empty finite V39() set
the addF of f1 . [f,(p1 + c1)] is set
p2 is right_complementable Element of the carrier of R
c2 is right_complementable Element of the carrier of R
p2 + c2 is right_complementable Element of the carrier of R
the addF of R . (p2,c2) is right_complementable Element of the carrier of R
[p2,c2] is set
{p2,c2} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,c2},{p2}} is non empty finite V39() set
the addF of R . [p2,c2] is set
c is right_complementable Element of the carrier of R
c2 + c is right_complementable Element of the carrier of R
the addF of R . (c2,c) is right_complementable Element of the carrier of R
[c2,c] is set
{c2,c} is non empty finite set
{c2} is non empty trivial finite 1 -element set
{{c2,c},{c2}} is non empty finite V39() set
the addF of R . [c2,c] is set
(p2 + c2) + c is right_complementable Element of the carrier of R
the addF of R . ((p2 + c2),c) is right_complementable Element of the carrier of R
[(p2 + c2),c] is set
{(p2 + c2),c} is non empty finite set
{(p2 + c2)} is non empty trivial finite 1 -element set
{{(p2 + c2),c},{(p2 + c2)}} is non empty finite V39() set
the addF of R . [(p2 + c2),c] is set
p2 + (c2 + c) is right_complementable Element of the carrier of R
the addF of R . (p2,(c2 + c)) is right_complementable Element of the carrier of R
[p2,(c2 + c)] is set
{p2,(c2 + c)} is non empty finite set
{{p2,(c2 + c)},{p2}} is non empty finite V39() set
the addF of R . [p2,(c2 + c)] is set
f is Element of the carrier of f1
f + (0. f1) is Element of the carrier of f1
the addF of f1 is Relation-like [: the carrier of f1, the carrier of f1:] -defined the carrier of f1 -valued Function-like quasi_total Element of bool [:[: the carrier of f1, the carrier of f1:], the carrier of f1:]
the addF of f1 . (f,(0. f1)) is Element of the carrier of f1
[f,(0. f1)] is set
{f,(0. f1)} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,(0. f1)},{f}} is non empty finite V39() set
the addF of f1 . [f,(0. f1)] is set
p1 is right_complementable Element of the carrier of R
p1 + (0. R) is right_complementable Element of the carrier of R
the addF of R . (p1,(0. R)) is right_complementable Element of the carrier of R
[p1,(0. R)] is set
{p1,(0. R)} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,(0. R)},{p1}} is non empty finite V39() set
the addF of R . [p1,(0. R)] is set
f is Element of the carrier of f1
p1 is right_complementable Element of the carrier of R
c1 is right_complementable Element of the carrier of R
p1 + c1 is right_complementable Element of the carrier of R
the addF of R . (p1,c1) is right_complementable Element of the carrier of R
[p1,c1] is set
{p1,c1} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c1},{p1}} is non empty finite V39() set
the addF of R . [p1,c1] is set
p2 is right_complementable Element of the carrier of R
p2 * p1 is right_complementable Element of the carrier of R
the multF of R . (p2,p1) is right_complementable Element of the carrier of R
[p2,p1] is set
{p2,p1} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,p1},{p2}} is non empty finite V39() set
the multF of R . [p2,p1] is set
p1 * p2 is right_complementable Element of the carrier of R
the multF of R . (p1,p2) is right_complementable Element of the carrier of R
[p1,p2] is set
{p1,p2} is non empty finite set
{{p1,p2},{p1}} is non empty finite V39() set
the multF of R . [p1,p2] is set
(0. R) * p2 is right_complementable Element of the carrier of R
the multF of R . ((0. R),p2) is right_complementable Element of the carrier of R
[(0. R),p2] is set
{(0. R),p2} is non empty finite set
{{(0. R),p2},{(0. R)}} is non empty finite V39() set
the multF of R . [(0. R),p2] is set
p2 * (0. R) is right_complementable Element of the carrier of R
the multF of R . (p2,(0. R)) is right_complementable Element of the carrier of R
[p2,(0. R)] is set
{p2,(0. R)} is non empty finite set
{{p2,(0. R)},{p2}} is non empty finite V39() set
the multF of R . [p2,(0. R)] is set
c1 * p2 is right_complementable Element of the carrier of R
the multF of R . (c1,p2) is right_complementable Element of the carrier of R
[c1,p2] is set
{c1,p2} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p2},{c1}} is non empty finite V39() set
the multF of R . [c1,p2] is set
(p1 * p2) + (c1 * p2) is right_complementable Element of the carrier of R
the addF of R . ((p1 * p2),(c1 * p2)) is right_complementable Element of the carrier of R
[(p1 * p2),(c1 * p2)] is set
{(p1 * p2),(c1 * p2)} is non empty finite set
{(p1 * p2)} is non empty trivial finite 1 -element set
{{(p1 * p2),(c1 * p2)},{(p1 * p2)}} is non empty finite V39() set
the addF of R . [(p1 * p2),(c1 * p2)] is set
p2 * (p1 + c1) is right_complementable Element of the carrier of R
the multF of R . (p2,(p1 + c1)) is right_complementable Element of the carrier of R
[p2,(p1 + c1)] is set
{p2,(p1 + c1)} is non empty finite set
{{p2,(p1 + c1)},{p2}} is non empty finite V39() set
the multF of R . [p2,(p1 + c1)] is set
p2 * c1 is right_complementable Element of the carrier of R
the multF of R . (p2,c1) is right_complementable Element of the carrier of R
[p2,c1] is set
{p2,c1} is non empty finite set
{{p2,c1},{p2}} is non empty finite V39() set
the multF of R . [p2,c1] is set
(p2 * p1) + (p2 * c1) is right_complementable Element of the carrier of R
the addF of R . ((p2 * p1),(p2 * c1)) is right_complementable Element of the carrier of R
[(p2 * p1),(p2 * c1)] is set
{(p2 * p1),(p2 * c1)} is non empty finite set
{(p2 * p1)} is non empty trivial finite 1 -element set
{{(p2 * p1),(p2 * c1)},{(p2 * p1)}} is non empty finite V39() set
the addF of R . [(p2 * p1),(p2 * c1)] is set
- (p1 * p2) is right_complementable Element of the carrier of R
(- (p1 * p2)) + (p1 * p2) is right_complementable Element of the carrier of R
the addF of R . ((- (p1 * p2)),(p1 * p2)) is right_complementable Element of the carrier of R
[(- (p1 * p2)),(p1 * p2)] is set
{(- (p1 * p2)),(p1 * p2)} is non empty finite set
{(- (p1 * p2))} is non empty trivial finite 1 -element set
{{(- (p1 * p2)),(p1 * p2)},{(- (p1 * p2))}} is non empty finite V39() set
the addF of R . [(- (p1 * p2)),(p1 * p2)] is set
((- (p1 * p2)) + (p1 * p2)) + (c1 * p2) is right_complementable Element of the carrier of R
the addF of R . (((- (p1 * p2)) + (p1 * p2)),(c1 * p2)) is right_complementable Element of the carrier of R
[((- (p1 * p2)) + (p1 * p2)),(c1 * p2)] is set
{((- (p1 * p2)) + (p1 * p2)),(c1 * p2)} is non empty finite set
{((- (p1 * p2)) + (p1 * p2))} is non empty trivial finite 1 -element set
{{((- (p1 * p2)) + (p1 * p2)),(c1 * p2)},{((- (p1 * p2)) + (p1 * p2))}} is non empty finite V39() set
the addF of R . [((- (p1 * p2)) + (p1 * p2)),(c1 * p2)] is set
- (p2 * p1) is right_complementable Element of the carrier of R
(- (p2 * p1)) + ((p2 * p1) + (p2 * c1)) is right_complementable Element of the carrier of R
the addF of R . ((- (p2 * p1)),((p2 * p1) + (p2 * c1))) is right_complementable Element of the carrier of R
[(- (p2 * p1)),((p2 * p1) + (p2 * c1))] is set
{(- (p2 * p1)),((p2 * p1) + (p2 * c1))} is non empty finite set
{(- (p2 * p1))} is non empty trivial finite 1 -element set
{{(- (p2 * p1)),((p2 * p1) + (p2 * c1))},{(- (p2 * p1))}} is non empty finite V39() set
the addF of R . [(- (p2 * p1)),((p2 * p1) + (p2 * c1))] is set
(0. R) + (c1 * p2) is right_complementable Element of the carrier of R
the addF of R . ((0. R),(c1 * p2)) is right_complementable Element of the carrier of R
[(0. R),(c1 * p2)] is set
{(0. R),(c1 * p2)} is non empty finite set
{{(0. R),(c1 * p2)},{(0. R)}} is non empty finite V39() set
the addF of R . [(0. R),(c1 * p2)] is set
(- (p2 * p1)) + (p2 * p1) is right_complementable Element of the carrier of R
the addF of R . ((- (p2 * p1)),(p2 * p1)) is right_complementable Element of the carrier of R
[(- (p2 * p1)),(p2 * p1)] is set
{(- (p2 * p1)),(p2 * p1)} is non empty finite set
{{(- (p2 * p1)),(p2 * p1)},{(- (p2 * p1))}} is non empty finite V39() set
the addF of R . [(- (p2 * p1)),(p2 * p1)] is set
((- (p2 * p1)) + (p2 * p1)) + (p2 * c1) is right_complementable Element of the carrier of R
the addF of R . (((- (p2 * p1)) + (p2 * p1)),(p2 * c1)) is right_complementable Element of the carrier of R
[((- (p2 * p1)) + (p2 * p1)),(p2 * c1)] is set
{((- (p2 * p1)) + (p2 * p1)),(p2 * c1)} is non empty finite set
{((- (p2 * p1)) + (p2 * p1))} is non empty trivial finite 1 -element set
{{((- (p2 * p1)) + (p2 * p1)),(p2 * c1)},{((- (p2 * p1)) + (p2 * p1))}} is non empty finite V39() set
the addF of R . [((- (p2 * p1)) + (p2 * p1)),(p2 * c1)] is set
(0. R) + (p2 * c1) is right_complementable Element of the carrier of R
the addF of R . ((0. R),(p2 * c1)) is right_complementable Element of the carrier of R
[(0. R),(p2 * c1)] is set
{(0. R),(p2 * c1)} is non empty finite set
{{(0. R),(p2 * c1)},{(0. R)}} is non empty finite V39() set
the addF of R . [(0. R),(p2 * c1)] is set
p2 is Element of the carrier of f1
f + p2 is Element of the carrier of f1
the addF of f1 is Relation-like [: the carrier of f1, the carrier of f1:] -defined the carrier of f1 -valued Function-like quasi_total Element of bool [:[: the carrier of f1, the carrier of f1:], the carrier of f1:]
the addF of f1 . (f,p2) is Element of the carrier of f1
[f,p2] is set
{f,p2} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p2},{f}} is non empty finite V39() set
the addF of f1 . [f,p2] is set
f is Element of the carrier of f1
p1 is Element of the carrier of f1
f * p1 is Element of the carrier of f1
the multF of f1 . (f,p1) is Element of the carrier of f1
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
the multF of f1 . [f,p1] is set
c1 is Element of the carrier of f1
(f * p1) * c1 is Element of the carrier of f1
the multF of f1 . ((f * p1),c1) is Element of the carrier of f1
[(f * p1),c1] is set
{(f * p1),c1} is non empty finite set
{(f * p1)} is non empty trivial finite 1 -element set
{{(f * p1),c1},{(f * p1)}} is non empty finite V39() set
the multF of f1 . [(f * p1),c1] is set
p1 * c1 is Element of the carrier of f1
the multF of f1 . (p1,c1) is Element of the carrier of f1
[p1,c1] is set
{p1,c1} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c1},{p1}} is non empty finite V39() set
the multF of f1 . [p1,c1] is set
f * (p1 * c1) is Element of the carrier of f1
the multF of f1 . (f,(p1 * c1)) is Element of the carrier of f1
[f,(p1 * c1)] is set
{f,(p1 * c1)} is non empty finite set
{{f,(p1 * c1)},{f}} is non empty finite V39() set
the multF of f1 . [f,(p1 * c1)] is set
p2 is right_complementable Element of the carrier of R
c2 is right_complementable Element of the carrier of R
p2 * c2 is right_complementable Element of the carrier of R
the multF of R . (p2,c2) is right_complementable Element of the carrier of R
[p2,c2] is set
{p2,c2} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,c2},{p2}} is non empty finite V39() set
the multF of R . [p2,c2] is set
c is right_complementable Element of the carrier of R
c2 * c is right_complementable Element of the carrier of R
the multF of R . (c2,c) is right_complementable Element of the carrier of R
[c2,c] is set
{c2,c} is non empty finite set
{c2} is non empty trivial finite 1 -element set
{{c2,c},{c2}} is non empty finite V39() set
the multF of R . [c2,c] is set
(p2 * c2) * c is right_complementable Element of the carrier of R
the multF of R . ((p2 * c2),c) is right_complementable Element of the carrier of R
[(p2 * c2),c] is set
{(p2 * c2),c} is non empty finite set
{(p2 * c2)} is non empty trivial finite 1 -element set
{{(p2 * c2),c},{(p2 * c2)}} is non empty finite V39() set
the multF of R . [(p2 * c2),c] is set
p2 * (c2 * c) is right_complementable Element of the carrier of R
the multF of R . (p2,(c2 * c)) is right_complementable Element of the carrier of R
[p2,(c2 * c)] is set
{p2,(c2 * c)} is non empty finite set
{{p2,(c2 * c)},{p2}} is non empty finite V39() set
the multF of R . [p2,(c2 * c)] is set
f is Element of the carrier of f1
p1 is Element of the carrier of f1
f * p1 is Element of the carrier of f1
the multF of f1 . (f,p1) is Element of the carrier of f1
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
the multF of f1 . [f,p1] is set
p1 * f is Element of the carrier of f1
the multF of f1 . (p1,f) is Element of the carrier of f1
[p1,f] is set
{p1,f} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,f},{p1}} is non empty finite V39() set
the multF of f1 . [p1,f] is set
c1 is right_complementable Element of the carrier of R
p2 is right_complementable Element of the carrier of R
c1 * p2 is right_complementable Element of the carrier of R
the multF of R . (c1,p2) is right_complementable Element of the carrier of R
[c1,p2] is set
{c1,p2} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p2},{c1}} is non empty finite V39() set
the multF of R . [c1,p2] is set
p2 * c1 is right_complementable Element of the carrier of R
the multF of R . (p2,c1) is right_complementable Element of the carrier of R
[p2,c1] is set
{p2,c1} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,c1},{p2}} is non empty finite V39() set
the multF of R . [p2,c1] is set
p1 is Element of the carrier of f1
f is Element of the carrier of f1
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
f * p1 is Element of the carrier of f1
the multF of f1 . (f,p1) is Element of the carrier of f1
the multF of f1 . [f,p1] is set
c1 is right_complementable Element of the carrier of R
c1 * (1_ R) is right_complementable Element of the carrier of R
the multF of R . (c1,(1_ R)) is right_complementable Element of the carrier of R
[c1,(1_ R)] is set
{c1,(1_ R)} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,(1_ R)},{c1}} is non empty finite V39() set
the multF of R . [c1,(1_ R)] is set
p1 * f is Element of the carrier of f1
the multF of f1 . (p1,f) is Element of the carrier of f1
[p1,f] is set
{p1,f} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,f},{p1}} is non empty finite V39() set
the multF of f1 . [p1,f] is set
f is Element of the carrier of f1
1. f1 is Element of the carrier of f1
the OneF of f1 is Element of the carrier of f1
f * (1. f1) is Element of the carrier of f1
the multF of f1 . (f,(1. f1)) is Element of the carrier of f1
[f,(1. f1)] is set
{f,(1. f1)} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,(1. f1)},{f}} is non empty finite V39() set
the multF of f1 . [f,(1. f1)] is set
(1. f1) * f is Element of the carrier of f1
the multF of f1 . ((1. f1),f) is Element of the carrier of f1
[(1. f1),f] is set
{(1. f1),f} is non empty finite set
{(1. f1)} is non empty trivial finite 1 -element set
{{(1. f1),f},{(1. f1)}} is non empty finite V39() set
the multF of f1 . [(1. f1),f] is set
1. f1 is Element of the carrier of f1
the OneF of f1 is Element of the carrier of f1
f is Element of the carrier of f1
p1 is Element of the carrier of f1
c1 is Element of the carrier of f1
p1 + c1 is Element of the carrier of f1
the addF of f1 is Relation-like [: the carrier of f1, the carrier of f1:] -defined the carrier of f1 -valued Function-like quasi_total Element of bool [:[: the carrier of f1, the carrier of f1:], the carrier of f1:]
the addF of f1 . (p1,c1) is Element of the carrier of f1
[p1,c1] is set
{p1,c1} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c1},{p1}} is non empty finite V39() set
the addF of f1 . [p1,c1] is set
f * (p1 + c1) is Element of the carrier of f1
the multF of f1 . (f,(p1 + c1)) is Element of the carrier of f1
[f,(p1 + c1)] is set
{f,(p1 + c1)} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,(p1 + c1)},{f}} is non empty finite V39() set
the multF of f1 . [f,(p1 + c1)] is set
f * p1 is Element of the carrier of f1
the multF of f1 . (f,p1) is Element of the carrier of f1
[f,p1] is set
{f,p1} is non empty finite set
{{f,p1},{f}} is non empty finite V39() set
the multF of f1 . [f,p1] is set
f * c1 is Element of the carrier of f1
the multF of f1 . (f,c1) is Element of the carrier of f1
[f,c1] is set
{f,c1} is non empty finite set
{{f,c1},{f}} is non empty finite V39() set
the multF of f1 . [f,c1] is set
(f * p1) + (f * c1) is Element of the carrier of f1
the addF of f1 . ((f * p1),(f * c1)) is Element of the carrier of f1
[(f * p1),(f * c1)] is set
{(f * p1),(f * c1)} is non empty finite set
{(f * p1)} is non empty trivial finite 1 -element set
{{(f * p1),(f * c1)},{(f * p1)}} is non empty finite V39() set
the addF of f1 . [(f * p1),(f * c1)] is set
(p1 + c1) * f is Element of the carrier of f1
the multF of f1 . ((p1 + c1),f) is Element of the carrier of f1
[(p1 + c1),f] is set
{(p1 + c1),f} is non empty finite set
{(p1 + c1)} is non empty trivial finite 1 -element set
{{(p1 + c1),f},{(p1 + c1)}} is non empty finite V39() set
the multF of f1 . [(p1 + c1),f] is set
p1 * f is Element of the carrier of f1
the multF of f1 . (p1,f) is Element of the carrier of f1
[p1,f] is set
{p1,f} is non empty finite set
{{p1,f},{p1}} is non empty finite V39() set
the multF of f1 . [p1,f] is set
c1 * f is Element of the carrier of f1
the multF of f1 . (c1,f) is Element of the carrier of f1
[c1,f] is set
{c1,f} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,f},{c1}} is non empty finite V39() set
the multF of f1 . [c1,f] is set
(p1 * f) + (c1 * f) is Element of the carrier of f1
the addF of f1 . ((p1 * f),(c1 * f)) is Element of the carrier of f1
[(p1 * f),(c1 * f)] is set
{(p1 * f),(c1 * f)} is non empty finite set
{(p1 * f)} is non empty trivial finite 1 -element set
{{(p1 * f),(c1 * f)},{(p1 * f)}} is non empty finite V39() set
the addF of f1 . [(p1 * f),(c1 * f)] is set
c2 is right_complementable Element of the carrier of R
c is right_complementable Element of the carrier of R
c2 + c is right_complementable Element of the carrier of R
the addF of R . (c2,c) is right_complementable Element of the carrier of R
[c2,c] is set
{c2,c} is non empty finite set
{c2} is non empty trivial finite 1 -element set
{{c2,c},{c2}} is non empty finite V39() set
the addF of R . [c2,c] is set
p2 is right_complementable Element of the carrier of R
p2 * c2 is right_complementable Element of the carrier of R
the multF of R . (p2,c2) is right_complementable Element of the carrier of R
[p2,c2] is set
{p2,c2} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,c2},{p2}} is non empty finite V39() set
the multF of R . [p2,c2] is set
p2 * c is right_complementable Element of the carrier of R
the multF of R . (p2,c) is right_complementable Element of the carrier of R
[p2,c] is set
{p2,c} is non empty finite set
{{p2,c},{p2}} is non empty finite V39() set
the multF of R . [p2,c] is set
c2 * p2 is right_complementable Element of the carrier of R
the multF of R . (c2,p2) is right_complementable Element of the carrier of R
[c2,p2] is set
{c2,p2} is non empty finite set
{{c2,p2},{c2}} is non empty finite V39() set
the multF of R . [c2,p2] is set
c * p2 is right_complementable Element of the carrier of R
the multF of R . (c,p2) is right_complementable Element of the carrier of R
[c,p2] is set
{c,p2} is non empty finite set
{c} is non empty trivial finite 1 -element set
{{c,p2},{c}} is non empty finite V39() set
the multF of R . [c,p2] is set
p2 * (c2 + c) is right_complementable Element of the carrier of R
the multF of R . (p2,(c2 + c)) is right_complementable Element of the carrier of R
[p2,(c2 + c)] is set
{p2,(c2 + c)} is non empty finite set
{{p2,(c2 + c)},{p2}} is non empty finite V39() set
the multF of R . [p2,(c2 + c)] is set
(p2 * c2) + (p2 * c) is right_complementable Element of the carrier of R
the addF of R . ((p2 * c2),(p2 * c)) is right_complementable Element of the carrier of R
[(p2 * c2),(p2 * c)] is set
{(p2 * c2),(p2 * c)} is non empty finite set
{(p2 * c2)} is non empty trivial finite 1 -element set
{{(p2 * c2),(p2 * c)},{(p2 * c2)}} is non empty finite V39() set
the addF of R . [(p2 * c2),(p2 * c)] is set
(c2 + c) * p2 is right_complementable Element of the carrier of R
the multF of R . ((c2 + c),p2) is right_complementable Element of the carrier of R
[(c2 + c),p2] is set
{(c2 + c),p2} is non empty finite set
{(c2 + c)} is non empty trivial finite 1 -element set
{{(c2 + c),p2},{(c2 + c)}} is non empty finite V39() set
the multF of R . [(c2 + c),p2] is set
(c2 * p2) + (c * p2) is right_complementable Element of the carrier of R
the addF of R . ((c2 * p2),(c * p2)) is right_complementable Element of the carrier of R
[(c2 * p2),(c * p2)] is set
{(c2 * p2),(c * p2)} is non empty finite set
{(c2 * p2)} is non empty trivial finite 1 -element set
{{(c2 * p2),(c * p2)},{(c2 * p2)}} is non empty finite V39() set
the addF of R . [(c2 * p2),(c * p2)] is set
f is Element of the carrier of f1
p1 is right_complementable Element of the carrier of R
c1 is right_complementable Element of the carrier of R
c1 * p1 is right_complementable Element of the carrier of R
the multF of R . (c1,p1) is right_complementable Element of the carrier of R
[c1,p1] is set
{c1,p1} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p1},{c1}} is non empty finite V39() set
the multF of R . [c1,p1] is set
p1 * c1 is right_complementable Element of the carrier of R
the multF of R . (p1,c1) is right_complementable Element of the carrier of R
[p1,c1] is set
{p1,c1} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c1},{p1}} is non empty finite V39() set
the multF of R . [p1,c1] is set
p2 is right_complementable Element of the carrier of R
(1_ R) * p2 is right_complementable Element of the carrier of R
the multF of R . ((1_ R),p2) is right_complementable Element of the carrier of R
[(1_ R),p2] is set
{(1_ R),p2} is non empty finite set
{{(1_ R),p2},{(1_ R)}} is non empty finite V39() set
the multF of R . [(1_ R),p2] is set
p2 * (1_ R) is right_complementable Element of the carrier of R
the multF of R . (p2,(1_ R)) is right_complementable Element of the carrier of R
[p2,(1_ R)] is set
{p2,(1_ R)} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,(1_ R)},{p2}} is non empty finite V39() set
the multF of R . [p2,(1_ R)] is set
(p1 * c1) * p2 is right_complementable Element of the carrier of R
the multF of R . ((p1 * c1),p2) is right_complementable Element of the carrier of R
[(p1 * c1),p2] is set
{(p1 * c1),p2} is non empty finite set
{(p1 * c1)} is non empty trivial finite 1 -element set
{{(p1 * c1),p2},{(p1 * c1)}} is non empty finite V39() set
the multF of R . [(p1 * c1),p2] is set
p2 * p1 is right_complementable Element of the carrier of R
the multF of R . (p2,p1) is right_complementable Element of the carrier of R
[p2,p1] is set
{p2,p1} is non empty finite set
{{p2,p1},{p2}} is non empty finite V39() set
the multF of R . [p2,p1] is set
(p2 * p1) * c1 is right_complementable Element of the carrier of R
the multF of R . ((p2 * p1),c1) is right_complementable Element of the carrier of R
[(p2 * p1),c1] is set
{(p2 * p1),c1} is non empty finite set
{(p2 * p1)} is non empty trivial finite 1 -element set
{{(p2 * p1),c1},{(p2 * p1)}} is non empty finite V39() set
the multF of R . [(p2 * p1),c1] is set
p1 * p2 is right_complementable Element of the carrier of R
the multF of R . (p1,p2) is right_complementable Element of the carrier of R
[p1,p2] is set
{p1,p2} is non empty finite set
{{p1,p2},{p1}} is non empty finite V39() set
the multF of R . [p1,p2] is set
(p1 * p2) * c1 is right_complementable Element of the carrier of R
the multF of R . ((p1 * p2),c1) is right_complementable Element of the carrier of R
[(p1 * p2),c1] is set
{(p1 * p2),c1} is non empty finite set
{(p1 * p2)} is non empty trivial finite 1 -element set
{{(p1 * p2),c1},{(p1 * p2)}} is non empty finite V39() set
the multF of R . [(p1 * p2),c1] is set
p1 " is right_complementable Element of the carrier of R
(p1 ") * (p1 * c1) is right_complementable Element of the carrier of R
the multF of R . ((p1 "),(p1 * c1)) is right_complementable Element of the carrier of R
[(p1 "),(p1 * c1)] is set
{(p1 "),(p1 * c1)} is non empty finite set
{(p1 ")} is non empty trivial finite 1 -element set
{{(p1 "),(p1 * c1)},{(p1 ")}} is non empty finite V39() set
the multF of R . [(p1 "),(p1 * c1)] is set
((p1 ") * (p1 * c1)) * p2 is right_complementable Element of the carrier of R
the multF of R . (((p1 ") * (p1 * c1)),p2) is right_complementable Element of the carrier of R
[((p1 ") * (p1 * c1)),p2] is set
{((p1 ") * (p1 * c1)),p2} is non empty finite set
{((p1 ") * (p1 * c1))} is non empty trivial finite 1 -element set
{{((p1 ") * (p1 * c1)),p2},{((p1 ") * (p1 * c1))}} is non empty finite V39() set
the multF of R . [((p1 ") * (p1 * c1)),p2] is set
(p1 ") * ((p1 * p2) * c1) is right_complementable Element of the carrier of R
the multF of R . ((p1 "),((p1 * p2) * c1)) is right_complementable Element of the carrier of R
[(p1 "),((p1 * p2) * c1)] is set
{(p1 "),((p1 * p2) * c1)} is non empty finite set
{{(p1 "),((p1 * p2) * c1)},{(p1 ")}} is non empty finite V39() set
the multF of R . [(p1 "),((p1 * p2) * c1)] is set
(p1 ") * (p1 * p2) is right_complementable Element of the carrier of R
the multF of R . ((p1 "),(p1 * p2)) is right_complementable Element of the carrier of R
[(p1 "),(p1 * p2)] is set
{(p1 "),(p1 * p2)} is non empty finite set
{{(p1 "),(p1 * p2)},{(p1 ")}} is non empty finite V39() set
the multF of R . [(p1 "),(p1 * p2)] is set
((p1 ") * (p1 * p2)) * c1 is right_complementable Element of the carrier of R
the multF of R . (((p1 ") * (p1 * p2)),c1) is right_complementable Element of the carrier of R
[((p1 ") * (p1 * p2)),c1] is set
{((p1 ") * (p1 * p2)),c1} is non empty finite set
{((p1 ") * (p1 * p2))} is non empty trivial finite 1 -element set
{{((p1 ") * (p1 * p2)),c1},{((p1 ") * (p1 * p2))}} is non empty finite V39() set
the multF of R . [((p1 ") * (p1 * p2)),c1] is set
(p1 ") * p1 is right_complementable Element of the carrier of R
the multF of R . ((p1 "),p1) is right_complementable Element of the carrier of R
[(p1 "),p1] is set
{(p1 "),p1} is non empty finite set
{{(p1 "),p1},{(p1 ")}} is non empty finite V39() set
the multF of R . [(p1 "),p1] is set
((p1 ") * p1) * c1 is right_complementable Element of the carrier of R
the multF of R . (((p1 ") * p1),c1) is right_complementable Element of the carrier of R
[((p1 ") * p1),c1] is set
{((p1 ") * p1),c1} is non empty finite set
{((p1 ") * p1)} is non empty trivial finite 1 -element set
{{((p1 ") * p1),c1},{((p1 ") * p1)}} is non empty finite V39() set
the multF of R . [((p1 ") * p1),c1] is set
(((p1 ") * p1) * c1) * p2 is right_complementable Element of the carrier of R
the multF of R . ((((p1 ") * p1) * c1),p2) is right_complementable Element of the carrier of R
[(((p1 ") * p1) * c1),p2] is set
{(((p1 ") * p1) * c1),p2} is non empty finite set
{(((p1 ") * p1) * c1)} is non empty trivial finite 1 -element set
{{(((p1 ") * p1) * c1),p2},{(((p1 ") * p1) * c1)}} is non empty finite V39() set
the multF of R . [(((p1 ") * p1) * c1),p2] is set
((p1 ") * p1) * p2 is right_complementable Element of the carrier of R
the multF of R . (((p1 ") * p1),p2) is right_complementable Element of the carrier of R
[((p1 ") * p1),p2] is set
{((p1 ") * p1),p2} is non empty finite set
{{((p1 ") * p1),p2},{((p1 ") * p1)}} is non empty finite V39() set
the multF of R . [((p1 ") * p1),p2] is set
(((p1 ") * p1) * p2) * c1 is right_complementable Element of the carrier of R
the multF of R . ((((p1 ") * p1) * p2),c1) is right_complementable Element of the carrier of R
[(((p1 ") * p1) * p2),c1] is set
{(((p1 ") * p1) * p2),c1} is non empty finite set
{(((p1 ") * p1) * p2)} is non empty trivial finite 1 -element set
{{(((p1 ") * p1) * p2),c1},{(((p1 ") * p1) * p2)}} is non empty finite V39() set
the multF of R . [(((p1 ") * p1) * p2),c1] is set
(1_ R) * c1 is right_complementable Element of the carrier of R
the multF of R . ((1_ R),c1) is right_complementable Element of the carrier of R
[(1_ R),c1] is set
{(1_ R),c1} is non empty finite set
{{(1_ R),c1},{(1_ R)}} is non empty finite V39() set
the multF of R . [(1_ R),c1] is set
((1_ R) * c1) * p2 is right_complementable Element of the carrier of R
the multF of R . (((1_ R) * c1),p2) is right_complementable Element of the carrier of R
[((1_ R) * c1),p2] is set
{((1_ R) * c1),p2} is non empty finite set
{((1_ R) * c1)} is non empty trivial finite 1 -element set
{{((1_ R) * c1),p2},{((1_ R) * c1)}} is non empty finite V39() set
the multF of R . [((1_ R) * c1),p2] is set
((1_ R) * p2) * c1 is right_complementable Element of the carrier of R
the multF of R . (((1_ R) * p2),c1) is right_complementable Element of the carrier of R
[((1_ R) * p2),c1] is set
{((1_ R) * p2),c1} is non empty finite set
{((1_ R) * p2)} is non empty trivial finite 1 -element set
{{((1_ R) * p2),c1},{((1_ R) * p2)}} is non empty finite V39() set
the multF of R . [((1_ R) * p2),c1] is set
c1 * p2 is right_complementable Element of the carrier of R
the multF of R . (c1,p2) is right_complementable Element of the carrier of R
[c1,p2] is set
{c1,p2} is non empty finite set
{{c1,p2},{c1}} is non empty finite V39() set
the multF of R . [c1,p2] is set
p2 * c1 is right_complementable Element of the carrier of R
the multF of R . (p2,c1) is right_complementable Element of the carrier of R
[p2,c1] is set
{p2,c1} is non empty finite set
{{p2,c1},{p2}} is non empty finite V39() set
the multF of R . [p2,c1] is set
p2 is Element of the carrier of f1
p2 * f is Element of the carrier of f1
the multF of f1 . (p2,f) is Element of the carrier of f1
[p2,f] is set
{p2,f} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,f},{p2}} is non empty finite V39() set
the multF of f1 . [p2,f] is set
f is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of f is non empty non trivial set
the addF of f is Relation-like [: the carrier of f, the carrier of f:] -defined the carrier of f -valued Function-like quasi_total Element of bool [:[: the carrier of f, the carrier of f:], the carrier of f:]
[: the carrier of f, the carrier of f:] is non empty set
[:[: the carrier of f, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of f, the carrier of f:], the carrier of f:] is non empty set
the addF of R || the carrier of f is set
the addF of R | [: the carrier of f, the carrier of f:] is Relation-like Function-like set
the multF of f is Relation-like [: the carrier of f, the carrier of f:] -defined the carrier of f -valued Function-like quasi_total Element of bool [:[: the carrier of f, the carrier of f:], the carrier of f:]
the multF of R || the carrier of f is set
the multF of R | [: the carrier of f, the carrier of f:] is Relation-like Function-like set
0. f is V104(f) right_complementable Element of the carrier of f
the ZeroF of f is right_complementable Element of the carrier of f
1. f is V104(f) right_complementable Element of the carrier of f
the OneF of f is right_complementable Element of the carrier of f
Z is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of Z is non empty non trivial set
the addF of Z is Relation-like [: the carrier of Z, the carrier of Z:] -defined the carrier of Z -valued Function-like quasi_total Element of bool [:[: the carrier of Z, the carrier of Z:], the carrier of Z:]
[: the carrier of Z, the carrier of Z:] is non empty set
[:[: the carrier of Z, the carrier of Z:], the carrier of Z:] is non empty set
bool [:[: the carrier of Z, the carrier of Z:], the carrier of Z:] is non empty set
the addF of R || the carrier of Z is set
the addF of R | [: the carrier of Z, the carrier of Z:] is Relation-like Function-like set
the multF of Z is Relation-like [: the carrier of Z, the carrier of Z:] -defined the carrier of Z -valued Function-like quasi_total Element of bool [:[: the carrier of Z, the carrier of Z:], the carrier of Z:]
the multF of R || the carrier of Z is set
the multF of R | [: the carrier of Z, the carrier of Z:] is Relation-like Function-like set
0. Z is V104(Z) right_complementable Element of the carrier of Z
the ZeroF of Z is right_complementable Element of the carrier of Z
1. Z is V104(Z) right_complementable Element of the carrier of Z
the OneF of Z is right_complementable Element of the carrier of Z
cZ is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of cZ is non empty non trivial set
the addF of cZ is Relation-like [: the carrier of cZ, the carrier of cZ:] -defined the carrier of cZ -valued Function-like quasi_total Element of bool [:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:]
[: the carrier of cZ, the carrier of cZ:] is non empty set
[:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:] is non empty set
bool [:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:] is non empty set
the addF of R || the carrier of cZ is set
the addF of R | [: the carrier of cZ, the carrier of cZ:] is Relation-like Function-like set
the multF of cZ is Relation-like [: the carrier of cZ, the carrier of cZ:] -defined the carrier of cZ -valued Function-like quasi_total Element of bool [:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:]
the multF of R || the carrier of cZ is set
the multF of R | [: the carrier of cZ, the carrier of cZ:] is Relation-like Function-like set
0. cZ is V104(cZ) right_complementable Element of the carrier of cZ
the ZeroF of cZ is right_complementable Element of the carrier of cZ
1. cZ is V104(cZ) right_complementable Element of the carrier of cZ
the OneF of cZ is right_complementable Element of the carrier of cZ
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial set
the carrier of R is non empty non trivial set
Z is set
{ b₁ where b₁ is right_complementable Element of the carrier of R : for b₂ being right_complementable Element of the carrier of R holds b₁ * b₂ = b₂ * b₁ } is set
cZ is right_complementable Element of the carrier of R
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial set
the carrier of R is non empty non trivial finite set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
Z is right_complementable Element of the carrier of R
the carrier of (R) is non empty non trivial set
{ b₁ where b₁ is right_complementable Element of the carrier of R : for b₂ being right_complementable Element of the carrier of R holds b₁ * b₂ = b₂ * b₁ } is set
cZ is right_complementable Element of the carrier of R
Z * cZ is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (Z,cZ) is right_complementable Element of the carrier of R
[Z,cZ] is set
{Z,cZ} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,cZ},{Z}} is non empty finite V39() set
the multF of R . [Z,cZ] is set
cZ * Z is right_complementable Element of the carrier of R
the multF of R . (cZ,Z) is right_complementable Element of the carrier of R
[cZ,Z] is set
{cZ,Z} is non empty finite set
{cZ} is non empty trivial finite 1 -element set
{{cZ,Z},{cZ}} is non empty finite V39() set
the multF of R . [cZ,Z] is set
q is right_complementable Element of the carrier of R
cZ is right_complementable Element of the carrier of R
Z * cZ is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (Z,cZ) is right_complementable Element of the carrier of R
[Z,cZ] is set
{Z,cZ} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,cZ},{Z}} is non empty finite V39() set
the multF of R . [Z,cZ] is set
cZ * Z is right_complementable Element of the carrier of R
the multF of R . (cZ,Z) is right_complementable Element of the carrier of R
[cZ,Z] is set
{cZ,Z} is non empty finite set
{cZ} is non empty trivial finite 1 -element set
{{cZ,Z},{cZ}} is non empty finite V39() set
the multF of R . [cZ,Z] is set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
0. R is V104(R) right_complementable Element of the carrier of R
the carrier of R is non empty non trivial set
the ZeroF of R is right_complementable Element of the carrier of R
Z is right_complementable Element of the carrier of R
(0. R) * Z is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . ((0. R),Z) is right_complementable Element of the carrier of R
[(0. R),Z] is set
{(0. R),Z} is non empty finite set
{(0. R)} is non empty trivial finite 1 -element set
{{(0. R),Z},{(0. R)}} is non empty finite V39() set
the multF of R . [(0. R),Z] is set
Z * (0. R) is right_complementable Element of the carrier of R
the multF of R . (Z,(0. R)) is right_complementable Element of the carrier of R
[Z,(0. R)] is set
{Z,(0. R)} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,(0. R)},{Z}} is non empty finite V39() set
the multF of R . [Z,(0. R)] is set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
1_ R is right_complementable Element of the carrier of R
the carrier of R is non empty non trivial set
1. R is V104(R) right_complementable Element of the carrier of R
the OneF of R is right_complementable Element of the carrier of R
Z is right_complementable Element of the carrier of R
(1_ R) * Z is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . ((1_ R),Z) is right_complementable Element of the carrier of R
[(1_ R),Z] is set
{(1_ R),Z} is non empty finite set
{(1_ R)} is non empty trivial finite 1 -element set
{{(1_ R),Z},{(1_ R)}} is non empty finite V39() set
the multF of R . [(1_ R),Z] is set
Z * (1_ R) is right_complementable Element of the carrier of R
the multF of R . (Z,(1_ R)) is right_complementable Element of the carrier of R
[Z,(1_ R)] is set
{Z,(1_ R)} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,(1_ R)},{Z}} is non empty finite V39() set
the multF of R . [Z,(1_ R)] is set
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial finite set
card the carrier of (R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
0. R is V104(R) right_complementable Element of the carrier of R
the carrier of R is non empty non trivial finite set
the ZeroF of R is right_complementable Element of the carrier of R
1. R is V104(R) right_complementable Element of the carrier of R
the OneF of R is right_complementable Element of the carrier of R
{(0. R),(1. R)} is non empty finite set
card {(0. R),(1. R)} is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
Z is right_complementable Element of the carrier of R
(1. R) * Z is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total finite Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty finite set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite V39() set
the multF of R . ((1. R),Z) is right_complementable Element of the carrier of R
[(1. R),Z] is set
{(1. R),Z} is non empty finite set
{(1. R)} is non empty trivial finite 1 -element set
{{(1. R),Z},{(1. R)}} is non empty finite V39() set
the multF of R . [(1. R),Z] is set
Z * (1. R) is right_complementable Element of the carrier of R
the multF of R . (Z,(1. R)) is right_complementable Element of the carrier of R
[Z,(1. R)] is set
{Z,(1. R)} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,(1. R)},{Z}} is non empty finite V39() set
the multF of R . [Z,(1. R)] is set
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial finite set
card the carrier of (R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
the carrier of R is non empty non trivial finite set
card the carrier of R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
the carrier of R \ the carrier of (R) is finite Element of bool the carrier of R
bool the carrier of R is non empty finite V39() set
card ( the carrier of R \ the carrier of (R)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(card the carrier of R) - (card the carrier of R) is V31() V32() integer ext-real set
q is right_complementable Element of the carrier of R
vR is right_complementable Element of the carrier of R
q * vR is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total finite Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty finite set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite V39() set
the multF of R . (q,vR) is right_complementable Element of the carrier of R
[q,vR] is set
{q,vR} is non empty finite set
{q} is non empty trivial finite 1 -element set
{{q,vR},{q}} is non empty finite V39() set
the multF of R . [q,vR] is set
vR * q is right_complementable Element of the carrier of R
the multF of R . (vR,q) is right_complementable Element of the carrier of R
[vR,q] is set
{vR,q} is non empty finite set
{vR} is non empty trivial finite 1 -element set
{{vR,q},{vR}} is non empty finite V39() set
the multF of R . [vR,q] is set
q is set
vR is right_complementable Element of the carrier of R
n is right_complementable Element of the carrier of R
vR * n is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total finite Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty finite set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite V39() set
the multF of R . (vR,n) is right_complementable Element of the carrier of R
[vR,n] is set
{vR,n} is non empty finite set
{vR} is non empty trivial finite 1 -element set
{{vR,n},{vR}} is non empty finite V39() set
the multF of R . [vR,n] is set
n * vR is right_complementable Element of the carrier of R
the multF of R . (n,vR) is right_complementable Element of the carrier of R
[n,vR] is set
{n,vR} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,vR},{n}} is non empty finite V39() set
the multF of R . [n,vR] is set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial set
MultGroup R is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
center (MultGroup R) is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of MultGroup R
the carrier of (center (MultGroup R)) is non empty set
0. R is V104(R) right_complementable Element of the carrier of R
the carrier of R is non empty non trivial set
the ZeroF of R is right_complementable Element of the carrier of R
{(0. R)} is non empty trivial finite 1 -element set
the carrier of (center (MultGroup R)) \/ {(0. R)} is non empty set
the carrier of (MultGroup R) is non empty set
NonZero R is non empty Element of bool the carrier of R
bool the carrier of R is non empty set
[#] R is non empty non proper Element of bool the carrier of R
([#] R) \ {(0. R)} is Element of bool the carrier of R
the carrier of (MultGroup R) \/ {(0. R)} is non empty set
Z is set
cZ is Element of the carrier of (MultGroup R)
q is right_complementable Element of the carrier of R
vR is right_complementable Element of the carrier of R
q * vR is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (q,vR) is right_complementable Element of the carrier of R
[q,vR] is set
{q,vR} is non empty finite set
{q} is non empty trivial finite 1 -element set
{{q,vR},{q}} is non empty finite V39() set
the multF of R . [q,vR] is set
vR * q is right_complementable Element of the carrier of R
the multF of R . (vR,q) is right_complementable Element of the carrier of R
[vR,q] is set
{vR,q} is non empty finite set
{vR} is non empty trivial finite 1 -element set
{{vR,q},{vR}} is non empty finite V39() set
the multF of R . [vR,q] is set
n is Element of the carrier of (MultGroup R)
cZ * n is Element of the carrier of (MultGroup R)
the multF of (MultGroup R) is Relation-like [: the carrier of (MultGroup R), the carrier of (MultGroup R):] -defined the carrier of (MultGroup R) -valued Function-like quasi_total Element of bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):]
[: the carrier of (MultGroup R), the carrier of (MultGroup R):] is non empty set
[:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty set
bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty set
the multF of (MultGroup R) . (cZ,n) is Element of the carrier of (MultGroup R)
[cZ,n] is set
{cZ,n} is non empty finite set
{cZ} is non empty trivial finite 1 -element set
{{cZ,n},{cZ}} is non empty finite V39() set
the multF of (MultGroup R) . [cZ,n] is set
n * cZ is Element of the carrier of (MultGroup R)
the multF of (MultGroup R) . (n,cZ) is Element of the carrier of (MultGroup R)
[n,cZ] is set
{n,cZ} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,cZ},{n}} is non empty finite V39() set
the multF of (MultGroup R) . [n,cZ] is set
Z is set
cZ is right_complementable Element of the carrier of (R)
q is right_complementable Element of the carrier of R
q is right_complementable Element of the carrier of R
n is Element of the carrier of (MultGroup R)
vR is Element of the carrier of (MultGroup R)
vR * n is Element of the carrier of (MultGroup R)
the multF of (MultGroup R) is Relation-like [: the carrier of (MultGroup R), the carrier of (MultGroup R):] -defined the carrier of (MultGroup R) -valued Function-like quasi_total Element of bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):]
[: the carrier of (MultGroup R), the carrier of (MultGroup R):] is non empty set
[:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty set
bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty set
the multF of (MultGroup R) . (vR,n) is Element of the carrier of (MultGroup R)
[vR,n] is set
{vR,n} is non empty finite set
{vR} is non empty trivial finite 1 -element set
{{vR,n},{vR}} is non empty finite V39() set
the multF of (MultGroup R) . [vR,n] is set
Rs is right_complementable Element of the carrier of R
q * Rs is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (q,Rs) is right_complementable Element of the carrier of R
[q,Rs] is set
{q,Rs} is non empty finite set
{q} is non empty trivial finite 1 -element set
{{q,Rs},{q}} is non empty finite V39() set
the multF of R . [q,Rs] is set
Rs * q is right_complementable Element of the carrier of R
the multF of R . (Rs,q) is right_complementable Element of the carrier of R
[Rs,q] is set
{Rs,q} is non empty finite set
{Rs} is non empty trivial finite 1 -element set
{{Rs,q},{Rs}} is non empty finite V39() set
the multF of R . [Rs,q] is set
n * vR is Element of the carrier of (MultGroup R)
the multF of (MultGroup R) . (n,vR) is Element of the carrier of (MultGroup R)
[n,vR] is set
{n,vR} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,vR},{n}} is non empty finite V39() set
the multF of (MultGroup R) . [n,vR] is set
q is right_complementable Element of the carrier of R
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
1. R is V104(R) right_complementable Element of the carrier of R
the OneF of R is right_complementable Element of the carrier of R
1_ R is right_complementable Element of the carrier of R
Z is right_complementable Element of the carrier of R
{ b₁ where b₁ is right_complementable Element of the carrier of R : b₁ * Z = Z * b₁ } is set
the addF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
0. R is V104(R) right_complementable Element of the carrier of R
the ZeroF of R is right_complementable Element of the carrier of R
(0. R) * Z is right_complementable Element of the carrier of R
the multF of R . ((0. R),Z) is right_complementable Element of the carrier of R
[(0. R),Z] is set
{(0. R),Z} is non empty finite set
{(0. R)} is non empty trivial finite 1 -element set
{{(0. R),Z},{(0. R)}} is non empty finite V39() set
the multF of R . [(0. R),Z] is set
Z * (0. R) is right_complementable Element of the carrier of R
the multF of R . (Z,(0. R)) is right_complementable Element of the carrier of R
[Z,(0. R)] is set
{Z,(0. R)} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,(0. R)},{Z}} is non empty finite V39() set
the multF of R . [Z,(0. R)] is set
vR is non empty set
n is set
Rs is right_complementable Element of the carrier of R
Rs * Z is right_complementable Element of the carrier of R
the multF of R . (Rs,Z) is right_complementable Element of the carrier of R
[Rs,Z] is set
{Rs,Z} is non empty finite set
{Rs} is non empty trivial finite 1 -element set
{{Rs,Z},{Rs}} is non empty finite V39() set
the multF of R . [Rs,Z] is set
Z * Rs is right_complementable Element of the carrier of R
the multF of R . (Z,Rs) is right_complementable Element of the carrier of R
[Z,Rs] is set
{Z,Rs} is non empty finite set
{{Z,Rs},{Z}} is non empty finite V39() set
the multF of R . [Z,Rs] is set
the addF of R || vR is set
[:vR,vR:] is non empty set
the addF of R | [:vR,vR:] is Relation-like Function-like set
the multF of R || vR is set
the multF of R | [:vR,vR:] is Relation-like Function-like set
cZs is set
natq1 is set
A is set
[natq1,A] is set
{natq1,A} is non empty finite set
{natq1} is non empty trivial finite 1 -element set
{{natq1,A},{natq1}} is non empty finite V39() set
[:[:vR,vR:], the carrier of R:] is non empty set
bool [:[:vR,vR:], the carrier of R:] is non empty set
cZs is Relation-like [:vR,vR:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[:vR,vR:], the carrier of R:]
rng cZs is Element of bool the carrier of R
bool the carrier of R is non empty set
natq1 is set
dom cZs is Relation-like vR -defined vR -valued Element of bool [:vR,vR:]
bool [:vR,vR:] is non empty set
A is set
cZs . A is set
B is set
f is set
[B,f] is set
{B,f} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,f},{B}} is non empty finite V39() set
f1 is right_complementable Element of the carrier of R
f2 is right_complementable Element of the carrier of R
[f1,f2] is set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V39() set
f1 + f2 is right_complementable Element of the carrier of R
the addF of R . (f1,f2) is right_complementable Element of the carrier of R
the addF of R . [f1,f2] is set
(f1 + f2) * Z is right_complementable Element of the carrier of R
the multF of R . ((f1 + f2),Z) is right_complementable Element of the carrier of R
[(f1 + f2),Z] is set
{(f1 + f2),Z} is non empty finite set
{(f1 + f2)} is non empty trivial finite 1 -element set
{{(f1 + f2),Z},{(f1 + f2)}} is non empty finite V39() set
the multF of R . [(f1 + f2),Z] is set
Z * f1 is right_complementable Element of the carrier of R
the multF of R . (Z,f1) is right_complementable Element of the carrier of R
[Z,f1] is set
{Z,f1} is non empty finite set
{{Z,f1},{Z}} is non empty finite V39() set
the multF of R . [Z,f1] is set
Z * f2 is right_complementable Element of the carrier of R
the multF of R . (Z,f2) is right_complementable Element of the carrier of R
[Z,f2] is set
{Z,f2} is non empty finite set
{{Z,f2},{Z}} is non empty finite V39() set
the multF of R . [Z,f2] is set
(Z * f1) + (Z * f2) is right_complementable Element of the carrier of R
the addF of R . ((Z * f1),(Z * f2)) is right_complementable Element of the carrier of R
[(Z * f1),(Z * f2)] is set
{(Z * f1),(Z * f2)} is non empty finite set
{(Z * f1)} is non empty trivial finite 1 -element set
{{(Z * f1),(Z * f2)},{(Z * f1)}} is non empty finite V39() set
the addF of R . [(Z * f1),(Z * f2)] is set
Z * (f1 + f2) is right_complementable Element of the carrier of R
the multF of R . (Z,(f1 + f2)) is right_complementable Element of the carrier of R
[Z,(f1 + f2)] is set
{Z,(f1 + f2)} is non empty finite set
{{Z,(f1 + f2)},{Z}} is non empty finite V39() set
the multF of R . [Z,(f1 + f2)] is set
f is right_complementable Element of the carrier of R
f * Z is right_complementable Element of the carrier of R
the multF of R . (f,Z) is right_complementable Element of the carrier of R
[f,Z] is set
{f,Z} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,Z},{f}} is non empty finite V39() set
the multF of R . [f,Z] is set
Z * f is right_complementable Element of the carrier of R
the multF of R . (Z,f) is right_complementable Element of the carrier of R
[Z,f] is set
{Z,f} is non empty finite set
{{Z,f},{Z}} is non empty finite V39() set
the multF of R . [Z,f] is set
p1 is right_complementable Element of the carrier of R
p1 * Z is right_complementable Element of the carrier of R
the multF of R . (p1,Z) is right_complementable Element of the carrier of R
[p1,Z] is set
{p1,Z} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,Z},{p1}} is non empty finite V39() set
the multF of R . [p1,Z] is set
Z * p1 is right_complementable Element of the carrier of R
the multF of R . (Z,p1) is right_complementable Element of the carrier of R
[Z,p1] is set
{Z,p1} is non empty finite set
{{Z,p1},{Z}} is non empty finite V39() set
the multF of R . [Z,p1] is set
[:[:vR,vR:],vR:] is non empty set
bool [:[:vR,vR:],vR:] is non empty set
A is Relation-like [:vR,vR:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[:vR,vR:], the carrier of R:]
rng A is Element of bool the carrier of R
B is set
dom A is Relation-like vR -defined vR -valued Element of bool [:vR,vR:]
bool [:vR,vR:] is non empty set
f is set
A . f is set
f1 is set
f2 is set
[f1,f2] is set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V39() set
f is right_complementable Element of the carrier of R
p1 is right_complementable Element of the carrier of R
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
f * p1 is right_complementable Element of the carrier of R
the multF of R . (f,p1) is right_complementable Element of the carrier of R
the multF of R . [f,p1] is set
(f * p1) * Z is right_complementable Element of the carrier of R
the multF of R . ((f * p1),Z) is right_complementable Element of the carrier of R
[(f * p1),Z] is set
{(f * p1),Z} is non empty finite set
{(f * p1)} is non empty trivial finite 1 -element set
{{(f * p1),Z},{(f * p1)}} is non empty finite V39() set
the multF of R . [(f * p1),Z] is set
Z * p1 is right_complementable Element of the carrier of R
the multF of R . (Z,p1) is right_complementable Element of the carrier of R
[Z,p1] is set
{Z,p1} is non empty finite set
{{Z,p1},{Z}} is non empty finite V39() set
the multF of R . [Z,p1] is set
f * (Z * p1) is right_complementable Element of the carrier of R
the multF of R . (f,(Z * p1)) is right_complementable Element of the carrier of R
[f,(Z * p1)] is set
{f,(Z * p1)} is non empty finite set
{{f,(Z * p1)},{f}} is non empty finite V39() set
the multF of R . [f,(Z * p1)] is set
f * Z is right_complementable Element of the carrier of R
the multF of R . (f,Z) is right_complementable Element of the carrier of R
[f,Z] is set
{f,Z} is non empty finite set
{{f,Z},{f}} is non empty finite V39() set
the multF of R . [f,Z] is set
(f * Z) * p1 is right_complementable Element of the carrier of R
the multF of R . ((f * Z),p1) is right_complementable Element of the carrier of R
[(f * Z),p1] is set
{(f * Z),p1} is non empty finite set
{(f * Z)} is non empty trivial finite 1 -element set
{{(f * Z),p1},{(f * Z)}} is non empty finite V39() set
the multF of R . [(f * Z),p1] is set
Z * (f * p1) is right_complementable Element of the carrier of R
the multF of R . (Z,(f * p1)) is right_complementable Element of the carrier of R
[Z,(f * p1)] is set
{Z,(f * p1)} is non empty finite set
{{Z,(f * p1)},{Z}} is non empty finite V39() set
the multF of R . [Z,(f * p1)] is set
c1 is right_complementable Element of the carrier of R
c1 * Z is right_complementable Element of the carrier of R
the multF of R . (c1,Z) is right_complementable Element of the carrier of R
[c1,Z] is set
{c1,Z} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,Z},{c1}} is non empty finite V39() set
the multF of R . [c1,Z] is set
Z * c1 is right_complementable Element of the carrier of R
the multF of R . (Z,c1) is right_complementable Element of the carrier of R
[Z,c1] is set
{Z,c1} is non empty finite set
{{Z,c1},{Z}} is non empty finite V39() set
the multF of R . [Z,c1] is set
c1 is right_complementable Element of the carrier of R
c1 * Z is right_complementable Element of the carrier of R
the multF of R . (c1,Z) is right_complementable Element of the carrier of R
[c1,Z] is set
{c1,Z} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,Z},{c1}} is non empty finite V39() set
the multF of R . [c1,Z] is set
Z * c1 is right_complementable Element of the carrier of R
the multF of R . (Z,c1) is right_complementable Element of the carrier of R
[Z,c1] is set
{Z,c1} is non empty finite set
{{Z,c1},{Z}} is non empty finite V39() set
the multF of R . [Z,c1] is set
(1. R) * Z is right_complementable Element of the carrier of R
the multF of R . ((1. R),Z) is right_complementable Element of the carrier of R
[(1. R),Z] is set
{(1. R),Z} is non empty finite set
{(1. R)} is non empty trivial finite 1 -element set
{{(1. R),Z},{(1. R)}} is non empty finite V39() set
the multF of R . [(1. R),Z] is set
Z * (1. R) is right_complementable Element of the carrier of R
the multF of R . (Z,(1. R)) is right_complementable Element of the carrier of R
[Z,(1. R)] is set
{Z,(1. R)} is non empty finite set
{{Z,(1. R)},{Z}} is non empty finite V39() set
the multF of R . [Z,(1. R)] is set
natq1 is Relation-like [:vR,vR:] -defined vR -valued Function-like quasi_total Element of bool [:[:vR,vR:],vR:]
B is Relation-like [:vR,vR:] -defined vR -valued Function-like quasi_total Element of bool [:[:vR,vR:],vR:]
f1 is Element of vR
f is Element of vR
doubleLoopStr(# vR,natq1,B,f1,f #) is non empty strict doubleLoopStr
f2 is non empty doubleLoopStr
0. f2 is V104(f2) Element of the carrier of f2
the carrier of f2 is non empty set
the ZeroF of f2 is Element of the carrier of f2
1. f2 is Element of the carrier of f2
the OneF of f2 is Element of the carrier of f2
p1 is Element of the carrier of f2
f is Element of the carrier of f2
[f,p1] is set
{f,p1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,p1},{f}} is non empty finite V39() set
[p1,f] is set
{p1,f} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,f},{p1}} is non empty finite V39() set
f * p1 is Element of the carrier of f2
the multF of f2 is Relation-like [: the carrier of f2, the carrier of f2:] -defined the carrier of f2 -valued Function-like quasi_total Element of bool [:[: the carrier of f2, the carrier of f2:], the carrier of f2:]
[: the carrier of f2, the carrier of f2:] is non empty set
[:[: the carrier of f2, the carrier of f2:], the carrier of f2:] is non empty set
bool [:[: the carrier of f2, the carrier of f2:], the carrier of f2:] is non empty set
the multF of f2 . (f,p1) is Element of the carrier of f2
the multF of f2 . [f,p1] is set
c1 is right_complementable Element of the carrier of R
c1 * (1. R) is right_complementable Element of the carrier of R
the multF of R . (c1,(1. R)) is right_complementable Element of the carrier of R
[c1,(1. R)] is set
{c1,(1. R)} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,(1. R)},{c1}} is non empty finite V39() set
the multF of R . [c1,(1. R)] is set
p1 * f is Element of the carrier of f2
the multF of f2 . (p1,f) is Element of the carrier of f2
the multF of f2 . [p1,f] is set
(1. R) * c1 is right_complementable Element of the carrier of R
the multF of R . ((1. R),c1) is right_complementable Element of the carrier of R
[(1. R),c1] is set
{(1. R),c1} is non empty finite set
{{(1. R),c1},{(1. R)}} is non empty finite V39() set
the multF of R . [(1. R),c1] is set
f is Element of the carrier of f2
f * (1. f2) is Element of the carrier of f2
the multF of f2 . (f,(1. f2)) is Element of the carrier of f2
[f,(1. f2)] is set
{f,(1. f2)} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,(1. f2)},{f}} is non empty finite V39() set
the multF of f2 . [f,(1. f2)] is set
(1. f2) * f is Element of the carrier of f2
the multF of f2 . ((1. f2),f) is Element of the carrier of f2
[(1. f2),f] is set
{(1. f2),f} is non empty finite set
{(1. f2)} is non empty trivial finite 1 -element set
{{(1. f2),f},{(1. f2)}} is non empty finite V39() set
the multF of f2 . [(1. f2),f] is set
p1 is right_complementable Element of the carrier of R
p1 * Z is right_complementable Element of the carrier of R
the multF of R . (p1,Z) is right_complementable Element of the carrier of R
[p1,Z] is set
{p1,Z} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,Z},{p1}} is non empty finite V39() set
the multF of R . [p1,Z] is set
Z * p1 is right_complementable Element of the carrier of R
the multF of R . (Z,p1) is right_complementable Element of the carrier of R
[Z,p1] is set
{Z,p1} is non empty finite set
{{Z,p1},{Z}} is non empty finite V39() set
the multF of R . [Z,p1] is set
c1 is right_complementable Element of the carrier of R
c1 * Z is right_complementable Element of the carrier of R
the multF of R . (c1,Z) is right_complementable Element of the carrier of R
[c1,Z] is set
{c1,Z} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,Z},{c1}} is non empty finite V39() set
the multF of R . [c1,Z] is set
Z * c1 is right_complementable Element of the carrier of R
the multF of R . (Z,c1) is right_complementable Element of the carrier of R
[Z,c1] is set
{Z,c1} is non empty finite set
{{Z,c1},{Z}} is non empty finite V39() set
the multF of R . [Z,c1] is set
p1 is right_complementable Element of the carrier of R
p2 is Element of the carrier of f2
c1 is right_complementable Element of the carrier of R
c2 is Element of the carrier of f2
[p2,c2] is set
{p2,c2} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,c2},{p2}} is non empty finite V39() set
p1 * c1 is right_complementable Element of the carrier of R
the multF of R . (p1,c1) is right_complementable Element of the carrier of R
[p1,c1] is set
{p1,c1} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c1},{p1}} is non empty finite V39() set
the multF of R . [p1,c1] is set
p2 * c2 is Element of the carrier of f2
the multF of f2 . (p2,c2) is Element of the carrier of f2
the multF of f2 . [p2,c2] is set
p1 is right_complementable Element of the carrier of R
c1 is right_complementable Element of the carrier of R
p1 + c1 is right_complementable Element of the carrier of R
the addF of R . (p1,c1) is right_complementable Element of the carrier of R
[p1,c1] is set
{p1,c1} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c1},{p1}} is non empty finite V39() set
the addF of R . [p1,c1] is set
p2 is Element of the carrier of f2
c2 is Element of the carrier of f2
p2 + c2 is Element of the carrier of f2
the addF of f2 is Relation-like [: the carrier of f2, the carrier of f2:] -defined the carrier of f2 -valued Function-like quasi_total Element of bool [:[: the carrier of f2, the carrier of f2:], the carrier of f2:]
the addF of f2 . (p2,c2) is Element of the carrier of f2
[p2,c2] is set
{p2,c2} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,c2},{p2}} is non empty finite V39() set
the addF of f2 . [p2,c2] is set
p1 is Element of the carrier of f2
c1 is Element of the carrier of f2
p1 + c1 is Element of the carrier of f2
the addF of f2 is Relation-like [: the carrier of f2, the carrier of f2:] -defined the carrier of f2 -valued Function-like quasi_total Element of bool [:[: the carrier of f2, the carrier of f2:], the carrier of f2:]
the addF of f2 . (p1,c1) is Element of the carrier of f2
[p1,c1] is set
{p1,c1} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c1},{p1}} is non empty finite V39() set
the addF of f2 . [p1,c1] is set
c1 + p1 is Element of the carrier of f2
the addF of f2 . (c1,p1) is Element of the carrier of f2
[c1,p1] is set
{c1,p1} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p1},{c1}} is non empty finite V39() set
the addF of f2 . [c1,p1] is set
c2 is right_complementable Element of the carrier of R
p2 is right_complementable Element of the carrier of R
c2 + p2 is right_complementable Element of the carrier of R
the addF of R . (c2,p2) is right_complementable Element of the carrier of R
[c2,p2] is set
{c2,p2} is non empty finite set
{c2} is non empty trivial finite 1 -element set
{{c2,p2},{c2}} is non empty finite V39() set
the addF of R . [c2,p2] is set
p1 is Element of the carrier of f2
c1 is Element of the carrier of f2
p1 + c1 is Element of the carrier of f2
the addF of f2 is Relation-like [: the carrier of f2, the carrier of f2:] -defined the carrier of f2 -valued Function-like quasi_total Element of bool [:[: the carrier of f2, the carrier of f2:], the carrier of f2:]
the addF of f2 . (p1,c1) is Element of the carrier of f2
[p1,c1] is set
{p1,c1} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c1},{p1}} is non empty finite V39() set
the addF of f2 . [p1,c1] is set
p2 is Element of the carrier of f2
(p1 + c1) + p2 is Element of the carrier of f2
the addF of f2 . ((p1 + c1),p2) is Element of the carrier of f2
[(p1 + c1),p2] is set
{(p1 + c1),p2} is non empty finite set
{(p1 + c1)} is non empty trivial finite 1 -element set
{{(p1 + c1),p2},{(p1 + c1)}} is non empty finite V39() set
the addF of f2 . [(p1 + c1),p2] is set
c1 + p2 is Element of the carrier of f2
the addF of f2 . (c1,p2) is Element of the carrier of f2
[c1,p2] is set
{c1,p2} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p2},{c1}} is non empty finite V39() set
the addF of f2 . [c1,p2] is set
p1 + (c1 + p2) is Element of the carrier of f2
the addF of f2 . (p1,(c1 + p2)) is Element of the carrier of f2
[p1,(c1 + p2)] is set
{p1,(c1 + p2)} is non empty finite set
{{p1,(c1 + p2)},{p1}} is non empty finite V39() set
the addF of f2 . [p1,(c1 + p2)] is set
c2 is right_complementable Element of the carrier of R
c is right_complementable Element of the carrier of R
c2 + c is right_complementable Element of the carrier of R
the addF of R . (c2,c) is right_complementable Element of the carrier of R
[c2,c] is set
{c2,c} is non empty finite set
{c2} is non empty trivial finite 1 -element set
{{c2,c},{c2}} is non empty finite V39() set
the addF of R . [c2,c] is set
c is right_complementable Element of the carrier of R
c + c is right_complementable Element of the carrier of R
the addF of R . (c,c) is right_complementable Element of the carrier of R
[c,c] is set
{c,c} is non empty finite set
{c} is non empty trivial finite 1 -element set
{{c,c},{c}} is non empty finite V39() set
the addF of R . [c,c] is set
(c2 + c) + c is right_complementable Element of the carrier of R
the addF of R . ((c2 + c),c) is right_complementable Element of the carrier of R
[(c2 + c),c] is set
{(c2 + c),c} is non empty finite set
{(c2 + c)} is non empty trivial finite 1 -element set
{{(c2 + c),c},{(c2 + c)}} is non empty finite V39() set
the addF of R . [(c2 + c),c] is set
c2 + (c + c) is right_complementable Element of the carrier of R
the addF of R . (c2,(c + c)) is right_complementable Element of the carrier of R
[c2,(c + c)] is set
{c2,(c + c)} is non empty finite set
{{c2,(c + c)},{c2}} is non empty finite V39() set
the addF of R . [c2,(c + c)] is set
p1 is Element of the carrier of f2
p1 + (0. f2) is Element of the carrier of f2
the addF of f2 is Relation-like [: the carrier of f2, the carrier of f2:] -defined the carrier of f2 -valued Function-like quasi_total Element of bool [:[: the carrier of f2, the carrier of f2:], the carrier of f2:]
the addF of f2 . (p1,(0. f2)) is Element of the carrier of f2
[p1,(0. f2)] is set
{p1,(0. f2)} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,(0. f2)},{p1}} is non empty finite V39() set
the addF of f2 . [p1,(0. f2)] is set
c1 is right_complementable Element of the carrier of R
c1 + (0. R) is right_complementable Element of the carrier of R
the addF of R . (c1,(0. R)) is right_complementable Element of the carrier of R
[c1,(0. R)] is set
{c1,(0. R)} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,(0. R)},{c1}} is non empty finite V39() set
the addF of R . [c1,(0. R)] is set
p1 is Element of the carrier of f2
c1 is right_complementable Element of the carrier of R
p2 is right_complementable Element of the carrier of R
c1 + p2 is right_complementable Element of the carrier of R
the addF of R . (c1,p2) is right_complementable Element of the carrier of R
[c1,p2] is set
{c1,p2} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p2},{c1}} is non empty finite V39() set
the addF of R . [c1,p2] is set
Z * c1 is right_complementable Element of the carrier of R
the multF of R . (Z,c1) is right_complementable Element of the carrier of R
[Z,c1] is set
{Z,c1} is non empty finite set
{{Z,c1},{Z}} is non empty finite V39() set
the multF of R . [Z,c1] is set
c1 * Z is right_complementable Element of the carrier of R
the multF of R . (c1,Z) is right_complementable Element of the carrier of R
[c1,Z] is set
{c1,Z} is non empty finite set
{{c1,Z},{c1}} is non empty finite V39() set
the multF of R . [c1,Z] is set
p2 * Z is right_complementable Element of the carrier of R
the multF of R . (p2,Z) is right_complementable Element of the carrier of R
[p2,Z] is set
{p2,Z} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,Z},{p2}} is non empty finite V39() set
the multF of R . [p2,Z] is set
(c1 * Z) + (p2 * Z) is right_complementable Element of the carrier of R
the addF of R . ((c1 * Z),(p2 * Z)) is right_complementable Element of the carrier of R
[(c1 * Z),(p2 * Z)] is set
{(c1 * Z),(p2 * Z)} is non empty finite set
{(c1 * Z)} is non empty trivial finite 1 -element set
{{(c1 * Z),(p2 * Z)},{(c1 * Z)}} is non empty finite V39() set
the addF of R . [(c1 * Z),(p2 * Z)] is set
Z * (c1 + p2) is right_complementable Element of the carrier of R
the multF of R . (Z,(c1 + p2)) is right_complementable Element of the carrier of R
[Z,(c1 + p2)] is set
{Z,(c1 + p2)} is non empty finite set
{{Z,(c1 + p2)},{Z}} is non empty finite V39() set
the multF of R . [Z,(c1 + p2)] is set
Z * p2 is right_complementable Element of the carrier of R
the multF of R . (Z,p2) is right_complementable Element of the carrier of R
[Z,p2] is set
{Z,p2} is non empty finite set
{{Z,p2},{Z}} is non empty finite V39() set
the multF of R . [Z,p2] is set
(Z * c1) + (Z * p2) is right_complementable Element of the carrier of R
the addF of R . ((Z * c1),(Z * p2)) is right_complementable Element of the carrier of R
[(Z * c1),(Z * p2)] is set
{(Z * c1),(Z * p2)} is non empty finite set
{(Z * c1)} is non empty trivial finite 1 -element set
{{(Z * c1),(Z * p2)},{(Z * c1)}} is non empty finite V39() set
the addF of R . [(Z * c1),(Z * p2)] is set
- (c1 * Z) is right_complementable Element of the carrier of R
(- (c1 * Z)) + (c1 * Z) is right_complementable Element of the carrier of R
the addF of R . ((- (c1 * Z)),(c1 * Z)) is right_complementable Element of the carrier of R
[(- (c1 * Z)),(c1 * Z)] is set
{(- (c1 * Z)),(c1 * Z)} is non empty finite set
{(- (c1 * Z))} is non empty trivial finite 1 -element set
{{(- (c1 * Z)),(c1 * Z)},{(- (c1 * Z))}} is non empty finite V39() set
the addF of R . [(- (c1 * Z)),(c1 * Z)] is set
((- (c1 * Z)) + (c1 * Z)) + (p2 * Z) is right_complementable Element of the carrier of R
the addF of R . (((- (c1 * Z)) + (c1 * Z)),(p2 * Z)) is right_complementable Element of the carrier of R
[((- (c1 * Z)) + (c1 * Z)),(p2 * Z)] is set
{((- (c1 * Z)) + (c1 * Z)),(p2 * Z)} is non empty finite set
{((- (c1 * Z)) + (c1 * Z))} is non empty trivial finite 1 -element set
{{((- (c1 * Z)) + (c1 * Z)),(p2 * Z)},{((- (c1 * Z)) + (c1 * Z))}} is non empty finite V39() set
the addF of R . [((- (c1 * Z)) + (c1 * Z)),(p2 * Z)] is set
- (Z * c1) is right_complementable Element of the carrier of R
(- (Z * c1)) + ((Z * c1) + (Z * p2)) is right_complementable Element of the carrier of R
the addF of R . ((- (Z * c1)),((Z * c1) + (Z * p2))) is right_complementable Element of the carrier of R
[(- (Z * c1)),((Z * c1) + (Z * p2))] is set
{(- (Z * c1)),((Z * c1) + (Z * p2))} is non empty finite set
{(- (Z * c1))} is non empty trivial finite 1 -element set
{{(- (Z * c1)),((Z * c1) + (Z * p2))},{(- (Z * c1))}} is non empty finite V39() set
the addF of R . [(- (Z * c1)),((Z * c1) + (Z * p2))] is set
(0. R) + (p2 * Z) is right_complementable Element of the carrier of R
the addF of R . ((0. R),(p2 * Z)) is right_complementable Element of the carrier of R
[(0. R),(p2 * Z)] is set
{(0. R),(p2 * Z)} is non empty finite set
{{(0. R),(p2 * Z)},{(0. R)}} is non empty finite V39() set
the addF of R . [(0. R),(p2 * Z)] is set
(- (Z * c1)) + (Z * c1) is right_complementable Element of the carrier of R
the addF of R . ((- (Z * c1)),(Z * c1)) is right_complementable Element of the carrier of R
[(- (Z * c1)),(Z * c1)] is set
{(- (Z * c1)),(Z * c1)} is non empty finite set
{{(- (Z * c1)),(Z * c1)},{(- (Z * c1))}} is non empty finite V39() set
the addF of R . [(- (Z * c1)),(Z * c1)] is set
((- (Z * c1)) + (Z * c1)) + (Z * p2) is right_complementable Element of the carrier of R
the addF of R . (((- (Z * c1)) + (Z * c1)),(Z * p2)) is right_complementable Element of the carrier of R
[((- (Z * c1)) + (Z * c1)),(Z * p2)] is set
{((- (Z * c1)) + (Z * c1)),(Z * p2)} is non empty finite set
{((- (Z * c1)) + (Z * c1))} is non empty trivial finite 1 -element set
{{((- (Z * c1)) + (Z * c1)),(Z * p2)},{((- (Z * c1)) + (Z * c1))}} is non empty finite V39() set
the addF of R . [((- (Z * c1)) + (Z * c1)),(Z * p2)] is set
(0. R) + (Z * p2) is right_complementable Element of the carrier of R
the addF of R . ((0. R),(Z * p2)) is right_complementable Element of the carrier of R
[(0. R),(Z * p2)] is set
{(0. R),(Z * p2)} is non empty finite set
{{(0. R),(Z * p2)},{(0. R)}} is non empty finite V39() set
the addF of R . [(0. R),(Z * p2)] is set
c2 is Element of the carrier of f2
p1 + c2 is Element of the carrier of f2
the addF of f2 is Relation-like [: the carrier of f2, the carrier of f2:] -defined the carrier of f2 -valued Function-like quasi_total Element of bool [:[: the carrier of f2, the carrier of f2:], the carrier of f2:]
the addF of f2 . (p1,c2) is Element of the carrier of f2
[p1,c2] is set
{p1,c2} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c2},{p1}} is non empty finite V39() set
the addF of f2 . [p1,c2] is set
p1 is Element of the carrier of f2
c1 is Element of the carrier of f2
p1 * c1 is Element of the carrier of f2
the multF of f2 . (p1,c1) is Element of the carrier of f2
[p1,c1] is set
{p1,c1} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,c1},{p1}} is non empty finite V39() set
the multF of f2 . [p1,c1] is set
p2 is Element of the carrier of f2
(p1 * c1) * p2 is Element of the carrier of f2
the multF of f2 . ((p1 * c1),p2) is Element of the carrier of f2
[(p1 * c1),p2] is set
{(p1 * c1),p2} is non empty finite set
{(p1 * c1)} is non empty trivial finite 1 -element set
{{(p1 * c1),p2},{(p1 * c1)}} is non empty finite V39() set
the multF of f2 . [(p1 * c1),p2] is set
c1 * p2 is Element of the carrier of f2
the multF of f2 . (c1,p2) is Element of the carrier of f2
[c1,p2] is set
{c1,p2} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p2},{c1}} is non empty finite V39() set
the multF of f2 . [c1,p2] is set
p1 * (c1 * p2) is Element of the carrier of f2
the multF of f2 . (p1,(c1 * p2)) is Element of the carrier of f2
[p1,(c1 * p2)] is set
{p1,(c1 * p2)} is non empty finite set
{{p1,(c1 * p2)},{p1}} is non empty finite V39() set
the multF of f2 . [p1,(c1 * p2)] is set
c2 is right_complementable Element of the carrier of R
c is right_complementable Element of the carrier of R
c2 * c is right_complementable Element of the carrier of R
the multF of R . (c2,c) is right_complementable Element of the carrier of R
[c2,c] is set
{c2,c} is non empty finite set
{c2} is non empty trivial finite 1 -element set
{{c2,c},{c2}} is non empty finite V39() set
the multF of R . [c2,c] is set
c is right_complementable Element of the carrier of R
c * c is right_complementable Element of the carrier of R
the multF of R . (c,c) is right_complementable Element of the carrier of R
[c,c] is set
{c,c} is non empty finite set
{c} is non empty trivial finite 1 -element set
{{c,c},{c}} is non empty finite V39() set
the multF of R . [c,c] is set
(c2 * c) * c is right_complementable Element of the carrier of R
the multF of R . ((c2 * c),c) is right_complementable Element of the carrier of R
[(c2 * c),c] is set
{(c2 * c),c} is non empty finite set
{(c2 * c)} is non empty trivial finite 1 -element set
{{(c2 * c),c},{(c2 * c)}} is non empty finite V39() set
the multF of R . [(c2 * c),c] is set
c2 * (c * c) is right_complementable Element of the carrier of R
the multF of R . (c2,(c * c)) is right_complementable Element of the carrier of R
[c2,(c * c)] is set
{c2,(c * c)} is non empty finite set
{{c2,(c * c)},{c2}} is non empty finite V39() set
the multF of R . [c2,(c * c)] is set
p1 is Element of the carrier of f2
c1 is Element of the carrier of f2
p2 is Element of the carrier of f2
c1 + p2 is Element of the carrier of f2
the addF of f2 is Relation-like [: the carrier of f2, the carrier of f2:] -defined the carrier of f2 -valued Function-like quasi_total Element of bool [:[: the carrier of f2, the carrier of f2:], the carrier of f2:]
the addF of f2 . (c1,p2) is Element of the carrier of f2
[c1,p2] is set
{c1,p2} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p2},{c1}} is non empty finite V39() set
the addF of f2 . [c1,p2] is set
p1 * (c1 + p2) is Element of the carrier of f2
the multF of f2 . (p1,(c1 + p2)) is Element of the carrier of f2
[p1,(c1 + p2)] is set
{p1,(c1 + p2)} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,(c1 + p2)},{p1}} is non empty finite V39() set
the multF of f2 . [p1,(c1 + p2)] is set
p1 * c1 is Element of the carrier of f2
the multF of f2 . (p1,c1) is Element of the carrier of f2
[p1,c1] is set
{p1,c1} is non empty finite set
{{p1,c1},{p1}} is non empty finite V39() set
the multF of f2 . [p1,c1] is set
p1 * p2 is Element of the carrier of f2
the multF of f2 . (p1,p2) is Element of the carrier of f2
[p1,p2] is set
{p1,p2} is non empty finite set
{{p1,p2},{p1}} is non empty finite V39() set
the multF of f2 . [p1,p2] is set
(p1 * c1) + (p1 * p2) is Element of the carrier of f2
the addF of f2 . ((p1 * c1),(p1 * p2)) is Element of the carrier of f2
[(p1 * c1),(p1 * p2)] is set
{(p1 * c1),(p1 * p2)} is non empty finite set
{(p1 * c1)} is non empty trivial finite 1 -element set
{{(p1 * c1),(p1 * p2)},{(p1 * c1)}} is non empty finite V39() set
the addF of f2 . [(p1 * c1),(p1 * p2)] is set
(c1 + p2) * p1 is Element of the carrier of f2
the multF of f2 . ((c1 + p2),p1) is Element of the carrier of f2
[(c1 + p2),p1] is set
{(c1 + p2),p1} is non empty finite set
{(c1 + p2)} is non empty trivial finite 1 -element set
{{(c1 + p2),p1},{(c1 + p2)}} is non empty finite V39() set
the multF of f2 . [(c1 + p2),p1] is set
c1 * p1 is Element of the carrier of f2
the multF of f2 . (c1,p1) is Element of the carrier of f2
[c1,p1] is set
{c1,p1} is non empty finite set
{{c1,p1},{c1}} is non empty finite V39() set
the multF of f2 . [c1,p1] is set
p2 * p1 is Element of the carrier of f2
the multF of f2 . (p2,p1) is Element of the carrier of f2
[p2,p1] is set
{p2,p1} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,p1},{p2}} is non empty finite V39() set
the multF of f2 . [p2,p1] is set
(c1 * p1) + (p2 * p1) is Element of the carrier of f2
the addF of f2 . ((c1 * p1),(p2 * p1)) is Element of the carrier of f2
[(c1 * p1),(p2 * p1)] is set
{(c1 * p1),(p2 * p1)} is non empty finite set
{(c1 * p1)} is non empty trivial finite 1 -element set
{{(c1 * p1),(p2 * p1)},{(c1 * p1)}} is non empty finite V39() set
the addF of f2 . [(c1 * p1),(p2 * p1)] is set
c is right_complementable Element of the carrier of R
c is right_complementable Element of the carrier of R
c + c is right_complementable Element of the carrier of R
the addF of R . (c,c) is right_complementable Element of the carrier of R
[c,c] is set
{c,c} is non empty finite set
{c} is non empty trivial finite 1 -element set
{{c,c},{c}} is non empty finite V39() set
the addF of R . [c,c] is set
c2 is right_complementable Element of the carrier of R
c2 * c is right_complementable Element of the carrier of R
the multF of R . (c2,c) is right_complementable Element of the carrier of R
[c2,c] is set
{c2,c} is non empty finite set
{c2} is non empty trivial finite 1 -element set
{{c2,c},{c2}} is non empty finite V39() set
the multF of R . [c2,c] is set
c2 * c is right_complementable Element of the carrier of R
the multF of R . (c2,c) is right_complementable Element of the carrier of R
[c2,c] is set
{c2,c} is non empty finite set
{{c2,c},{c2}} is non empty finite V39() set
the multF of R . [c2,c] is set
c * c2 is right_complementable Element of the carrier of R
the multF of R . (c,c2) is right_complementable Element of the carrier of R
[c,c2] is set
{c,c2} is non empty finite set
{{c,c2},{c}} is non empty finite V39() set
the multF of R . [c,c2] is set
c * c2 is right_complementable Element of the carrier of R
the multF of R . (c,c2) is right_complementable Element of the carrier of R
[c,c2] is set
{c,c2} is non empty finite set
{c} is non empty trivial finite 1 -element set
{{c,c2},{c}} is non empty finite V39() set
the multF of R . [c,c2] is set
c2 * (c + c) is right_complementable Element of the carrier of R
the multF of R . (c2,(c + c)) is right_complementable Element of the carrier of R
[c2,(c + c)] is set
{c2,(c + c)} is non empty finite set
{{c2,(c + c)},{c2}} is non empty finite V39() set
the multF of R . [c2,(c + c)] is set
(c2 * c) + (c2 * c) is right_complementable Element of the carrier of R
the addF of R . ((c2 * c),(c2 * c)) is right_complementable Element of the carrier of R
[(c2 * c),(c2 * c)] is set
{(c2 * c),(c2 * c)} is non empty finite set
{(c2 * c)} is non empty trivial finite 1 -element set
{{(c2 * c),(c2 * c)},{(c2 * c)}} is non empty finite V39() set
the addF of R . [(c2 * c),(c2 * c)] is set
(c + c) * c2 is right_complementable Element of the carrier of R
the multF of R . ((c + c),c2) is right_complementable Element of the carrier of R
[(c + c),c2] is set
{(c + c),c2} is non empty finite set
{(c + c)} is non empty trivial finite 1 -element set
{{(c + c),c2},{(c + c)}} is non empty finite V39() set
the multF of R . [(c + c),c2] is set
(c * c2) + (c * c2) is right_complementable Element of the carrier of R
the addF of R . ((c * c2),(c * c2)) is right_complementable Element of the carrier of R
[(c * c2),(c * c2)] is set
{(c * c2),(c * c2)} is non empty finite set
{(c * c2)} is non empty trivial finite 1 -element set
{{(c * c2),(c * c2)},{(c * c2)}} is non empty finite V39() set
the addF of R . [(c * c2),(c * c2)] is set
p1 is Element of the carrier of f2
c1 is right_complementable Element of the carrier of R
p2 is right_complementable Element of the carrier of R
p2 * c1 is right_complementable Element of the carrier of R
the multF of R . (p2,c1) is right_complementable Element of the carrier of R
[p2,c1] is set
{p2,c1} is non empty finite set
{p2} is non empty trivial finite 1 -element set
{{p2,c1},{p2}} is non empty finite V39() set
the multF of R . [p2,c1] is set
c1 * p2 is right_complementable Element of the carrier of R
the multF of R . (c1,p2) is right_complementable Element of the carrier of R
[c1,p2] is set
{c1,p2} is non empty finite set
{c1} is non empty trivial finite 1 -element set
{{c1,p2},{c1}} is non empty finite V39() set
the multF of R . [c1,p2] is set
(c1 * p2) * Z is right_complementable Element of the carrier of R
the multF of R . ((c1 * p2),Z) is right_complementable Element of the carrier of R
[(c1 * p2),Z] is set
{(c1 * p2),Z} is non empty finite set
{(c1 * p2)} is non empty trivial finite 1 -element set
{{(c1 * p2),Z},{(c1 * p2)}} is non empty finite V39() set
the multF of R . [(c1 * p2),Z] is set
Z * c1 is right_complementable Element of the carrier of R
the multF of R . (Z,c1) is right_complementable Element of the carrier of R
[Z,c1] is set
{Z,c1} is non empty finite set
{{Z,c1},{Z}} is non empty finite V39() set
the multF of R . [Z,c1] is set
(Z * c1) * p2 is right_complementable Element of the carrier of R
the multF of R . ((Z * c1),p2) is right_complementable Element of the carrier of R
[(Z * c1),p2] is set
{(Z * c1),p2} is non empty finite set
{(Z * c1)} is non empty trivial finite 1 -element set
{{(Z * c1),p2},{(Z * c1)}} is non empty finite V39() set
the multF of R . [(Z * c1),p2] is set
c1 * Z is right_complementable Element of the carrier of R
the multF of R . (c1,Z) is right_complementable Element of the carrier of R
[c1,Z] is set
{c1,Z} is non empty finite set
{{c1,Z},{c1}} is non empty finite V39() set
the multF of R . [c1,Z] is set
(c1 * Z) * p2 is right_complementable Element of the carrier of R
the multF of R . ((c1 * Z),p2) is right_complementable Element of the carrier of R
[(c1 * Z),p2] is set
{(c1 * Z),p2} is non empty finite set
{(c1 * Z)} is non empty trivial finite 1 -element set
{{(c1 * Z),p2},{(c1 * Z)}} is non empty finite V39() set
the multF of R . [(c1 * Z),p2] is set
c1 " is right_complementable Element of the carrier of R
(c1 ") * (c1 * p2) is right_complementable Element of the carrier of R
the multF of R . ((c1 "),(c1 * p2)) is right_complementable Element of the carrier of R
[(c1 "),(c1 * p2)] is set
{(c1 "),(c1 * p2)} is non empty finite set
{(c1 ")} is non empty trivial finite 1 -element set
{{(c1 "),(c1 * p2)},{(c1 ")}} is non empty finite V39() set
the multF of R . [(c1 "),(c1 * p2)] is set
((c1 ") * (c1 * p2)) * Z is right_complementable Element of the carrier of R
the multF of R . (((c1 ") * (c1 * p2)),Z) is right_complementable Element of the carrier of R
[((c1 ") * (c1 * p2)),Z] is set
{((c1 ") * (c1 * p2)),Z} is non empty finite set
{((c1 ") * (c1 * p2))} is non empty trivial finite 1 -element set
{{((c1 ") * (c1 * p2)),Z},{((c1 ") * (c1 * p2))}} is non empty finite V39() set
the multF of R . [((c1 ") * (c1 * p2)),Z] is set
(c1 ") * ((c1 * Z) * p2) is right_complementable Element of the carrier of R
the multF of R . ((c1 "),((c1 * Z) * p2)) is right_complementable Element of the carrier of R
[(c1 "),((c1 * Z) * p2)] is set
{(c1 "),((c1 * Z) * p2)} is non empty finite set
{{(c1 "),((c1 * Z) * p2)},{(c1 ")}} is non empty finite V39() set
the multF of R . [(c1 "),((c1 * Z) * p2)] is set
(c1 ") * (c1 * Z) is right_complementable Element of the carrier of R
the multF of R . ((c1 "),(c1 * Z)) is right_complementable Element of the carrier of R
[(c1 "),(c1 * Z)] is set
{(c1 "),(c1 * Z)} is non empty finite set
{{(c1 "),(c1 * Z)},{(c1 ")}} is non empty finite V39() set
the multF of R . [(c1 "),(c1 * Z)] is set
((c1 ") * (c1 * Z)) * p2 is right_complementable Element of the carrier of R
the multF of R . (((c1 ") * (c1 * Z)),p2) is right_complementable Element of the carrier of R
[((c1 ") * (c1 * Z)),p2] is set
{((c1 ") * (c1 * Z)),p2} is non empty finite set
{((c1 ") * (c1 * Z))} is non empty trivial finite 1 -element set
{{((c1 ") * (c1 * Z)),p2},{((c1 ") * (c1 * Z))}} is non empty finite V39() set
the multF of R . [((c1 ") * (c1 * Z)),p2] is set
(c1 ") * c1 is right_complementable Element of the carrier of R
the multF of R . ((c1 "),c1) is right_complementable Element of the carrier of R
[(c1 "),c1] is set
{(c1 "),c1} is non empty finite set
{{(c1 "),c1},{(c1 ")}} is non empty finite V39() set
the multF of R . [(c1 "),c1] is set
((c1 ") * c1) * p2 is right_complementable Element of the carrier of R
the multF of R . (((c1 ") * c1),p2) is right_complementable Element of the carrier of R
[((c1 ") * c1),p2] is set
{((c1 ") * c1),p2} is non empty finite set
{((c1 ") * c1)} is non empty trivial finite 1 -element set
{{((c1 ") * c1),p2},{((c1 ") * c1)}} is non empty finite V39() set
the multF of R . [((c1 ") * c1),p2] is set
(((c1 ") * c1) * p2) * Z is right_complementable Element of the carrier of R
the multF of R . ((((c1 ") * c1) * p2),Z) is right_complementable Element of the carrier of R
[(((c1 ") * c1) * p2),Z] is set
{(((c1 ") * c1) * p2),Z} is non empty finite set
{(((c1 ") * c1) * p2)} is non empty trivial finite 1 -element set
{{(((c1 ") * c1) * p2),Z},{(((c1 ") * c1) * p2)}} is non empty finite V39() set
the multF of R . [(((c1 ") * c1) * p2),Z] is set
((c1 ") * c1) * Z is right_complementable Element of the carrier of R
the multF of R . (((c1 ") * c1),Z) is right_complementable Element of the carrier of R
[((c1 ") * c1),Z] is set
{((c1 ") * c1),Z} is non empty finite set
{{((c1 ") * c1),Z},{((c1 ") * c1)}} is non empty finite V39() set
the multF of R . [((c1 ") * c1),Z] is set
(((c1 ") * c1) * Z) * p2 is right_complementable Element of the carrier of R
the multF of R . ((((c1 ") * c1) * Z),p2) is right_complementable Element of the carrier of R
[(((c1 ") * c1) * Z),p2] is set
{(((c1 ") * c1) * Z),p2} is non empty finite set
{(((c1 ") * c1) * Z)} is non empty trivial finite 1 -element set
{{(((c1 ") * c1) * Z),p2},{(((c1 ") * c1) * Z)}} is non empty finite V39() set
the multF of R . [(((c1 ") * c1) * Z),p2] is set
(1_ R) * p2 is right_complementable Element of the carrier of R
the multF of R . ((1_ R),p2) is right_complementable Element of the carrier of R
[(1_ R),p2] is set
{(1_ R),p2} is non empty finite set
{(1_ R)} is non empty trivial finite 1 -element set
{{(1_ R),p2},{(1_ R)}} is non empty finite V39() set
the multF of R . [(1_ R),p2] is set
((1_ R) * p2) * Z is right_complementable Element of the carrier of R
the multF of R . (((1_ R) * p2),Z) is right_complementable Element of the carrier of R
[((1_ R) * p2),Z] is set
{((1_ R) * p2),Z} is non empty finite set
{((1_ R) * p2)} is non empty trivial finite 1 -element set
{{((1_ R) * p2),Z},{((1_ R) * p2)}} is non empty finite V39() set
the multF of R . [((1_ R) * p2),Z] is set
(1_ R) * Z is right_complementable Element of the carrier of R
the multF of R . ((1_ R),Z) is right_complementable Element of the carrier of R
[(1_ R),Z] is set
{(1_ R),Z} is non empty finite set
{{(1_ R),Z},{(1_ R)}} is non empty finite V39() set
the multF of R . [(1_ R),Z] is set
((1_ R) * Z) * p2 is right_complementable Element of the carrier of R
the multF of R . (((1_ R) * Z),p2) is right_complementable Element of the carrier of R
[((1_ R) * Z),p2] is set
{((1_ R) * Z),p2} is non empty finite set
{((1_ R) * Z)} is non empty trivial finite 1 -element set
{{((1_ R) * Z),p2},{((1_ R) * Z)}} is non empty finite V39() set
the multF of R . [((1_ R) * Z),p2] is set
p2 * Z is right_complementable Element of the carrier of R
the multF of R . (p2,Z) is right_complementable Element of the carrier of R
[p2,Z] is set
{p2,Z} is non empty finite set
{{p2,Z},{p2}} is non empty finite V39() set
the multF of R . [p2,Z] is set
Z * p2 is right_complementable Element of the carrier of R
the multF of R . (Z,p2) is right_complementable Element of the carrier of R
[Z,p2] is set
{Z,p2} is non empty finite set
{{Z,p2},{Z}} is non empty finite V39() set
the multF of R . [Z,p2] is set
c2 is Element of the carrier of f2
c2 * p1 is Element of the carrier of f2
the multF of f2 . (c2,p1) is Element of the carrier of f2
[c2,p1] is set
{c2,p1} is non empty finite set
{c2} is non empty trivial finite 1 -element set
{{c2,p1},{c2}} is non empty finite V39() set
the multF of f2 . [c2,p1] is set
cZ is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of cZ is non empty non trivial set
the addF of cZ is Relation-like [: the carrier of cZ, the carrier of cZ:] -defined the carrier of cZ -valued Function-like quasi_total Element of bool [:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:]
[: the carrier of cZ, the carrier of cZ:] is non empty set
[:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:] is non empty set
bool [:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:] is non empty set
the addF of R || the carrier of cZ is set
the addF of R | [: the carrier of cZ, the carrier of cZ:] is Relation-like Function-like set
the multF of cZ is Relation-like [: the carrier of cZ, the carrier of cZ:] -defined the carrier of cZ -valued Function-like quasi_total Element of bool [:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:]
the multF of R || the carrier of cZ is set
the multF of R | [: the carrier of cZ, the carrier of cZ:] is Relation-like Function-like set
0. cZ is V104(cZ) right_complementable Element of the carrier of cZ
the ZeroF of cZ is right_complementable Element of the carrier of cZ
1. cZ is V104(cZ) right_complementable Element of the carrier of cZ
the OneF of cZ is right_complementable Element of the carrier of cZ
q is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of q is non empty non trivial set
the addF of q is Relation-like [: the carrier of q, the carrier of q:] -defined the carrier of q -valued Function-like quasi_total Element of bool [:[: the carrier of q, the carrier of q:], the carrier of q:]
[: the carrier of q, the carrier of q:] is non empty set
[:[: the carrier of q, the carrier of q:], the carrier of q:] is non empty set
bool [:[: the carrier of q, the carrier of q:], the carrier of q:] is non empty set
the addF of R || the carrier of q is set
the addF of R | [: the carrier of q, the carrier of q:] is Relation-like Function-like set
the multF of q is Relation-like [: the carrier of q, the carrier of q:] -defined the carrier of q -valued Function-like quasi_total Element of bool [:[: the carrier of q, the carrier of q:], the carrier of q:]
the multF of R || the carrier of q is set
the multF of R | [: the carrier of q, the carrier of q:] is Relation-like Function-like set
0. q is V104(q) right_complementable Element of the carrier of q
the ZeroF of q is right_complementable Element of the carrier of q
1. q is V104(q) right_complementable Element of the carrier of q
the OneF of q is right_complementable Element of the carrier of q
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial set
{ b₁ where b₁ is right_complementable Element of the carrier of R : b₁ * Z = Z * b₁ } is set
vR is set
n is right_complementable Element of the carrier of R
n * Z is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (n,Z) is right_complementable Element of the carrier of R
[n,Z] is set
{n,Z} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,Z},{n}} is non empty finite V39() set
the multF of R . [n,Z] is set
Z * n is right_complementable Element of the carrier of R
the multF of R . (Z,n) is right_complementable Element of the carrier of R
[Z,n] is set
{Z,n} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,n},{Z}} is non empty finite V39() set
the multF of R . [Z,n] is set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
cZ is right_complementable Element of the carrier of R
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial set
cZ * Z is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (cZ,Z) is right_complementable Element of the carrier of R
[cZ,Z] is set
{cZ,Z} is non empty finite set
{cZ} is non empty trivial finite 1 -element set
{{cZ,Z},{cZ}} is non empty finite V39() set
the multF of R . [cZ,Z] is set
Z * cZ is right_complementable Element of the carrier of R
the multF of R . (Z,cZ) is right_complementable Element of the carrier of R
[Z,cZ] is set
{Z,cZ} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,cZ},{Z}} is non empty finite V39() set
the multF of R . [Z,cZ] is set
{ b₁ where b₁ is right_complementable Element of the carrier of R : b₁ * Z = Z * b₁ } is set
n is right_complementable Element of the carrier of R
n * Z is right_complementable Element of the carrier of R
the multF of R . (n,Z) is right_complementable Element of the carrier of R
[n,Z] is set
{n,Z} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,Z},{n}} is non empty finite V39() set
the multF of R . [n,Z] is set
Z * n is right_complementable Element of the carrier of R
the multF of R . (Z,n) is right_complementable Element of the carrier of R
[Z,n] is set
{Z,n} is non empty finite set
{{Z,n},{Z}} is non empty finite V39() set
the multF of R . [Z,n] is set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial set
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial set
cZ is set
q is right_complementable Element of the carrier of R
q * Z is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (q,Z) is right_complementable Element of the carrier of R
[q,Z] is set
{q,Z} is non empty finite set
{q} is non empty trivial finite 1 -element set
{{q,Z},{q}} is non empty finite V39() set
the multF of R . [q,Z] is set
Z * q is right_complementable Element of the carrier of R
the multF of R . (Z,q) is right_complementable Element of the carrier of R
[Z,q] is set
{Z,q} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,q},{Z}} is non empty finite V39() set
the multF of R . [Z,q] is set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial set
cZ is right_complementable Element of the carrier of R
q is right_complementable Element of the carrier of R
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial set
cZ * q is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (cZ,q) is right_complementable Element of the carrier of R
[cZ,q] is set
{cZ,q} is non empty finite set
{cZ} is non empty trivial finite 1 -element set
{{cZ,q},{cZ}} is non empty finite V39() set
the multF of R . [cZ,q] is set
{ b₁ where b₁ is right_complementable Element of the carrier of R : b₁ * Z = Z * b₁ } is set
(cZ * q) * Z is right_complementable Element of the carrier of R
the multF of R . ((cZ * q),Z) is right_complementable Element of the carrier of R
[(cZ * q),Z] is set
{(cZ * q),Z} is non empty finite set
{(cZ * q)} is non empty trivial finite 1 -element set
{{(cZ * q),Z},{(cZ * q)}} is non empty finite V39() set
the multF of R . [(cZ * q),Z] is set
q * Z is right_complementable Element of the carrier of R
the multF of R . (q,Z) is right_complementable Element of the carrier of R
[q,Z] is set
{q,Z} is non empty finite set
{q} is non empty trivial finite 1 -element set
{{q,Z},{q}} is non empty finite V39() set
the multF of R . [q,Z] is set
cZ * (q * Z) is right_complementable Element of the carrier of R
the multF of R . (cZ,(q * Z)) is right_complementable Element of the carrier of R
[cZ,(q * Z)] is set
{cZ,(q * Z)} is non empty finite set
{{cZ,(q * Z)},{cZ}} is non empty finite V39() set
the multF of R . [cZ,(q * Z)] is set
(q * Z) * cZ is right_complementable Element of the carrier of R
the multF of R . ((q * Z),cZ) is right_complementable Element of the carrier of R
[(q * Z),cZ] is set
{(q * Z),cZ} is non empty finite set
{(q * Z)} is non empty trivial finite 1 -element set
{{(q * Z),cZ},{(q * Z)}} is non empty finite V39() set
the multF of R . [(q * Z),cZ] is set
Z * q is right_complementable Element of the carrier of R
the multF of R . (Z,q) is right_complementable Element of the carrier of R
[Z,q] is set
{Z,q} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,q},{Z}} is non empty finite V39() set
the multF of R . [Z,q] is set
(Z * q) * cZ is right_complementable Element of the carrier of R
the multF of R . ((Z * q),cZ) is right_complementable Element of the carrier of R
[(Z * q),cZ] is set
{(Z * q),cZ} is non empty finite set
{(Z * q)} is non empty trivial finite 1 -element set
{{(Z * q),cZ},{(Z * q)}} is non empty finite V39() set
the multF of R . [(Z * q),cZ] is set
q * cZ is right_complementable Element of the carrier of R
the multF of R . (q,cZ) is right_complementable Element of the carrier of R
[q,cZ] is set
{q,cZ} is non empty finite set
{{q,cZ},{q}} is non empty finite V39() set
the multF of R . [q,cZ] is set
Z * (q * cZ) is right_complementable Element of the carrier of R
the multF of R . (Z,(q * cZ)) is right_complementable Element of the carrier of R
[Z,(q * cZ)] is set
{Z,(q * cZ)} is non empty finite set
{{Z,(q * cZ)},{Z}} is non empty finite V39() set
the multF of R . [Z,(q * cZ)] is set
Z * (cZ * q) is right_complementable Element of the carrier of R
the multF of R . (Z,(cZ * q)) is right_complementable Element of the carrier of R
[Z,(cZ * q)] is set
{Z,(cZ * q)} is non empty finite set
{{Z,(cZ * q)},{Z}} is non empty finite V39() set
the multF of R . [Z,(cZ * q)] is set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
0. R is V104(R) right_complementable Element of the carrier of R
the ZeroF of R is right_complementable Element of the carrier of R
1_ R is right_complementable Element of the carrier of R
1. R is V104(R) right_complementable Element of the carrier of R
the OneF of R is right_complementable Element of the carrier of R
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial set
0. (R,Z) is V104((R,Z)) right_complementable Element of the carrier of (R,Z)
the ZeroF of (R,Z) is right_complementable Element of the carrier of (R,Z)
1. (R,Z) is V104((R,Z)) right_complementable Element of the carrier of (R,Z)
the OneF of (R,Z) is right_complementable Element of the carrier of (R,Z)
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial finite set
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial finite set
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial finite set
card the carrier of (R,Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
0. R is V104(R) right_complementable Element of the carrier of R
the ZeroF of R is right_complementable Element of the carrier of R
1. R is V104(R) right_complementable Element of the carrier of R
the OneF of R is right_complementable Element of the carrier of R
{(0. R),(1. R)} is non empty finite set
card {(0. R),(1. R)} is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
1_ R is right_complementable Element of the carrier of R
{(0. R),(1_ R)} is non empty finite set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
MultGroup R is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of (MultGroup R) is non empty set
0. R is V104(R) right_complementable Element of the carrier of R
the ZeroF of R is right_complementable Element of the carrier of R
{(0. R)} is non empty trivial finite 1 -element set
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial set
cZ is Element of the carrier of (MultGroup R)
((MultGroup R),cZ) is non empty strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of MultGroup R
the carrier of ((MultGroup R),cZ) is non empty set
the carrier of ((MultGroup R),cZ) \/ {(0. R)} is non empty set
NonZero R is non empty Element of bool the carrier of R
bool the carrier of R is non empty set
[#] R is non empty non proper Element of bool the carrier of R
([#] R) \ {(0. R)} is Element of bool the carrier of R
{ b₁ where b₁ is Element of the carrier of (MultGroup R) : cZ * b₁ = b₁ * cZ } is set
{ b₁ where b₁ is right_complementable Element of the carrier of R : b₁ * Z = Z * b₁ } is set
cR is set
cRs is right_complementable Element of the carrier of R
cRs * Z is right_complementable Element of the carrier of R
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the multF of R . (cRs,Z) is right_complementable Element of the carrier of R
[cRs,Z] is set
{cRs,Z} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,Z},{cRs}} is non empty finite V39() set
the multF of R . [cRs,Z] is set
Z * cRs is right_complementable Element of the carrier of R
the multF of R . (Z,cRs) is right_complementable Element of the carrier of R
[Z,cRs] is set
{Z,cRs} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,cRs},{Z}} is non empty finite V39() set
the multF of R . [Z,cRs] is set
cZs is Element of the carrier of (MultGroup R)
cZ * cZs is Element of the carrier of (MultGroup R)
the multF of (MultGroup R) is Relation-like [: the carrier of (MultGroup R), the carrier of (MultGroup R):] -defined the carrier of (MultGroup R) -valued Function-like quasi_total Element of bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):]
[: the carrier of (MultGroup R), the carrier of (MultGroup R):] is non empty set
[:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty set
bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty set
the multF of (MultGroup R) . (cZ,cZs) is Element of the carrier of (MultGroup R)
[cZ,cZs] is set
{cZ,cZs} is non empty finite set
{cZ} is non empty trivial finite 1 -element set
{{cZ,cZs},{cZ}} is non empty finite V39() set
the multF of (MultGroup R) . [cZ,cZs] is set
cZs * cZ is Element of the carrier of (MultGroup R)
the multF of (MultGroup R) . (cZs,cZ) is Element of the carrier of (MultGroup R)
[cZs,cZ] is set
{cZs,cZ} is non empty finite set
{cZs} is non empty trivial finite 1 -element set
{{cZs,cZ},{cZs}} is non empty finite V39() set
the multF of (MultGroup R) . [cZs,cZ] is set
cRs is Element of the carrier of (MultGroup R)
cZ * cRs is Element of the carrier of (MultGroup R)
the multF of (MultGroup R) is Relation-like [: the carrier of (MultGroup R), the carrier of (MultGroup R):] -defined the carrier of (MultGroup R) -valued Function-like quasi_total Element of bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):]
[: the carrier of (MultGroup R), the carrier of (MultGroup R):] is non empty set
[:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty set
bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty set
the multF of (MultGroup R) . (cZ,cRs) is Element of the carrier of (MultGroup R)
[cZ,cRs] is set
{cZ,cRs} is non empty finite set
{cZ} is non empty trivial finite 1 -element set
{{cZ,cRs},{cZ}} is non empty finite V39() set
the multF of (MultGroup R) . [cZ,cRs] is set
cRs * cZ is Element of the carrier of (MultGroup R)
the multF of (MultGroup R) . (cRs,cZ) is Element of the carrier of (MultGroup R)
[cRs,cZ] is set
{cRs,cZ} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,cZ},{cRs}} is non empty finite V39() set
the multF of (MultGroup R) . [cRs,cZ] is set
cZs is right_complementable Element of the carrier of R
cZs * Z is right_complementable Element of the carrier of R
the multF of R . (cZs,Z) is right_complementable Element of the carrier of R
[cZs,Z] is set
{cZs,Z} is non empty finite set
{cZs} is non empty trivial finite 1 -element set
{{cZs,Z},{cZs}} is non empty finite V39() set
the multF of R . [cZs,Z] is set
Z * cZs is right_complementable Element of the carrier of R
the multF of R . (Z,cZs) is right_complementable Element of the carrier of R
[Z,cZs] is set
{Z,cZs} is non empty finite set
{{Z,cZs},{Z}} is non empty finite V39() set
the multF of R . [Z,cZs] is set
(0. R) * Z is right_complementable Element of the carrier of R
the multF of R . ((0. R),Z) is right_complementable Element of the carrier of R
[(0. R),Z] is set
{(0. R),Z} is non empty finite set
{{(0. R),Z},{(0. R)}} is non empty finite V39() set
the multF of R . [(0. R),Z] is set
Z * (0. R) is right_complementable Element of the carrier of R
the multF of R . (Z,(0. R)) is right_complementable Element of the carrier of R
[Z,(0. R)] is set
{Z,(0. R)} is non empty finite set
{{Z,(0. R)},{Z}} is non empty finite V39() set
the multF of R . [Z,(0. R)] is set
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial finite set
MultGroup R is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of (MultGroup R) is non empty finite set
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial finite set
card the carrier of (R,Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(card the carrier of (R,Z)) - 1 is V31() V32() integer ext-real set
cZ is Element of the carrier of (MultGroup R)
((MultGroup R),cZ) is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of MultGroup R
card ((MultGroup R),cZ) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
the carrier of ((MultGroup R),cZ) is non empty finite set
card the carrier of ((MultGroup R),cZ) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
NonZero R is non empty finite Element of bool the carrier of R
bool the carrier of R is non empty finite V39() set
[#] R is non empty non proper finite Element of bool the carrier of R
0. R is V104(R) right_complementable Element of the carrier of R
the ZeroF of R is right_complementable Element of the carrier of R
{(0. R)} is non empty trivial finite 1 -element set
([#] R) \ {(0. R)} is finite Element of bool the carrier of R
the carrier of ((MultGroup R),cZ) \/ {(0. R)} is non empty finite set
card the carrier of ((MultGroup R),cZ) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(card the carrier of ((MultGroup R),cZ)) + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
the addF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the ZeroF of R is right_complementable Element of the carrier of R
addLoopStr(# the carrier of R, the addF of R, the ZeroF of R #) is non empty non trivial strict addLoopStr
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
the carrier of (R) is non empty non trivial set
[: the carrier of (R), the carrier of R:] is non empty set
the multF of R | [: the carrier of (R), the carrier of R:] is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
dom the multF of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
n is set
Rs is set
cR is set
[Rs,cR] is set
{Rs,cR} is non empty finite set
{Rs} is non empty trivial finite 1 -element set
{{Rs,cR},{Rs}} is non empty finite V39() set
dom ( the multF of R | [: the carrier of (R), the carrier of R:]) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
n is set
Rs is set
cR is set
[Rs,cR] is set
{Rs,cR} is non empty finite set
{Rs} is non empty trivial finite 1 -element set
{{Rs,cR},{Rs}} is non empty finite V39() set
( the multF of R | [: the carrier of (R), the carrier of R:]) . n is set
cRs is right_complementable Element of the carrier of R
cZs is right_complementable Element of the carrier of R
cRs * cZs is right_complementable Element of the carrier of R
the multF of R . (cRs,cZs) is right_complementable Element of the carrier of R
[cRs,cZs] is set
{cRs,cZs} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,cZs},{cRs}} is non empty finite V39() set
the multF of R . [cRs,cZs] is set
[:[: the carrier of (R), the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of (R), the carrier of R:], the carrier of R:] is non empty set
0. R is V104(R) right_complementable Element of the carrier of R
n is Relation-like [: the carrier of (R), the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of R:], the carrier of R:]
VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is non empty strict VectSpStr over (R)
the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is non empty set
the multF of (R) is Relation-like [: the carrier of (R), the carrier of (R):] -defined the carrier of (R) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of (R):], the carrier of (R):]
[: the carrier of (R), the carrier of (R):] is non empty set
[:[: the carrier of (R), the carrier of (R):], the carrier of (R):] is non empty set
bool [:[: the carrier of (R), the carrier of (R):], the carrier of (R):] is non empty set
the multF of R || the carrier of (R) is set
the multF of R | [: the carrier of (R), the carrier of (R):] is Relation-like Function-like set
the addF of (R) is Relation-like [: the carrier of (R), the carrier of (R):] -defined the carrier of (R) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of (R):], the carrier of (R):]
the addF of R || the carrier of (R) is set
the addF of R | [: the carrier of (R), the carrier of (R):] is Relation-like Function-like set
cRs is right_complementable Element of the carrier of (R)
cZs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
cZs + natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Relation-like [: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] -defined the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) -valued Function-like quasi_total Element of bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):]
[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
[:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cZs,natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cZs,natq1] is set
{cZs,natq1} is non empty finite set
{cZs} is non empty trivial finite 1 -element set
{{cZs,natq1},{cZs}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cZs,natq1] is set
cRs * (cZs + natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Relation-like [: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] -defined the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):]
[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
[:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cRs,(cZs + natq1)) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cRs,(cZs + natq1)] is set
{cRs,(cZs + natq1)} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,(cZs + natq1)},{cRs}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cRs,(cZs + natq1)] is set
cRs * cZs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cRs,cZs) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cRs,cZs] is set
{cRs,cZs} is non empty finite set
{{cRs,cZs},{cRs}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cRs,cZs] is set
cRs * natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cRs,natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cRs,natq1] is set
{cRs,natq1} is non empty finite set
{{cRs,natq1},{cRs}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cRs,natq1] is set
(cRs * cZs) + (cRs * natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . ((cRs * cZs),(cRs * natq1)) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[(cRs * cZs),(cRs * natq1)] is set
{(cRs * cZs),(cRs * natq1)} is non empty finite set
{(cRs * cZs)} is non empty trivial finite 1 -element set
{{(cRs * cZs),(cRs * natq1)},{(cRs * cZs)}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [(cRs * cZs),(cRs * natq1)] is set
A is right_complementable Element of the carrier of R
B is right_complementable Element of the carrier of R
f is right_complementable Element of the carrier of R
B + f is right_complementable Element of the carrier of R
the addF of R . (B,f) is right_complementable Element of the carrier of R
[B,f] is set
{B,f} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,f},{B}} is non empty finite V39() set
the addF of R . [B,f] is set
A * (B + f) is right_complementable Element of the carrier of R
the multF of R . (A,(B + f)) is right_complementable Element of the carrier of R
[A,(B + f)] is set
{A,(B + f)} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,(B + f)},{A}} is non empty finite V39() set
the multF of R . [A,(B + f)] is set
A * B is right_complementable Element of the carrier of R
the multF of R . (A,B) is right_complementable Element of the carrier of R
[A,B] is set
{A,B} is non empty finite set
{{A,B},{A}} is non empty finite V39() set
the multF of R . [A,B] is set
A * f is right_complementable Element of the carrier of R
the multF of R . (A,f) is right_complementable Element of the carrier of R
[A,f] is set
{A,f} is non empty finite set
{{A,f},{A}} is non empty finite V39() set
the multF of R . [A,f] is set
(A * B) + (A * f) is right_complementable Element of the carrier of R
the addF of R . ((A * B),(A * f)) is right_complementable Element of the carrier of R
[(A * B),(A * f)] is set
{(A * B),(A * f)} is non empty finite set
{(A * B)} is non empty trivial finite 1 -element set
{{(A * B),(A * f)},{(A * B)}} is non empty finite V39() set
the addF of R . [(A * B),(A * f)] is set
[(cRs * cZs),( the multF of R . [A,f])] is set
{(cRs * cZs),( the multF of R . [A,f])} is non empty finite set
{{(cRs * cZs),( the multF of R . [A,f])},{(cRs * cZs)}} is non empty finite V39() set
the addF of R . [(cRs * cZs),( the multF of R . [A,f])] is set
cRs is right_complementable Element of the carrier of (R)
cZs is right_complementable Element of the carrier of (R)
cRs + cZs is right_complementable Element of the carrier of (R)
the addF of (R) . (cRs,cZs) is right_complementable Element of the carrier of (R)
[cRs,cZs] is set
{cRs,cZs} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,cZs},{cRs}} is non empty finite V39() set
the addF of (R) . [cRs,cZs] is set
natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
(cRs + cZs) * natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Relation-like [: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] -defined the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):]
[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
[:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . ((cRs + cZs),natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[(cRs + cZs),natq1] is set
{(cRs + cZs),natq1} is non empty finite set
{(cRs + cZs)} is non empty trivial finite 1 -element set
{{(cRs + cZs),natq1},{(cRs + cZs)}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [(cRs + cZs),natq1] is set
cRs * natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cRs,natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cRs,natq1] is set
{cRs,natq1} is non empty finite set
{{cRs,natq1},{cRs}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cRs,natq1] is set
cZs * natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cZs,natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cZs,natq1] is set
{cZs,natq1} is non empty finite set
{cZs} is non empty trivial finite 1 -element set
{{cZs,natq1},{cZs}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cZs,natq1] is set
(cRs * natq1) + (cZs * natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Relation-like [: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] -defined the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) -valued Function-like quasi_total Element of bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):]
[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
[:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . ((cRs * natq1),(cZs * natq1)) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[(cRs * natq1),(cZs * natq1)] is set
{(cRs * natq1),(cZs * natq1)} is non empty finite set
{(cRs * natq1)} is non empty trivial finite 1 -element set
{{(cRs * natq1),(cZs * natq1)},{(cRs * natq1)}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [(cRs * natq1),(cZs * natq1)] is set
cRs + cZs is right_complementable Element of the carrier of (R)
[(cRs + cZs),natq1] is set
{(cRs + cZs),natq1} is non empty finite set
{(cRs + cZs)} is non empty trivial finite 1 -element set
{{(cRs + cZs),natq1},{(cRs + cZs)}} is non empty finite V39() set
(cRs + cZs) * natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . ((cRs + cZs),natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [(cRs + cZs),natq1] is set
f is right_complementable Element of the carrier of R
[( the addF of (R) . [cRs,cZs]),f] is set
{( the addF of (R) . [cRs,cZs]),f} is non empty finite set
{( the addF of (R) . [cRs,cZs])} is non empty trivial finite 1 -element set
{{( the addF of (R) . [cRs,cZs]),f},{( the addF of (R) . [cRs,cZs])}} is non empty finite V39() set
the multF of R . [( the addF of (R) . [cRs,cZs]),f] is set
A is right_complementable Element of the carrier of R
B is right_complementable Element of the carrier of R
A + B is right_complementable Element of the carrier of R
the addF of R . (A,B) is right_complementable Element of the carrier of R
[A,B] is set
{A,B} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,B},{A}} is non empty finite V39() set
the addF of R . [A,B] is set
(A + B) * f is right_complementable Element of the carrier of R
the multF of R . ((A + B),f) is right_complementable Element of the carrier of R
[(A + B),f] is set
{(A + B),f} is non empty finite set
{(A + B)} is non empty trivial finite 1 -element set
{{(A + B),f},{(A + B)}} is non empty finite V39() set
the multF of R . [(A + B),f] is set
A * f is right_complementable Element of the carrier of R
the multF of R . (A,f) is right_complementable Element of the carrier of R
[A,f] is set
{A,f} is non empty finite set
{{A,f},{A}} is non empty finite V39() set
the multF of R . [A,f] is set
B * f is right_complementable Element of the carrier of R
the multF of R . (B,f) is right_complementable Element of the carrier of R
[B,f] is set
{B,f} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,f},{B}} is non empty finite V39() set
the multF of R . [B,f] is set
(A * f) + (B * f) is right_complementable Element of the carrier of R
the addF of R . ((A * f),(B * f)) is right_complementable Element of the carrier of R
[(A * f),(B * f)] is set
{(A * f),(B * f)} is non empty finite set
{(A * f)} is non empty trivial finite 1 -element set
{{(A * f),(B * f)},{(A * f)}} is non empty finite V39() set
the addF of R . [(A * f),(B * f)] is set
[(cRs * natq1),( the multF of R . [B,f])] is set
{(cRs * natq1),( the multF of R . [B,f])} is non empty finite set
{{(cRs * natq1),( the multF of R . [B,f])},{(cRs * natq1)}} is non empty finite V39() set
the addF of R . [(cRs * natq1),( the multF of R . [B,f])] is set
cRs is right_complementable Element of the carrier of (R)
cZs is right_complementable Element of the carrier of (R)
cRs * cZs is right_complementable Element of the carrier of (R)
the multF of (R) . (cRs,cZs) is right_complementable Element of the carrier of (R)
[cRs,cZs] is set
{cRs,cZs} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,cZs},{cRs}} is non empty finite V39() set
the multF of (R) . [cRs,cZs] is set
natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
(cRs * cZs) * natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Relation-like [: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] -defined the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):]
[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
[:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . ((cRs * cZs),natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[(cRs * cZs),natq1] is set
{(cRs * cZs),natq1} is non empty finite set
{(cRs * cZs)} is non empty trivial finite 1 -element set
{{(cRs * cZs),natq1},{(cRs * cZs)}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [(cRs * cZs),natq1] is set
cZs * natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cZs,natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cZs,natq1] is set
{cZs,natq1} is non empty finite set
{cZs} is non empty trivial finite 1 -element set
{{cZs,natq1},{cZs}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cZs,natq1] is set
cRs * (cZs * natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cRs,(cZs * natq1)) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cRs,(cZs * natq1)] is set
{cRs,(cZs * natq1)} is non empty finite set
{{cRs,(cZs * natq1)},{cRs}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cRs,(cZs * natq1)] is set
cRs * cZs is right_complementable Element of the carrier of (R)
[(cRs * cZs),natq1] is set
{(cRs * cZs),natq1} is non empty finite set
{(cRs * cZs)} is non empty trivial finite 1 -element set
{{(cRs * cZs),natq1},{(cRs * cZs)}} is non empty finite V39() set
(cRs * cZs) * natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . ((cRs * cZs),natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [(cRs * cZs),natq1] is set
f is right_complementable Element of the carrier of R
[( the multF of (R) . (cRs,cZs)),f] is set
{( the multF of (R) . (cRs,cZs)),f} is non empty finite set
{( the multF of (R) . (cRs,cZs))} is non empty trivial finite 1 -element set
{{( the multF of (R) . (cRs,cZs)),f},{( the multF of (R) . (cRs,cZs))}} is non empty finite V39() set
the multF of R . [( the multF of (R) . (cRs,cZs)),f] is set
A is right_complementable Element of the carrier of R
B is right_complementable Element of the carrier of R
A * B is right_complementable Element of the carrier of R
the multF of R . (A,B) is right_complementable Element of the carrier of R
[A,B] is set
{A,B} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,B},{A}} is non empty finite V39() set
the multF of R . [A,B] is set
(A * B) * f is right_complementable Element of the carrier of R
the multF of R . ((A * B),f) is right_complementable Element of the carrier of R
[(A * B),f] is set
{(A * B),f} is non empty finite set
{(A * B)} is non empty trivial finite 1 -element set
{{(A * B),f},{(A * B)}} is non empty finite V39() set
the multF of R . [(A * B),f] is set
B * f is right_complementable Element of the carrier of R
the multF of R . (B,f) is right_complementable Element of the carrier of R
[B,f] is set
{B,f} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,f},{B}} is non empty finite V39() set
the multF of R . [B,f] is set
A * (B * f) is right_complementable Element of the carrier of R
the multF of R . (A,(B * f)) is right_complementable Element of the carrier of R
[A,(B * f)] is set
{A,(B * f)} is non empty finite set
{{A,(B * f)},{A}} is non empty finite V39() set
the multF of R . [A,(B * f)] is set
n . (cZs,natq1) is set
n . [cZs,natq1] is set
[A,(n . (cZs,natq1))] is set
{A,(n . (cZs,natq1))} is non empty finite set
{{A,(n . (cZs,natq1))},{A}} is non empty finite V39() set
the multF of R . [A,(n . (cZs,natq1))] is set
1. (R) is V104((R)) right_complementable Element of the carrier of (R)
the OneF of (R) is right_complementable Element of the carrier of (R)
cRs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
(1. (R)) * cRs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Relation-like [: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] -defined the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):]
[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
[:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . ((1. (R)),cRs) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[(1. (R)),cRs] is set
{(1. (R)),cRs} is non empty finite set
{(1. (R))} is non empty trivial finite 1 -element set
{{(1. (R)),cRs},{(1. (R))}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [(1. (R)),cRs] is set
1_ R is right_complementable Element of the carrier of R
1. R is V104(R) right_complementable Element of the carrier of R
the OneF of R is right_complementable Element of the carrier of R
cZs is right_complementable Element of the carrier of R
[(1_ R),cZs] is set
{(1_ R),cZs} is non empty finite set
{(1_ R)} is non empty trivial finite 1 -element set
{{(1_ R),cZs},{(1_ R)}} is non empty finite V39() set
n . ((1. R),cZs) is set
[(1. R),cZs] is set
{(1. R),cZs} is non empty finite set
{(1. R)} is non empty trivial finite 1 -element set
{{(1. R),cZs},{(1. R)}} is non empty finite V39() set
n . [(1. R),cZs] is set
(1. R) * cZs is right_complementable Element of the carrier of R
the multF of R . ((1. R),cZs) is right_complementable Element of the carrier of R
the multF of R . [(1. R),cZs] is set
cRs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
cZs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
cRs + cZs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Relation-like [: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] -defined the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) -valued Function-like quasi_total Element of bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):]
[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
[:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cRs,cZs) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cRs,cZs] is set
{cRs,cZs} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,cZs},{cRs}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cRs,cZs] is set
natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
(cRs + cZs) + natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . ((cRs + cZs),natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[(cRs + cZs),natq1] is set
{(cRs + cZs),natq1} is non empty finite set
{(cRs + cZs)} is non empty trivial finite 1 -element set
{{(cRs + cZs),natq1},{(cRs + cZs)}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [(cRs + cZs),natq1] is set
cZs + natq1 is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cZs,natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cZs,natq1] is set
{cZs,natq1} is non empty finite set
{cZs} is non empty trivial finite 1 -element set
{{cZs,natq1},{cZs}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cZs,natq1] is set
cRs + (cZs + natq1) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cRs,(cZs + natq1)) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cRs,(cZs + natq1)] is set
{cRs,(cZs + natq1)} is non empty finite set
{{cRs,(cZs + natq1)},{cRs}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cRs,(cZs + natq1)] is set
A is right_complementable Element of the carrier of R
B is right_complementable Element of the carrier of R
A + B is right_complementable Element of the carrier of R
the addF of R . (A,B) is right_complementable Element of the carrier of R
[A,B] is set
{A,B} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,B},{A}} is non empty finite V39() set
the addF of R . [A,B] is set
f is right_complementable Element of the carrier of R
(A + B) + f is right_complementable Element of the carrier of R
the addF of R . ((A + B),f) is right_complementable Element of the carrier of R
[(A + B),f] is set
{(A + B),f} is non empty finite set
{(A + B)} is non empty trivial finite 1 -element set
{{(A + B),f},{(A + B)}} is non empty finite V39() set
the addF of R . [(A + B),f] is set
B + f is right_complementable Element of the carrier of R
the addF of R . (B,f) is right_complementable Element of the carrier of R
[B,f] is set
{B,f} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,f},{B}} is non empty finite V39() set
the addF of R . [B,f] is set
A + (B + f) is right_complementable Element of the carrier of R
the addF of R . (A,(B + f)) is right_complementable Element of the carrier of R
[A,(B + f)] is set
{A,(B + f)} is non empty finite set
{{A,(B + f)},{A}} is non empty finite V39() set
the addF of R . [A,(B + f)] is set
cRs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
0. VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is V104( VectSpStr(# the carrier of R, the addF of R,(0. R),n #)) Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the ZeroF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
cRs + (0. VectSpStr(# the carrier of R, the addF of R,(0. R),n #)) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Relation-like [: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] -defined the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) -valued Function-like quasi_total Element of bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):]
[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
[:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cRs,(0. VectSpStr(# the carrier of R, the addF of R,(0. R),n #))) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cRs,(0. VectSpStr(# the carrier of R, the addF of R,(0. R),n #))] is set
{cRs,(0. VectSpStr(# the carrier of R, the addF of R,(0. R),n #))} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,(0. VectSpStr(# the carrier of R, the addF of R,(0. R),n #))},{cRs}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cRs,(0. VectSpStr(# the carrier of R, the addF of R,(0. R),n #))] is set
cZs is right_complementable Element of the carrier of R
cZs + (0. R) is right_complementable Element of the carrier of R
the addF of R . (cZs,(0. R)) is right_complementable Element of the carrier of R
[cZs,(0. R)] is set
{cZs,(0. R)} is non empty finite set
{cZs} is non empty trivial finite 1 -element set
{{cZs,(0. R)},{cZs}} is non empty finite V39() set
the addF of R . [cZs,(0. R)] is set
cRs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
cZs is right_complementable Element of the carrier of R
natq1 is right_complementable Element of the carrier of R
cZs + natq1 is right_complementable Element of the carrier of R
the addF of R . (cZs,natq1) is right_complementable Element of the carrier of R
[cZs,natq1] is set
{cZs,natq1} is non empty finite set
{cZs} is non empty trivial finite 1 -element set
{{cZs,natq1},{cZs}} is non empty finite V39() set
the addF of R . [cZs,natq1] is set
A is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
cRs + A is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Relation-like [: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] -defined the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) -valued Function-like quasi_total Element of bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):]
[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
[:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cRs,A) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cRs,A] is set
{cRs,A} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,A},{cRs}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cRs,A] is set
0. VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is V104( VectSpStr(# the carrier of R, the addF of R,(0. R),n #)) Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the ZeroF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
cRs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
cZs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
cRs + cZs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) is Relation-like [: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] -defined the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) -valued Function-like quasi_total Element of bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):]
[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
[:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
bool [:[: the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #), the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):], the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #):] is non empty set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cRs,cZs) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cRs,cZs] is set
{cRs,cZs} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,cZs},{cRs}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cRs,cZs] is set
cZs + cRs is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . (cZs,cRs) is Element of the carrier of VectSpStr(# the carrier of R, the addF of R,(0. R),n #)
[cZs,cRs] is set
{cZs,cRs} is non empty finite set
{cZs} is non empty trivial finite 1 -element set
{{cZs,cRs},{cZs}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of R, the addF of R,(0. R),n #) . [cZs,cRs] is set
A is right_complementable Element of the carrier of R
natq1 is right_complementable Element of the carrier of R
A + natq1 is right_complementable Element of the carrier of R
the addF of R . (A,natq1) is right_complementable Element of the carrier of R
[A,natq1] is set
{A,natq1} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,natq1},{A}} is non empty finite V39() set
the addF of R . [A,natq1] is set
Z is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
the carrier of Z is non empty set
the addF of Z is Relation-like [: the carrier of Z, the carrier of Z:] -defined the carrier of Z -valued Function-like quasi_total Element of bool [:[: the carrier of Z, the carrier of Z:], the carrier of Z:]
[: the carrier of Z, the carrier of Z:] is non empty set
[:[: the carrier of Z, the carrier of Z:], the carrier of Z:] is non empty set
bool [:[: the carrier of Z, the carrier of Z:], the carrier of Z:] is non empty set
the ZeroF of Z is right_complementable Element of the carrier of Z
addLoopStr(# the carrier of Z, the addF of Z, the ZeroF of Z #) is non empty strict addLoopStr
the lmult of Z is Relation-like [: the carrier of (R), the carrier of Z:] -defined the carrier of Z -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of Z:], the carrier of Z:]
[: the carrier of (R), the carrier of Z:] is non empty set
[:[: the carrier of (R), the carrier of Z:], the carrier of Z:] is non empty set
bool [:[: the carrier of (R), the carrier of Z:], the carrier of Z:] is non empty set
cZ is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
the carrier of cZ is non empty set
the addF of cZ is Relation-like [: the carrier of cZ, the carrier of cZ:] -defined the carrier of cZ -valued Function-like quasi_total Element of bool [:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:]
[: the carrier of cZ, the carrier of cZ:] is non empty set
[:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:] is non empty set
bool [:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:] is non empty set
the ZeroF of cZ is right_complementable Element of the carrier of cZ
addLoopStr(# the carrier of cZ, the addF of cZ, the ZeroF of cZ #) is non empty strict addLoopStr
the lmult of cZ is Relation-like [: the carrier of (R), the carrier of cZ:] -defined the carrier of cZ -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of cZ:], the carrier of cZ:]
[: the carrier of (R), the carrier of cZ:] is non empty set
[:[: the carrier of (R), the carrier of cZ:], the carrier of cZ:] is non empty set
bool [:[: the carrier of (R), the carrier of cZ:], the carrier of cZ:] is non empty set
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial finite set
card the carrier of R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(R) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial finite set
card the carrier of (R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(R) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
dim (R) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
(card the carrier of (R)) |^ (dim (R)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
the carrier of (R) is non empty set
the addF of (R) is Relation-like [: the carrier of (R), the carrier of (R):] -defined the carrier of (R) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of (R):], the carrier of (R):]
[: the carrier of (R), the carrier of (R):] is non empty set
[:[: the carrier of (R), the carrier of (R):], the carrier of (R):] is non empty set
bool [:[: the carrier of (R), the carrier of (R):], the carrier of (R):] is non empty set
the ZeroF of (R) is right_complementable Element of the carrier of (R)
addLoopStr(# the carrier of (R), the addF of (R), the ZeroF of (R) #) is non empty strict addLoopStr
the addF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total finite Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty finite set
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty finite V39() set
the ZeroF of R is right_complementable Element of the carrier of R
addLoopStr(# the carrier of R, the addF of R, the ZeroF of R #) is non empty non trivial strict addLoopStr
the Basis of (R) is Basis of (R)
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
dim (R) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
the carrier of (R) is non empty non trivial finite set
card the carrier of (R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
MultGroup R is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
card R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
the carrier of R is non empty non trivial finite set
card the carrier of R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
(card the carrier of (R)) |^ (dim (R)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
card (MultGroup R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
the carrier of (MultGroup R) is non empty finite set
card the carrier of (MultGroup R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
((card the carrier of (R)) |^ (dim (R))) - 1 is V31() V32() integer ext-real set
(card the carrier of (R)) #Z (dim (R)) is set
1 - 1 is V31() V32() integer ext-real set
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial set
the addF of (R,Z) is Relation-like [: the carrier of (R,Z), the carrier of (R,Z):] -defined the carrier of (R,Z) -valued Function-like quasi_total Element of bool [:[: the carrier of (R,Z), the carrier of (R,Z):], the carrier of (R,Z):]
[: the carrier of (R,Z), the carrier of (R,Z):] is non empty set
[:[: the carrier of (R,Z), the carrier of (R,Z):], the carrier of (R,Z):] is non empty set
bool [:[: the carrier of (R,Z), the carrier of (R,Z):], the carrier of (R,Z):] is non empty set
the ZeroF of (R,Z) is right_complementable Element of the carrier of (R,Z)
addLoopStr(# the carrier of (R,Z), the addF of (R,Z), the ZeroF of (R,Z) #) is non empty non trivial strict addLoopStr
[: the carrier of R, the carrier of R:] is non empty set
the multF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
[:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
bool [:[: the carrier of R, the carrier of R:], the carrier of R:] is non empty set
the carrier of (R) is non empty non trivial set
[: the carrier of (R), the carrier of (R,Z):] is non empty set
the multF of R | [: the carrier of (R), the carrier of (R,Z):] is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
dom the multF of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
cR is set
cRs is set
cZs is set
[cRs,cZs] is set
{cRs,cZs} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,cZs},{cRs}} is non empty finite V39() set
dom ( the multF of R | [: the carrier of (R), the carrier of (R,Z):]) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
cR is set
cRs is set
cZs is set
[cRs,cZs] is set
{cRs,cZs} is non empty finite set
{cRs} is non empty trivial finite 1 -element set
{{cRs,cZs},{cRs}} is non empty finite V39() set
( the multF of R | [: the carrier of (R), the carrier of (R,Z):]) . cR is set
natq1 is right_complementable Element of the carrier of R
A is right_complementable Element of the carrier of R
natq1 * A is right_complementable Element of the carrier of R
the multF of R . (natq1,A) is right_complementable Element of the carrier of R
[natq1,A] is set
{natq1,A} is non empty finite set
{natq1} is non empty trivial finite 1 -element set
{{natq1,A},{natq1}} is non empty finite V39() set
the multF of R . [natq1,A] is set
[:[: the carrier of (R), the carrier of (R,Z):], the carrier of (R,Z):] is non empty set
bool [:[: the carrier of (R), the carrier of (R,Z):], the carrier of (R,Z):] is non empty set
0. (R,Z) is V104((R,Z)) right_complementable Element of the carrier of (R,Z)
cR is Relation-like [: the carrier of (R), the carrier of (R,Z):] -defined the carrier of (R,Z) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of (R,Z):], the carrier of (R,Z):]
VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is non empty strict VectSpStr over (R)
the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is non empty set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is Relation-like [: the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] -defined the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) -valued Function-like quasi_total Element of bool [:[: the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):]
[: the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
[:[: the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
bool [:[: the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
the multF of (R) is Relation-like [: the carrier of (R), the carrier of (R):] -defined the carrier of (R) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of (R):], the carrier of (R):]
[: the carrier of (R), the carrier of (R):] is non empty set
[:[: the carrier of (R), the carrier of (R):], the carrier of (R):] is non empty set
bool [:[: the carrier of (R), the carrier of (R):], the carrier of (R):] is non empty set
the multF of R || the carrier of (R) is set
the multF of R | [: the carrier of (R), the carrier of (R):] is Relation-like Function-like set
the addF of (R) is Relation-like [: the carrier of (R), the carrier of (R):] -defined the carrier of (R) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of (R):], the carrier of (R):]
the addF of R is Relation-like [: the carrier of R, the carrier of R:] -defined the carrier of R -valued Function-like quasi_total Element of bool [:[: the carrier of R, the carrier of R:], the carrier of R:]
the addF of R || the carrier of (R) is set
the addF of R | [: the carrier of (R), the carrier of (R):] is Relation-like Function-like set
the addF of R || the carrier of (R,Z) is set
the addF of R | [: the carrier of (R,Z), the carrier of (R,Z):] is Relation-like Function-like set
A is right_complementable Element of the carrier of (R)
B is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
B + f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (B,f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[B,f] is set
{B,f} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,f},{B}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [B,f] is set
A * (B + f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is Relation-like [: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] -defined the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):]
[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
[:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (A,(B + f)) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[A,(B + f)] is set
{A,(B + f)} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,(B + f)},{A}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [A,(B + f)] is set
A * B is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (A,B) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[A,B] is set
{A,B} is non empty finite set
{{A,B},{A}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [A,B] is set
A * f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (A,f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[A,f] is set
{A,f} is non empty finite set
{{A,f},{A}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [A,f] is set
(A * B) + (A * f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . ((A * B),(A * f)) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[(A * B),(A * f)] is set
{(A * B),(A * f)} is non empty finite set
{(A * B)} is non empty trivial finite 1 -element set
{{(A * B),(A * f)},{(A * B)}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [(A * B),(A * f)] is set
[A,( the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [B,f])] is set
{A,( the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [B,f])} is non empty finite set
{{A,( the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [B,f])},{A}} is non empty finite V39() set
the multF of R . [A,( the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [B,f])] is set
f1 is right_complementable Element of the carrier of R
f2 is right_complementable Element of the carrier of R
f is right_complementable Element of the carrier of R
f2 + f is right_complementable Element of the carrier of R
the addF of R . (f2,f) is right_complementable Element of the carrier of R
[f2,f] is set
{f2,f} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,f},{f2}} is non empty finite V39() set
the addF of R . [f2,f] is set
f1 * (f2 + f) is right_complementable Element of the carrier of R
the multF of R . (f1,(f2 + f)) is right_complementable Element of the carrier of R
[f1,(f2 + f)] is set
{f1,(f2 + f)} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,(f2 + f)},{f1}} is non empty finite V39() set
the multF of R . [f1,(f2 + f)] is set
f1 * f2 is right_complementable Element of the carrier of R
the multF of R . (f1,f2) is right_complementable Element of the carrier of R
[f1,f2] is set
{f1,f2} is non empty finite set
{{f1,f2},{f1}} is non empty finite V39() set
the multF of R . [f1,f2] is set
f1 * f is right_complementable Element of the carrier of R
the multF of R . (f1,f) is right_complementable Element of the carrier of R
[f1,f] is set
{f1,f} is non empty finite set
{{f1,f},{f1}} is non empty finite V39() set
the multF of R . [f1,f] is set
(f1 * f2) + (f1 * f) is right_complementable Element of the carrier of R
the addF of R . ((f1 * f2),(f1 * f)) is right_complementable Element of the carrier of R
[(f1 * f2),(f1 * f)] is set
{(f1 * f2),(f1 * f)} is non empty finite set
{(f1 * f2)} is non empty trivial finite 1 -element set
{{(f1 * f2),(f1 * f)},{(f1 * f2)}} is non empty finite V39() set
the addF of R . [(f1 * f2),(f1 * f)] is set
[(A * B),( the multF of R . [f1,f])] is set
{(A * B),( the multF of R . [f1,f])} is non empty finite set
{{(A * B),( the multF of R . [f1,f])},{(A * B)}} is non empty finite V39() set
the addF of R . [(A * B),( the multF of R . [f1,f])] is set
the addF of R . [(A * B),(A * f)] is set
A is right_complementable Element of the carrier of (R)
B is right_complementable Element of the carrier of (R)
A + B is right_complementable Element of the carrier of (R)
the addF of (R) . (A,B) is right_complementable Element of the carrier of (R)
[A,B] is set
{A,B} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,B},{A}} is non empty finite V39() set
the addF of (R) . [A,B] is set
f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
(A + B) * f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is Relation-like [: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] -defined the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):]
[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
[:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . ((A + B),f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[(A + B),f] is set
{(A + B),f} is non empty finite set
{(A + B)} is non empty trivial finite 1 -element set
{{(A + B),f},{(A + B)}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [(A + B),f] is set
A * f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (A,f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[A,f] is set
{A,f} is non empty finite set
{{A,f},{A}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [A,f] is set
B * f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (B,f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[B,f] is set
{B,f} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,f},{B}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [B,f] is set
(A * f) + (B * f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . ((A * f),(B * f)) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[(A * f),(B * f)] is set
{(A * f),(B * f)} is non empty finite set
{(A * f)} is non empty trivial finite 1 -element set
{{(A * f),(B * f)},{(A * f)}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [(A * f),(B * f)] is set
A + B is right_complementable Element of the carrier of (R)
[(A + B),f] is set
{(A + B),f} is non empty finite set
{(A + B)} is non empty trivial finite 1 -element set
{{(A + B),f},{(A + B)}} is non empty finite V39() set
(A + B) * f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . ((A + B),f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [(A + B),f] is set
f is right_complementable Element of the carrier of R
[( the addF of (R) . [A,B]),f] is set
{( the addF of (R) . [A,B]),f} is non empty finite set
{( the addF of (R) . [A,B])} is non empty trivial finite 1 -element set
{{( the addF of (R) . [A,B]),f},{( the addF of (R) . [A,B])}} is non empty finite V39() set
the multF of R . [( the addF of (R) . [A,B]),f] is set
f1 is right_complementable Element of the carrier of R
f2 is right_complementable Element of the carrier of R
f1 + f2 is right_complementable Element of the carrier of R
the addF of R . (f1,f2) is right_complementable Element of the carrier of R
[f1,f2] is set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V39() set
the addF of R . [f1,f2] is set
(f1 + f2) * f is right_complementable Element of the carrier of R
the multF of R . ((f1 + f2),f) is right_complementable Element of the carrier of R
[(f1 + f2),f] is set
{(f1 + f2),f} is non empty finite set
{(f1 + f2)} is non empty trivial finite 1 -element set
{{(f1 + f2),f},{(f1 + f2)}} is non empty finite V39() set
the multF of R . [(f1 + f2),f] is set
f1 * f is right_complementable Element of the carrier of R
the multF of R . (f1,f) is right_complementable Element of the carrier of R
[f1,f] is set
{f1,f} is non empty finite set
{{f1,f},{f1}} is non empty finite V39() set
the multF of R . [f1,f] is set
f2 * f is right_complementable Element of the carrier of R
the multF of R . (f2,f) is right_complementable Element of the carrier of R
[f2,f] is set
{f2,f} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,f},{f2}} is non empty finite V39() set
the multF of R . [f2,f] is set
(f1 * f) + (f2 * f) is right_complementable Element of the carrier of R
the addF of R . ((f1 * f),(f2 * f)) is right_complementable Element of the carrier of R
[(f1 * f),(f2 * f)] is set
{(f1 * f),(f2 * f)} is non empty finite set
{(f1 * f)} is non empty trivial finite 1 -element set
{{(f1 * f),(f2 * f)},{(f1 * f)}} is non empty finite V39() set
the addF of R . [(f1 * f),(f2 * f)] is set
[(A * f),( the multF of R . [f2,f])] is set
{(A * f),( the multF of R . [f2,f])} is non empty finite set
{{(A * f),( the multF of R . [f2,f])},{(A * f)}} is non empty finite V39() set
the addF of R . [(A * f),( the multF of R . [f2,f])] is set
cR . (B,f) is set
cR . [B,f] is set
[(A * f),(cR . (B,f))] is set
{(A * f),(cR . (B,f))} is non empty finite set
{{(A * f),(cR . (B,f))},{(A * f)}} is non empty finite V39() set
the addF of R . [(A * f),(cR . (B,f))] is set
A is right_complementable Element of the carrier of (R)
B is right_complementable Element of the carrier of (R)
A * B is right_complementable Element of the carrier of (R)
the multF of (R) . (A,B) is right_complementable Element of the carrier of (R)
[A,B] is set
{A,B} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,B},{A}} is non empty finite V39() set
the multF of (R) . [A,B] is set
f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
(A * B) * f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is Relation-like [: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] -defined the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):]
[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
[:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . ((A * B),f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[(A * B),f] is set
{(A * B),f} is non empty finite set
{(A * B)} is non empty trivial finite 1 -element set
{{(A * B),f},{(A * B)}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [(A * B),f] is set
B * f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (B,f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[B,f] is set
{B,f} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,f},{B}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [B,f] is set
A * (B * f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (A,(B * f)) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[A,(B * f)] is set
{A,(B * f)} is non empty finite set
{{A,(B * f)},{A}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [A,(B * f)] is set
A * B is right_complementable Element of the carrier of (R)
[(A * B),f] is set
{(A * B),f} is non empty finite set
{(A * B)} is non empty trivial finite 1 -element set
{{(A * B),f},{(A * B)}} is non empty finite V39() set
(A * B) * f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . ((A * B),f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [(A * B),f] is set
f is right_complementable Element of the carrier of R
[( the multF of (R) . (A,B)),f] is set
{( the multF of (R) . (A,B)),f} is non empty finite set
{( the multF of (R) . (A,B))} is non empty trivial finite 1 -element set
{{( the multF of (R) . (A,B)),f},{( the multF of (R) . (A,B))}} is non empty finite V39() set
the multF of R . [( the multF of (R) . (A,B)),f] is set
f1 is right_complementable Element of the carrier of R
f2 is right_complementable Element of the carrier of R
f1 * f2 is right_complementable Element of the carrier of R
the multF of R . (f1,f2) is right_complementable Element of the carrier of R
[f1,f2] is set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V39() set
the multF of R . [f1,f2] is set
(f1 * f2) * f is right_complementable Element of the carrier of R
the multF of R . ((f1 * f2),f) is right_complementable Element of the carrier of R
[(f1 * f2),f] is set
{(f1 * f2),f} is non empty finite set
{(f1 * f2)} is non empty trivial finite 1 -element set
{{(f1 * f2),f},{(f1 * f2)}} is non empty finite V39() set
the multF of R . [(f1 * f2),f] is set
f2 * f is right_complementable Element of the carrier of R
the multF of R . (f2,f) is right_complementable Element of the carrier of R
[f2,f] is set
{f2,f} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,f},{f2}} is non empty finite V39() set
the multF of R . [f2,f] is set
f1 * (f2 * f) is right_complementable Element of the carrier of R
the multF of R . (f1,(f2 * f)) is right_complementable Element of the carrier of R
[f1,(f2 * f)] is set
{f1,(f2 * f)} is non empty finite set
{{f1,(f2 * f)},{f1}} is non empty finite V39() set
the multF of R . [f1,(f2 * f)] is set
cR . (B,f) is set
cR . [B,f] is set
[f1,(cR . (B,f))] is set
{f1,(cR . (B,f))} is non empty finite set
{{f1,(cR . (B,f))},{f1}} is non empty finite V39() set
the multF of R . [f1,(cR . (B,f))] is set
1. (R) is V104((R)) right_complementable Element of the carrier of (R)
the OneF of (R) is right_complementable Element of the carrier of (R)
A is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
(1. (R)) * A is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is Relation-like [: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] -defined the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):]
[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
[:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
bool [:[: the carrier of (R), the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):], the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #):] is non empty set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . ((1. (R)),A) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[(1. (R)),A] is set
{(1. (R)),A} is non empty finite set
{(1. (R))} is non empty trivial finite 1 -element set
{{(1. (R)),A},{(1. (R))}} is non empty finite V39() set
the lmult of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [(1. (R)),A] is set
1_ R is right_complementable Element of the carrier of R
1. R is V104(R) right_complementable Element of the carrier of R
the OneF of R is right_complementable Element of the carrier of R
B is right_complementable Element of the carrier of R
[(1_ R),B] is set
{(1_ R),B} is non empty finite set
{(1_ R)} is non empty trivial finite 1 -element set
{{(1_ R),B},{(1_ R)}} is non empty finite V39() set
cR . ((1. R),B) is set
[(1. R),B] is set
{(1. R),B} is non empty finite set
{(1. R)} is non empty trivial finite 1 -element set
{{(1. R),B},{(1. R)}} is non empty finite V39() set
cR . [(1. R),B] is set
(1. R) * B is right_complementable Element of the carrier of R
the multF of R . ((1. R),B) is right_complementable Element of the carrier of R
the multF of R . [(1. R),B] is set
A is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
B is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
A + B is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (A,B) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[A,B] is set
{A,B} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,B},{A}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [A,B] is set
f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
(A + B) + f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . ((A + B),f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[(A + B),f] is set
{(A + B),f} is non empty finite set
{(A + B)} is non empty trivial finite 1 -element set
{{(A + B),f},{(A + B)}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [(A + B),f] is set
B + f is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (B,f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[B,f] is set
{B,f} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,f},{B}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [B,f] is set
A + (B + f) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (A,(B + f)) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[A,(B + f)] is set
{A,(B + f)} is non empty finite set
{{A,(B + f)},{A}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [A,(B + f)] is set
f1 is right_complementable Element of the carrier of (R,Z)
f2 is right_complementable Element of the carrier of (R,Z)
f1 + f2 is right_complementable Element of the carrier of (R,Z)
the addF of (R,Z) . (f1,f2) is right_complementable Element of the carrier of (R,Z)
[f1,f2] is set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V39() set
the addF of (R,Z) . [f1,f2] is set
f is right_complementable Element of the carrier of (R,Z)
(f1 + f2) + f is right_complementable Element of the carrier of (R,Z)
the addF of (R,Z) . ((f1 + f2),f) is right_complementable Element of the carrier of (R,Z)
[(f1 + f2),f] is set
{(f1 + f2),f} is non empty finite set
{(f1 + f2)} is non empty trivial finite 1 -element set
{{(f1 + f2),f},{(f1 + f2)}} is non empty finite V39() set
the addF of (R,Z) . [(f1 + f2),f] is set
f2 + f is right_complementable Element of the carrier of (R,Z)
the addF of (R,Z) . (f2,f) is right_complementable Element of the carrier of (R,Z)
[f2,f] is set
{f2,f} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,f},{f2}} is non empty finite V39() set
the addF of (R,Z) . [f2,f] is set
f1 + (f2 + f) is right_complementable Element of the carrier of (R,Z)
the addF of (R,Z) . (f1,(f2 + f)) is right_complementable Element of the carrier of (R,Z)
[f1,(f2 + f)] is set
{f1,(f2 + f)} is non empty finite set
{{f1,(f2 + f)},{f1}} is non empty finite V39() set
the addF of (R,Z) . [f1,(f2 + f)] is set
A is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
0. VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is V104( VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)) Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the ZeroF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
A + (0. VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (A,(0. VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #))) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[A,(0. VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #))] is set
{A,(0. VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #))} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,(0. VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #))},{A}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [A,(0. VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #))] is set
B is right_complementable Element of the carrier of (R,Z)
B + (0. (R,Z)) is right_complementable Element of the carrier of (R,Z)
the addF of (R,Z) . (B,(0. (R,Z))) is right_complementable Element of the carrier of (R,Z)
[B,(0. (R,Z))] is set
{B,(0. (R,Z))} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,(0. (R,Z))},{B}} is non empty finite V39() set
the addF of (R,Z) . [B,(0. (R,Z))] is set
A is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
B is right_complementable Element of the carrier of (R,Z)
f is right_complementable Element of the carrier of (R,Z)
B + f is right_complementable Element of the carrier of (R,Z)
the addF of (R,Z) . (B,f) is right_complementable Element of the carrier of (R,Z)
[B,f] is set
{B,f} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,f},{B}} is non empty finite V39() set
the addF of (R,Z) . [B,f] is set
f1 is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
A + f1 is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (A,f1) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[A,f1] is set
{A,f1} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,f1},{A}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [A,f1] is set
0. VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is V104( VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)) Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the ZeroF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
A is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
B is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
A + B is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (A,B) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[A,B] is set
{A,B} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,B},{A}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [A,B] is set
B + A is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . (B,A) is Element of the carrier of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #)
[B,A] is set
{B,A} is non empty finite set
{B} is non empty trivial finite 1 -element set
{{B,A},{B}} is non empty finite V39() set
the addF of VectSpStr(# the carrier of (R,Z), the addF of (R,Z),(0. (R,Z)),cR #) . [B,A] is set
f1 is right_complementable Element of the carrier of (R,Z)
f is right_complementable Element of the carrier of (R,Z)
f1 + f is right_complementable Element of the carrier of (R,Z)
the addF of (R,Z) . (f1,f) is right_complementable Element of the carrier of (R,Z)
[f1,f] is set
{f1,f} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f},{f1}} is non empty finite V39() set
the addF of (R,Z) . [f1,f] is set
cZ is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
the carrier of cZ is non empty set
the addF of cZ is Relation-like [: the carrier of cZ, the carrier of cZ:] -defined the carrier of cZ -valued Function-like quasi_total Element of bool [:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:]
[: the carrier of cZ, the carrier of cZ:] is non empty set
[:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:] is non empty set
bool [:[: the carrier of cZ, the carrier of cZ:], the carrier of cZ:] is non empty set
the ZeroF of cZ is right_complementable Element of the carrier of cZ
addLoopStr(# the carrier of cZ, the addF of cZ, the ZeroF of cZ #) is non empty strict addLoopStr
the lmult of cZ is Relation-like [: the carrier of (R), the carrier of cZ:] -defined the carrier of cZ -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of cZ:], the carrier of cZ:]
[: the carrier of (R), the carrier of cZ:] is non empty set
[:[: the carrier of (R), the carrier of cZ:], the carrier of cZ:] is non empty set
bool [:[: the carrier of (R), the carrier of cZ:], the carrier of cZ:] is non empty set
q is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
the carrier of q is non empty set
the addF of q is Relation-like [: the carrier of q, the carrier of q:] -defined the carrier of q -valued Function-like quasi_total Element of bool [:[: the carrier of q, the carrier of q:], the carrier of q:]
[: the carrier of q, the carrier of q:] is non empty set
[:[: the carrier of q, the carrier of q:], the carrier of q:] is non empty set
bool [:[: the carrier of q, the carrier of q:], the carrier of q:] is non empty set
the ZeroF of q is right_complementable Element of the carrier of q
addLoopStr(# the carrier of q, the addF of q, the ZeroF of q #) is non empty strict addLoopStr
the lmult of q is Relation-like [: the carrier of (R), the carrier of q:] -defined the carrier of q -valued Function-like quasi_total Element of bool [:[: the carrier of (R), the carrier of q:], the carrier of q:]
[: the carrier of (R), the carrier of q:] is non empty set
[:[: the carrier of (R), the carrier of q:], the carrier of q:] is non empty set
bool [:[: the carrier of (R), the carrier of q:], the carrier of q:] is non empty set
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial finite set
(R) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial finite set
card the carrier of (R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial finite set
card the carrier of (R,Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(R,Z) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
dim (R,Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
(card the carrier of (R)) |^ (dim (R,Z)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
the carrier of (R,Z) is non empty set
the addF of (R,Z) is Relation-like [: the carrier of (R,Z), the carrier of (R,Z):] -defined the carrier of (R,Z) -valued Function-like quasi_total Element of bool [:[: the carrier of (R,Z), the carrier of (R,Z):], the carrier of (R,Z):]
[: the carrier of (R,Z), the carrier of (R,Z):] is non empty set
[:[: the carrier of (R,Z), the carrier of (R,Z):], the carrier of (R,Z):] is non empty set
bool [:[: the carrier of (R,Z), the carrier of (R,Z):], the carrier of (R,Z):] is non empty set
the ZeroF of (R,Z) is right_complementable Element of the carrier of (R,Z)
addLoopStr(# the carrier of (R,Z), the addF of (R,Z), the ZeroF of (R,Z) #) is non empty strict addLoopStr
the addF of (R,Z) is Relation-like [: the carrier of (R,Z), the carrier of (R,Z):] -defined the carrier of (R,Z) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (R,Z), the carrier of (R,Z):], the carrier of (R,Z):]
[: the carrier of (R,Z), the carrier of (R,Z):] is non empty finite set
[:[: the carrier of (R,Z), the carrier of (R,Z):], the carrier of (R,Z):] is non empty finite set
bool [:[: the carrier of (R,Z), the carrier of (R,Z):], the carrier of (R,Z):] is non empty finite V39() set
the ZeroF of (R,Z) is right_complementable Element of the carrier of (R,Z)
addLoopStr(# the carrier of (R,Z), the addF of (R,Z), the ZeroF of (R,Z) #) is non empty non trivial strict addLoopStr
the Basis of (R,Z) is Basis of (R,Z)
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial finite set
(R) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
Z is right_complementable Element of the carrier of R
(R,Z) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
dim (R,Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
the carrier of (R) is non empty non trivial finite set
card the carrier of (R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(card the carrier of (R)) |^ (dim (R,Z)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
(card the carrier of (R)) #Z (dim (R,Z)) is set
(R,Z) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial finite set
card the carrier of (R,Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial finite set
MultGroup R is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of (MultGroup R) is non empty finite set
(R) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial finite set
card the carrier of (R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(R) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
dim (R) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
(card the carrier of (R)) |^ (dim (R)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
((card the carrier of (R)) |^ (dim (R))) - 1 is V31() V32() integer ext-real set
Z is right_complementable Element of the carrier of R
(R,Z) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
dim (R,Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
(card the carrier of (R)) |^ (dim (R,Z)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
((card the carrier of (R)) |^ (dim (R,Z))) - 1 is V31() V32() integer ext-real set
(R,Z) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,Z) is non empty non trivial finite set
card the carrier of (R,Z) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
card R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
card the carrier of R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
card (MultGroup R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
card the carrier of (MultGroup R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
Rs is Element of the carrier of (MultGroup R)
con_class Rs is non empty finite Element of bool the carrier of (MultGroup R)
bool the carrier of (MultGroup R) is non empty finite V39() set
(Omega). (MultGroup R) is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of MultGroup R
the multF of (MultGroup R) is Relation-like [: the carrier of (MultGroup R), the carrier of (MultGroup R):] -defined the carrier of (MultGroup R) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):]
[: the carrier of (MultGroup R), the carrier of (MultGroup R):] is non empty finite set
[:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty finite set
bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty finite V39() set
multMagma(# the carrier of (MultGroup R), the multF of (MultGroup R) #) is non empty strict multMagma
carr ((Omega). (MultGroup R)) is finite Element of bool the carrier of (MultGroup R)
the carrier of ((Omega). (MultGroup R)) is non empty finite set
Rs |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),Rs) is non empty trivial finite 1 -element Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),Rs) |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of (MultGroup R) : ( b₁ in K462( the carrier of (MultGroup R),Rs) & b₂ in carr ((Omega). (MultGroup R)) ) } is set
card (con_class Rs) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
((MultGroup R),Rs) is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of MultGroup R
card ((MultGroup R),Rs) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
the carrier of ((MultGroup R),Rs) is non empty finite set
card the carrier of ((MultGroup R),Rs) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
(card (con_class Rs)) * (card ((MultGroup R),Rs)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(card the carrier of (R,Z)) - 1 is V31() V32() integer ext-real set
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial finite set
MultGroup R is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of (MultGroup R) is non empty finite set
(R) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
dim (R) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
Z is right_complementable Element of the carrier of R
(R,Z) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
dim (R,Z) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
the carrier of (R) is non empty non trivial finite set
card the carrier of (R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(card the carrier of (R)) |^ (dim (R,Z)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
((card the carrier of (R)) |^ (dim (R,Z))) + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
0 + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(card the carrier of (R)) |^ (dim (R)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
((card the carrier of (R)) |^ (dim (R))) + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
((card the carrier of (R)) |^ (dim (R))) - 1 is V31() V32() integer ext-real set
((card the carrier of (R)) |^ (dim (R))) -' 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
((card the carrier of (R)) |^ (dim (R,Z))) - 1 is V31() V32() integer ext-real set
((card the carrier of (R)) |^ (dim (R,Z))) -' 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
MultGroup R is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
center (MultGroup R) is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of MultGroup R
the carrier of (center (MultGroup R)) is non empty finite set
card the carrier of (center (MultGroup R)) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(R) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial finite set
card the carrier of (R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(card the carrier of (R)) - 1 is V31() V32() integer ext-real set
the carrier of (MultGroup R) is non empty finite set
NonZero R is non empty finite Element of bool the carrier of R
the carrier of R is non empty non trivial finite set
bool the carrier of R is non empty finite V39() set
[#] R is non empty non proper finite Element of bool the carrier of R
0. R is V104(R) right_complementable Element of the carrier of R
the ZeroF of R is right_complementable Element of the carrier of R
{(0. R)} is non empty trivial finite 1 -element set
([#] R) \ {(0. R)} is finite Element of bool the carrier of R
the carrier of (center (MultGroup R)) \/ {(0. R)} is non empty finite set
(card the carrier of (center (MultGroup R))) + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
R is non empty non degenerated non trivial finite right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R) is non empty non trivial finite set
card the carrier of (R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(R) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
dim (R) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
MultGroup R is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() multMagma
the carrier of R is non empty non trivial finite set
the carrier of (MultGroup R) is non empty finite set
center (MultGroup R) is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of MultGroup R
the carrier of (center (MultGroup R)) is non empty finite set
card R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
card the carrier of R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
(card the carrier of (R)) |^ (dim (R)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
card (MultGroup R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
card the carrier of (MultGroup R) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
((card the carrier of (R)) |^ (dim (R))) - 1 is V31() V32() integer ext-real set
- 1 is V31() V32() integer ext-real non positive set
(card the carrier of (R)) + (- 1) is V31() V32() integer ext-real set
1 + (- 1) is V31() V32() integer ext-real set
(card the carrier of (R)) - 1 is V31() V32() integer ext-real set
(dim (R)) + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
0 + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
card the carrier of R is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(card the carrier of (R)) #Z (dim (R)) is set
bool the carrier of (MultGroup R) is non empty finite V39() set
((MultGroup R)) is non empty finite V39() V50() a_partition of the carrier of (MultGroup R)
{ (con_class b₁) where b₁ is Element of the carrier of (MultGroup R) : verum } is set
{ b₁ where b₁ is finite Element of bool the carrier of (MultGroup R) : ( b₁ in ((MultGroup R)) & card b₁ = 1 ) } is set
((MultGroup R)) \ { b₁ where b₁ is finite Element of bool the carrier of (MultGroup R) : ( b₁ in ((MultGroup R)) & card b₁ = 1 ) } is finite V39() Element of bool (bool the carrier of (MultGroup R))
bool (bool the carrier of (MultGroup R)) is non empty finite V39() set
f is set
f1 is finite Element of bool the carrier of (MultGroup R)
card f1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
{ b₁ where b₁ is finite Element of bool the carrier of (MultGroup R) : ( b₁ in ((MultGroup R)) & card b₁ = 1 ) } \/ (((MultGroup R)) \ { b₁ where b₁ is finite Element of bool the carrier of (MultGroup R) : ( b₁ in ((MultGroup R)) & card b₁ = 1 ) } ) is set
f is Relation-like Function-like set
dom f is set
f1 is set
f2 is set
f . f1 is set
f . f2 is set
{f1} is non empty trivial finite 1 -element set
{f2} is non empty trivial finite 1 -element set
f1 is set
rng f is set
f2 is set
f . f2 is set
{f2} is non empty trivial finite 1 -element set
p1 is Element of the carrier of (MultGroup R)
con_class p1 is non empty finite Element of bool the carrier of (MultGroup R)
(Omega). (MultGroup R) is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of MultGroup R
the multF of (MultGroup R) is Relation-like [: the carrier of (MultGroup R), the carrier of (MultGroup R):] -defined the carrier of (MultGroup R) -valued Function-like quasi_total finite Element of bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):]
[: the carrier of (MultGroup R), the carrier of (MultGroup R):] is non empty finite set
[:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty finite set
bool [:[: the carrier of (MultGroup R), the carrier of (MultGroup R):], the carrier of (MultGroup R):] is non empty finite V39() set
multMagma(# the carrier of (MultGroup R), the multF of (MultGroup R) #) is non empty strict multMagma
carr ((Omega). (MultGroup R)) is finite Element of bool the carrier of (MultGroup R)
the carrier of ((Omega). (MultGroup R)) is non empty finite set
p1 |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),p1) is non empty trivial finite 1 -element Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),p1) |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of (MultGroup R) : ( b₁ in K462( the carrier of (MultGroup R),p1) & b₂ in carr ((Omega). (MultGroup R)) ) } is set
{p1} is non empty trivial finite 1 -element set
f is finite Element of bool the carrier of (MultGroup R)
card f is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
f2 is finite Element of bool the carrier of (MultGroup R)
card f2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
f is Element of the carrier of (MultGroup R)
con_class f is non empty finite Element of bool the carrier of (MultGroup R)
f |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),f) is non empty trivial finite 1 -element Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),f) |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of (MultGroup R) : ( b₁ in K462( the carrier of (MultGroup R),f) & b₂ in carr ((Omega). (MultGroup R)) ) } is set
p1 is set
{p1} is non empty trivial finite 1 -element set
f . f is set
{f} is non empty trivial finite 1 -element set
card the carrier of (center (MultGroup R)) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
natq1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
card { b₁ where b₁ is finite Element of bool the carrier of (MultGroup R) : ( b₁ in ((MultGroup R)) & card b₁ = 1 ) } is V6() V7() V8() cardinal set
f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng f1 is finite set
f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng f2 is finite set
f1 ^ f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng (f1 ^ f2) is finite set
{ b₁ where b₁ is finite Element of bool the carrier of (MultGroup R) : ( b₁ in ((MultGroup R)) & card b₁ = 1 ) } /\ (((MultGroup R)) \ { b₁ where b₁ is finite Element of bool the carrier of (MultGroup R) : ( b₁ in ((MultGroup R)) & card b₁ = 1 ) } ) is finite V39() Element of bool (bool the carrier of (MultGroup R))
p1 is set
len f1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
p1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len p1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom p1 is finite Element of bool NAT
rng p1 is finite set
c1 is set
p2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
p1 . p2 is set
f1 . p2 is set
card (f1 . p2) is V6() V7() V8() cardinal set
dom f1 is finite Element of bool NAT
c2 is finite Element of bool the carrier of (MultGroup R)
card c2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
c1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len c1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom c1 is finite Element of bool NAT
p2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
c1 . p2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
dom f1 is finite Element of bool NAT
f1 . p2 is set
c2 is finite Element of bool the carrier of (MultGroup R)
card c2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
rng c1 is finite V72() V73() V74() V77() Element of bool REAL
{1} is non empty trivial finite V39() 1 -element set
p2 is set
c2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
c1 . c2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
p2 is set
Seg (len c1) is finite len c1 -element Element of bool NAT
c1 . (len c1) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
(dom c1) --> 1 is Relation-like non-empty dom c1 -defined NAT -valued RAT -valued INT -valued Function-like constant total quasi_total finite V62() V63() V64() V65() Element of bool [:(dom c1),NAT:]
[:(dom c1),NAT:] is set
bool [:(dom c1),NAT:] is non empty set
[:(dom c1),{1}:] is finite set
Seg (len c1) is finite len c1 -element Element of bool NAT
(Seg (len c1)) --> 1 is Relation-like non-empty Seg (len c1) -defined Seg (len c1) -defined NAT -valued RAT -valued INT -valued Function-like constant total total quasi_total finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() Element of bool [:(Seg (len c1)),NAT:]
[:(Seg (len c1)),NAT:] is set
bool [:(Seg (len c1)),NAT:] is non empty set
[:(Seg (len c1)),{1}:] is finite set
(len c1) |-> 1 is Relation-like NAT -defined NAT -valued Function-like finite len c1 -element FinSequence-like FinSubsequence-like V62() V63() V64() V65() Element of (len c1) -tuples_on NAT
(len c1) -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
Sum c1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(len c1) * 1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
len f2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
p2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len p2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom p2 is finite Element of bool NAT
rng p2 is finite set
c2 is set
c is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
p2 . c is set
f2 . c is set
card (f2 . c) is V6() V7() V8() cardinal set
dom f2 is finite Element of bool NAT
c is Element of the carrier of (MultGroup R)
con_class c is non empty finite Element of bool the carrier of (MultGroup R)
c |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),c) is non empty trivial finite 1 -element Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),c) |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of (MultGroup R) : ( b₁ in K462( the carrier of (MultGroup R),c) & b₂ in carr ((Omega). (MultGroup R)) ) } is set
card (con_class c) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
c2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
c1 ^ c2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() M24( REAL , NAT )
c is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V62() V63() V64() V65() FinSequence of NAT
len c is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(len f1) + (len f2) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
len (f1 ^ f2) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom c is finite Element of bool NAT
q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
c . q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
(f1 ^ f2) . q is set
card ((f1 ^ f2) . q) is V6() V7() V8() cardinal set
dom f1 is finite Element of bool NAT
c1 . q is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
f1 . q is set
card (f1 . q) is V6() V7() V8() cardinal set
dom c2 is finite Element of bool NAT
n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
(len c1) + n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
(len c1) + n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom f2 is finite Element of bool NAT
c2 . n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
f2 . n is set
card (f2 . n) is V6() V7() V8() cardinal set
dom c2 is finite Element of bool NAT
Sum c is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
Sum c2 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(Sum c2) + ((card the carrier of (R)) - 1) is V31() V32() integer ext-real set
q is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
n is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
cyclotomic_poly n is Relation-like NAT -defined the carrier of F_Complex -valued Function-like quasi_total V197( F_Complex ) Element of bool [:NAT, the carrier of F_Complex:]
qc is V31() right_complementable Element of the carrier of F_Complex
eval ((cyclotomic_poly n),qc) is V31() right_complementable Element of the carrier of F_Complex
pnq is V31() V32() integer ext-real set
abs pnq is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
q |^ n is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(q |^ n) + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(q |^ n) + (- 1) is V31() V32() integer ext-real set
(q |^ n) - 1 is V31() V32() integer ext-real set
abspnq is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
abs ((q |^ n) - 1) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
qn1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
dom c2 is finite Element of bool NAT
i is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
c2 /. i is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
c2 . i is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
f2 . i is set
card (f2 . i) is V6() V7() V8() cardinal set
dom f2 is finite Element of bool NAT
a is Element of the carrier of (MultGroup R)
con_class a is non empty finite Element of bool the carrier of (MultGroup R)
a |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),a) is non empty trivial finite 1 -element Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),a) |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of (MultGroup R) : ( b₁ in K462( the carrier of (MultGroup R),a) & b₂ in carr ((Omega). (MultGroup R)) ) } is set
a is Element of the carrier of (MultGroup R)
s is right_complementable Element of the carrier of R
(R,s) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over (R)
dim (R,s) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative set
con_class a is non empty finite Element of bool the carrier of (MultGroup R)
a |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),a) is non empty trivial finite 1 -element Element of bool the carrier of (MultGroup R)
K462( the carrier of (MultGroup R),a) |^ (carr ((Omega). (MultGroup R))) is finite Element of bool the carrier of (MultGroup R)
{ (b₁ |^ b₂) where b₁, b₂ is Element of the carrier of (MultGroup R) : ( b₁ in K462( the carrier of (MultGroup R),a) & b₂ in carr ((Omega). (MultGroup R)) ) } is set
card (con_class a) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
((MultGroup R),a) is non empty finite strict unital Group-like associative V190() V191() V192() V193() V194() V195() Subgroup of MultGroup R
card ((MultGroup R),a) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
the carrier of ((MultGroup R),a) is non empty finite set
card the carrier of ((MultGroup R),a) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative set
(card (con_class a)) * (card ((MultGroup R),a)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
((card (con_class a)) * (card ((MultGroup R),a))) + 0 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
(card (MultGroup R)) div (card ((MultGroup R),a)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
qn1 div (card ((MultGroup R),a)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
q |^ (dim (R,s)) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of REAL
(q |^ (dim (R,s))) + 1 is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(q |^ (dim (R,s))) + (- 1) is V31() V32() integer ext-real set
(q |^ (dim (R,s))) - 1 is V31() V32() integer ext-real set
(R,s) is non empty non degenerated non trivial finite right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of (R,s) is non empty non trivial finite set
card the carrier of (R,s) is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
(card the carrier of (R,s)) - 1 is V31() V32() integer ext-real set
qns1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
ns is V6() V7() V8() V12() non empty V31() V32() integer finite cardinal ext-real positive non negative Element of NAT
qn1 div qns1 is V31() V32() integer ext-real set
qn1 div qns1 is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
abs (qn1 div qns1) is V6() V7() V8() V12() V31() V32() integer finite cardinal ext-real non negative Element of NAT
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
(R) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
1. (R) is V104((R)) right_complementable Element of the carrier of (R)
the carrier of (R) is non empty non trivial set
the OneF of (R) is right_complementable Element of the carrier of (R)
1. R is V104(R) right_complementable Element of the carrier of R
the carrier of R is non empty non trivial set
the OneF of R is right_complementable Element of the carrier of R
R is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of R is non empty non trivial set
Z is right_complementable Element of the carrier of R
(R,Z) is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
1. (R,Z) is V104((R,Z)) right_complementable Element of the carrier of (R,Z)
the carrier of (R,Z) is non empty non trivial set
the OneF of (R,Z) is right_complementable Element of the carrier of (R,Z)
1. R is V104(R) right_complementable Element of the carrier of R
the OneF of R is right_complementable Element of the carrier of R