:: TOPREAL2 semantic presentation

REAL is V162() V163() V164() V168() set
NAT is V162() V163() V164() V165() V166() V167() V168() Element of K19(REAL)
K19(REAL) is set
NAT is V162() V163() V164() V165() V166() V167() V168() set
K19(NAT) is set
K208() is non empty strict TopSpace-like TopStruct
the carrier of K208() is non empty set
1 is non empty V27() V28() ext-real positive non negative V110() V114() V115() V162() V163() V164() V165() V166() V167() Element of NAT
K20(1,1) is set
K19(K20(1,1)) is set
K20(K20(1,1),1) is set
K19(K20(K20(1,1),1)) is set
K20(K20(1,1),REAL) is set
K19(K20(K20(1,1),REAL)) is set
K20(REAL,REAL) is set
K20(K20(REAL,REAL),REAL) is set
K19(K20(K20(REAL,REAL),REAL)) is set
2 is non empty V27() V28() ext-real positive non negative V110() V114() V115() V162() V163() V164() V165() V166() V167() Element of NAT
K20(2,2) is set
K20(K20(2,2),REAL) is set
K19(K20(K20(2,2),REAL)) is set
K236() is V95() L7()
K246() is TopSpace-like TopStruct
K19(NAT) is set
COMPLEX is V162() V168() set
RAT is V162() V163() V164() V165() V168() set
INT is V162() V163() V164() V165() V166() V168() set
K19(K20(REAL,REAL)) is set
TOP-REAL 2 is non empty TopSpace-like T_0 T_1 T_2 V128() V174() V175() V176() V177() V178() V179() V180() strict RLTopStruct
the carrier of (TOP-REAL 2) is functional non empty set
K19( the carrier of (TOP-REAL 2)) is set
{} is Function-like functional empty V162() V163() V164() V165() V166() V167() V168() set
0 is Function-like functional empty V27() V28() ext-real non positive non negative V110() V114() V115() V162() V163() V164() V165() V166() V167() V168() Element of NAT
K112(0,1) is V162() V163() V164() Element of K19(REAL)
K247(0,1) is non empty strict TopSpace-like SubSpace of K246()
I[01] is non empty strict TopSpace-like SubSpace of K246()
the carrier of I[01] is non empty set
R^2-unit_square is functional non empty Element of K19( the carrier of (TOP-REAL 2))
|[0,0]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
|[0,1]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,0]|,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
|[1,1]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,1]|,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
|[1,0]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (|[1,1]|,|[1,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,0]|,|[0,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[0,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,1]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[0,0]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = 0 & b<sub>1</sub> `2 <= 1 & 0 <= b₁ `2 ) } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `1 <= 1 & 0 <= b₁ `1 & b<sub>1</sub> `2 = 1 ) } is set
LSeg (|[0,0]|,|[1,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= 1 & 0 <= b<sub>1</sub> `1 & b₁ `2 = 0 ) } is set
LSeg (|[1,0]|,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `1 = 1 & b₁ `2 <= 1 & 0 <= b<sub>1</sub> `2 ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2) : ( ( b₁ `1 = 0 & b<sub>1</sub> `2 <= 1 & 0 <= b₁ `2 ) or ( b<sub>1</sub> `1 <= 1 & 0 <= b₁ `1 & b<sub>1</sub> `2 = 1 ) or ( b₁ `1 <= 1 & 0 <= b<sub>1</sub> `1 & b₁ `2 = 0 ) or ( b<sub>1</sub> `1 = 1 & b₁ `2 <= 1 & 0 <= b<sub>1</sub> `2 ) ) } is set
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{|[0,1]|} is functional non empty set
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{|[1,0]|} is functional non empty set
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{|[0,0]|} is functional non empty set
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{|[1,1]|} is functional non empty set
{|[0,0]|,|[1,1]|} is functional non empty set
p00 is set
p01 is set
{p00} is non empty set
{p00} /\ p01 is set
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
|[0,0]| `1 is V28() ext-real V110() Element of REAL
|[0,0]| `2 is V28() ext-real V110() Element of REAL
|[0,1]| `1 is V28() ext-real V110() Element of REAL
|[0,1]| `2 is V28() ext-real V110() Element of REAL
|[1,0]| `1 is V28() ext-real V110() Element of REAL
|[1,0]| `2 is V28() ext-real V110() Element of REAL
|[1,1]| `1 is V28() ext-real V110() Element of REAL
|[1,1]| `2 is V28() ext-real V110() Element of REAL
P is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
{P,f} is functional non empty set
LSeg (|[0,0]|,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
LSeg (P,|[0,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,1]|,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,P)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (P,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,P)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
R is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
R `1 is V28() ext-real V110() Element of REAL
R `2 is V28() ext-real V110() Element of REAL
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
|[(R `1),(R `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
|[(S `1),(S `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (P,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (P,|[0,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
P `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
|[0,(P `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
the Relation-like Function-like Element of (LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)) is Relation-like Function-like Element of (LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (f,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
(LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
|[0,(f `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,1]|,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) /\ (LSeg (|[1,1]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{} \/ {|[1,1]|} is non empty set
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (|[1,1]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{} \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is set
({} \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,1]|,|[0,1]|))) is set
{} \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,1]|,|[0,1]|))) is set
(LSeg (P,|[0,0]|)) /\ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) \/ (LSeg (f,P)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) \/ (LSeg (f,P))) \/ (LSeg (P,|[0,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) \/ (LSeg (|[0,1]|,f))) \/ (LSeg (P,|[0,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) \/ (LSeg (|[0,1]|,f))) \/ (LSeg (P,|[0,0]|))) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) \/ ((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) \/ ((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,1]|,f))) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) \/ (((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,1]|,f))) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) \/ ((LSeg (P,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((LSeg (P,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (P,|[0,0]|))) \/ ((LSeg (P,f)) /\ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (P,|[0,0]|))) \/ (((LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[1,1]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (P,|[0,0]|))) \/ ((((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,f)))) is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {} is set
(((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {}) \/ ((LSeg (P,f)) /\ (LSeg (|[1,1]|,|[0,1]|))) is set
((((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {}) \/ ((LSeg (P,f)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,f))) is set
{P} \/ (((((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {}) \/ ((LSeg (P,f)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,f)))) is non empty set
(LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f} is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f})) is non empty set
{P} \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
f `1 is V28() ext-real V110() Element of REAL
|[(f `1),(f `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (f,P)) /\ (LSeg (|[0,1]|,P)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
P `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
f `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
|[0,(P `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (f,|[0,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,|[0,0]|)) /\ (LSeg (|[0,1]|,P)) is functional Element of K19( the carrier of (TOP-REAL 2))
the Relation-like Function-like Element of (LSeg (f,|[0,0]|)) /\ (LSeg (|[0,1]|,P)) is Relation-like Function-like Element of (LSeg (f,|[0,0]|)) /\ (LSeg (|[0,1]|,P))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
P `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
f `2 is V28() ext-real V110() Element of REAL
(LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,P)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) /\ (LSeg (f,|[0,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() ext-real V110() Element of REAL
f `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
|[0,(f `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (|[1,1]|,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,P)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,P))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
{} \/ {|[1,1]|} is non empty set
(LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,P)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,P)) /\ (LSeg (|[1,1]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,P)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,1]|,P)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[0,1]|,P)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[0,1]|,P)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,1]|,P)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
{} \/ ((LSeg (|[0,1]|,P)) /\ (LSeg (|[1,0]|,|[1,1]|))) is set
({} \/ ((LSeg (|[0,1]|,P)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,1]|,P)) /\ (LSeg (|[1,1]|,|[0,1]|))) is set
((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,P))) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,|[0,0]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,|[0,0]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[0,1]|,P))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (f,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[0,1]|,P))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (f,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (f,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[0,1]|,P))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {} is set
(((LSeg (f,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {}) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|))) is set
((((LSeg (f,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {}) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,|[0,0]|)) /\ (LSeg (|[0,1]|,P))) is set
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (P,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,P)) \/ (LSeg (P,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,P)) \/ (LSeg (P,f))) \/ (LSeg (f,|[0,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) \/ (LSeg (|[0,1]|,P)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) \/ (LSeg (|[0,1]|,P))) \/ (LSeg (f,|[0,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (f,P)) \/ (LSeg (|[0,1]|,P))) \/ (LSeg (f,|[0,0]|))) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,|[0,0]|)) \/ (LSeg (|[0,1]|,P)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) \/ ((LSeg (f,|[0,0]|)) \/ (LSeg (|[0,1]|,P))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) \/ ((LSeg (f,|[0,0]|)) \/ (LSeg (|[0,1]|,P)))) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,|[0,0]|)) \/ (LSeg (|[0,1]|,P))) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) \/ (((LSeg (f,|[0,0]|)) \/ (LSeg (|[0,1]|,P))) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) /\ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,P))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) /\ (LSeg (f,|[0,0]|))) \/ ((LSeg (f,P)) /\ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,P)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,P))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) /\ (LSeg (f,|[0,0]|))) \/ (((LSeg (f,P)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,P)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (f,P)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,P))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) /\ (LSeg (f,|[0,0]|))) \/ ((((LSeg (f,P)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,P)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,P))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) /\ (LSeg (f,|[0,0]|))) \/ (((((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,P)))) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} \/ (((((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,P)))) is non empty set
((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {} is set
(((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {}) \/ ((LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|))) is set
((((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {}) \/ ((LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,P))) is set
{f} \/ (((((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {}) \/ ((LSeg (f,P)) /\ (LSeg (|[1,1]|,|[0,1]|)))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,P)))) is non empty set
(LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {P} is non empty set
{f} \/ ((((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {P}) is non empty set
((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {P} is non empty set
((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ (((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {P}) is non empty set
{f} \/ (((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ (((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {P})) is non empty set
{f} \/ ((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|))) is non empty set
({f} \/ ((LSeg (f,P)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {P}) is non empty set
{f} \/ (((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {P}) is non empty set
{f} \/ (((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {P}) is non empty set
{f} \/ (((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {P}) is non empty set
{f} \/ (((LSeg (f,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {P}) is non empty set
P `1 is V28() ext-real V110() Element of REAL
|[(P `1),(P `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (P,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,1]|,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) \/ ((LSeg (P,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((LSeg (P,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (P,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,1]|,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) \/ ((LSeg (P,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((LSeg (P,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ (LSeg (P,|[0,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
(LSeg (|[1,1]|,f)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
f `1 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
LSeg (f,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
|[(|[0,1]| `1),(|[0,1]| `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (P,|[0,0]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) \/ ((LSeg (P,|[0,1]|)) \/ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ ((LSeg (|[0,1]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
(LSeg (P,|[0,1]|)) /\ (LSeg (P,|[0,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ (LSeg (P,|[0,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,1]|)) /\ (LSeg (P,|[0,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
({P} \/ (((LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is non empty set
(LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
({P} \/ ((((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is non empty set
(LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is non empty set
(LSeg (|[0,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ (((LSeg (|[0,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
({P} \/ ((((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ (((LSeg (|[0,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f})) is non empty set
(LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ ((((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
({P} \/ ((((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ ((((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f})) is non empty set
((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f} is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f})) is non empty set
(LSeg (P,|[0,1]|)) /\ {f} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f}) is non empty set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
{P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f}) is non empty set
{|[0,1]|} /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f} is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f} is non empty set
(({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f}) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f}) is non empty set
(((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f}) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f}) \/ {f}) is non empty set
{f} \/ {f} is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ ({f} \/ {f}) is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ ({f} \/ {f})) is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[0,0]|))) \/ {f}) is non empty set
{P} /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ {P} is non empty set
({P} \/ {P}) \/ {f} is non empty set
(LSeg (|[0,1]|,f)) /\ {|[0,0]|} is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (LSeg (P,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
(LSeg (|[1,0]|,f)) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
f `1 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
LSeg (f,|[1,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
|[(|[0,0]| `1),(|[0,0]| `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,1]|,P)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) \/ ((LSeg (P,|[0,0]|)) \/ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f)))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ ((((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,f)) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,f)) \/ (LSeg (|[0,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ ((LSeg (|[0,1]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
(LSeg (P,|[0,0]|)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))))) \/ ((LSeg (|[0,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))))) \/ ((LSeg (|[0,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f)))) is non empty set
({P} \/ (((LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))))) \/ ((LSeg (|[0,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))))) is non empty set
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f)))) is non empty set
({P} \/ ((((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))))) \/ ((LSeg (|[0,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))))) is non empty set
(LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,f)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,f)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))))) is non empty set
(LSeg (|[0,0]|,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ (((LSeg (|[0,0]|,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
({P} \/ ((((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ (((LSeg (|[0,0]|,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f})) is non empty set
(LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
({P} \/ ((((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f})) is non empty set
((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f)))) is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f} is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f})) is non empty set
(LSeg (P,|[0,0]|)) /\ {f} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
{|[0,0]|} /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f}) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
(((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) \/ {f}) is non empty set
{f} \/ {f} is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ({f} \/ {f}) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ({f} \/ {f})) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
(LSeg (|[0,0]|,f)) /\ {P} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ {P} is non empty set
({P} \/ {P}) \/ {f} is non empty set
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
S is set
(LSeg (P,|[0,0]|)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
P `2 is V28() ext-real V110() Element of REAL
x is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
x `2 is V28() ext-real V110() Element of REAL
x `1 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
|[(P `1),(P `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
{P} is functional non empty set
LSeg (|[1,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
S is set
f `1 is V28() ext-real V110() Element of REAL
x is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
x `1 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
LSeg (f,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `2 is V28() ext-real V110() Element of REAL
x `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
|[(f `1),(f `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (LSeg (P,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ (LSeg (P,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) \/ (LSeg (P,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,1]|,f)) \/ (LSeg (|[1,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,1]|,f)) \/ (LSeg (|[1,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) \/ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[1,0]|,f)) \/ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,|[0,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is non empty set
(LSeg (|[0,0]|,|[1,0]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[1,0]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[1,0]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is non empty set
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is non empty set
((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
(LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[1,1]|,f)))) is non empty set
((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f} is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f}) is non empty set
(LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f} is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ ((((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f}) is non empty set
((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f} is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
(LSeg (|[0,0]|,|[1,0]|)) /\ {|[1,1]|} is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|)))) \/ {f} is non empty set
{|[1,0]|} /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
(((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ {f}) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ {f}) \/ {f}) is non empty set
{f} \/ {f} is non empty set
((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ({f} \/ {f}) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) \/ ({f} \/ {f})) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|)))) \/ {f} is non empty set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
|[(|[1,1]| `1),(|[1,1]| `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
|[(|[1,0]| `1),(|[1,0]| `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|)))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|)))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (P,|[0,1]|)))) \/ {f} is non empty set
(LSeg (|[0,0]|,|[1,0]|)) /\ {|[0,1]|} is functional Element of K19( the carrier of (TOP-REAL 2))
|[(|[0,1]| `1),(|[0,1]| `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
|[(|[0,0]| `1),(|[0,0]| `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{|[0,0]|} /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
P is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
{P,f} is functional non empty set
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,1]|,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,P)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (P,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (P,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
R is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
R `1 is V28() ext-real V110() Element of REAL
R `2 is V28() ext-real V110() Element of REAL
LSeg (|[0,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ (LSeg (P,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
f `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
|[(|[0,1]| `1),(|[0,1]| `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) \/ ((LSeg (P,|[0,1]|)) \/ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) \/ ((LSeg (|[0,1]|,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,f)) \/ (LSeg (|[0,1]|,f))) \/ ((LSeg (|[0,1]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
(LSeg (P,|[0,1]|)) /\ (LSeg (P,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ (LSeg (P,|[1,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,1]|)) /\ (LSeg (P,|[1,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
({P} \/ (((LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))))) is non empty set
(LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
({P} \/ ((((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))))) is non empty set
(LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,1]|))) \/ ((LSeg (|[0,1]|,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,1]|))) \/ ((LSeg (|[0,1]|,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))))) is non empty set
((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
(LSeg (|[0,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,1]|))) \/ (((LSeg (|[0,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,1]|))) \/ (((LSeg (|[0,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f})) is non empty set
(LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,1]|))) \/ ((((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,1]|))) \/ ((((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f})) is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f} is non empty set
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,1]|))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,1]|))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f})) is non empty set
{P} /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
{P} \/ ({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
({P} \/ ({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
(LSeg (|[0,1]|,f)) /\ {P} is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (P,|[0,1]|)) /\ {|[0,0]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{|[0,1]|} /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} \/ {f} is non empty set
{P} \/ ({f} \/ {f}) is non empty set
|[(R `1),(R `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (P,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
|[(S `1),(S `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (|[1,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (f,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
f `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
|[(f `1),1]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
the Relation-like Function-like Element of (LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f)) is Relation-like Function-like Element of (LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (f,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
(LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
f `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
|[(P `1),1]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) /\ (LSeg (|[1,1]|,f))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ {|[1,1]|} is non empty set
(LSeg (P,|[0,1]|)) /\ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,P)) \/ (LSeg (P,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,P)) \/ (LSeg (P,f))) \/ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,P)) \/ (LSeg (P,f))) \/ (LSeg (f,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,P)) \/ (LSeg (P,f))) \/ (LSeg (f,|[1,1]|))) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,f)) /\ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
{P} \/ (((LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
{P} \/ ((((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
{P} \/ (((((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f} is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f})) is non empty set
{P} \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
LSeg (|[0,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
p1 `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
f `2 is V28() ext-real V110() Element of REAL
|[(f `1),1]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
the Relation-like Function-like Element of (LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)) is Relation-like Function-like Element of (LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
(LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (P,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
p1 `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
f `2 is V28() ext-real V110() Element of REAL
|[(P `1),1]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) /\ (LSeg (|[0,1]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,f)))) \/ {|[0,1]|} is non empty set
(LSeg (P,|[1,1]|)) /\ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) \/ (LSeg (P,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) \/ (LSeg (P,|[1,1]|))) \/ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) \/ ((LSeg (f,P)) \/ (LSeg (P,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) \/ ((LSeg (f,P)) \/ (LSeg (P,|[1,1]|)))) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,f)) /\ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is non empty set
(LSeg (P,f)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
{P} \/ (((LSeg (P,f)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
{P} \/ ((((LSeg (P,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
{P} \/ (((((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f} is non empty set
((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f})) is non empty set
{P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,1]|,|[0,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[0,0]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[0,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,|[1,0]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (LSeg (P,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[1,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
(LSeg (P,|[1,1]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,P)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) \/ ((LSeg (|[1,0]|,f)) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ ((LSeg (|[1,0]|,f)) \/ (LSeg (|[0,0]|,f)))) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ ((LSeg (|[1,0]|,f)) \/ (LSeg (|[0,0]|,f)))) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) \/ (LSeg (|[0,0]|,f))) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) \/ (LSeg (|[0,0]|,f))) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f)))) \/ (LSeg (P,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f)))) \/ (LSeg (P,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f))) \/ (LSeg (P,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f))) \/ (LSeg (P,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f))) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f))) \/ (LSeg (P,|[0,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,0]|,f)))) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f))) \/ (LSeg (P,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) \/ ((LSeg (P,|[0,1]|)) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
((LSeg (P,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is non empty set
(LSeg (|[1,0]|,|[1,1]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,0]|,|[1,1]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
(({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,0]|,|[1,1]|)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is non empty set
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
(({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is non empty set
((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
(LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
(({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
(LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
(({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ ((((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f} is non empty set
(({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
(LSeg (|[1,0]|,|[1,1]|)) /\ {|[0,1]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{|[1,1]|} /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
P `1 is V28() ext-real V110() Element of REAL
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
(LSeg (|[1,0]|,|[1,1]|)) /\ {|[0,0]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{|[1,0]|} /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} \/ {f} is non empty set
{P} \/ ({f} \/ {f}) is non empty set
f `1 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
LSeg (|[1,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (LSeg (P,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
(LSeg (|[1,0]|,f)) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
f `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
|[(|[1,1]| `1),(|[1,1]| `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) \/ ((LSeg (P,|[1,1]|)) \/ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f)))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[1,0]|,f)) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[1,0]|,f)) \/ (LSeg (|[1,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
(LSeg (P,|[1,1]|)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))))) \/ ((LSeg (|[1,1]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))))) \/ ((LSeg (|[1,1]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f)))) is non empty set
({P} \/ (((LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))))) \/ ((LSeg (|[1,1]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))))) is non empty set
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f)))) is non empty set
({P} \/ ((((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))))) \/ ((LSeg (|[1,1]|,f)) /\ ((LSeg (P,|[0,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))))) is non empty set
(LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,1]|,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((LSeg (|[1,1]|,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))))) is non empty set
(LSeg (|[1,1]|,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,1]|,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f} is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ (((LSeg (|[1,1]|,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f}) is non empty set
({P} \/ ((((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ (((LSeg (|[1,1]|,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f})) is non empty set
(LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f} is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f}) is non empty set
({P} \/ ((((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ((((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f})) is non empty set
((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f)))) is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f} is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f})) is non empty set
(LSeg (P,|[1,1]|)) /\ {f} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
{|[1,1]|} /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
(({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
(((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) \/ {f}) is non empty set
{f} \/ {f} is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ({f} \/ {f}) is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ ({f} \/ {f})) is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f} is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[0,1]|))) \/ {f}) is non empty set
(LSeg (|[1,1]|,f)) /\ {P} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ {P} is non empty set
({P} \/ {P}) \/ {f} is non empty set
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
P is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
{P,f} is functional non empty set
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,0]|,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,P)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (P,|[0,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (P,|[1,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
LSeg (|[0,0]|,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,P)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
R is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
R `1 is V28() ext-real V110() Element of REAL
R `2 is V28() ext-real V110() Element of REAL
(LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (LSeg (P,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
f `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
(LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) \/ ((LSeg (P,|[0,0]|)) \/ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f))) \/ (LSeg (|[0,0]|,f))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))))) \/ ((LSeg (|[0,0]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (P,|[0,0]|)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (P,|[0,0]|)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))))) \/ ((LSeg (|[0,0]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[0,0]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) is non empty set
({P} \/ (((LSeg (P,|[0,0]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))))) \/ ((LSeg (|[0,0]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))))) is non empty set
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) is non empty set
({P} \/ ((((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))))) \/ ((LSeg (|[0,0]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))))) is non empty set
((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) is non empty set
(LSeg (|[0,0]|,f)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,f)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ (((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,f)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f))))) is non empty set
(LSeg (|[0,0]|,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[1,0]|))) \/ (((LSeg (|[0,0]|,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[1,0]|))) \/ (((LSeg (|[0,0]|,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f})) is non empty set
(LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((((LSeg (|[0,0]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f})) is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f} is non empty set
((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[1,0]|))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (P,|[1,0]|))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f})) is non empty set
{|[0,0]|} /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
{P} \/ ({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) is non empty set
({P} \/ ({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
(LSeg (|[0,0]|,f)) /\ {|[1,0]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[0,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{|[0,0]|} /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} \/ {f} is non empty set
{P} \/ ({f} \/ {f}) is non empty set
(LSeg (P,|[0,0]|)) /\ {|[0,1]|} is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
LSeg (f,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ ((LSeg (|[0,1]|,f)) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ ((LSeg (|[0,1]|,f)) \/ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) \/ (LSeg (|[1,1]|,f))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (LSeg (P,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) \/ (((LSeg (P,|[0,0]|)) \/ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((LSeg (P,|[1,0]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) \/ ((LSeg (P,|[0,0]|)) \/ ((LSeg (P,|[1,0]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[1,1]|,f))))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) \/ ((LSeg (P,|[0,0]|)) \/ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f)))) \/ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[0,1]|,f)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
(((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
(LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
(((LSeg (P,|[0,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) \/ ((((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
(LSeg (P,|[0,0]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f} is non empty set
(((LSeg (P,|[0,0]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
(LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,|[0,0]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is non empty set
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
(LSeg (|[0,0]|,|[0,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[0,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[0,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
(({P} \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ (((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{|[0,0]|} /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
({P} \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
(LSeg (|[0,0]|,|[0,1]|)) /\ {|[1,0]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
({P} \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
P `1 is V28() ext-real V110() Element of REAL
{P} \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
({P} \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
({P} \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
({P} \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{|[0,1]|} /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} \/ {f} is non empty set
{P} \/ ({f} \/ {f}) is non empty set
(LSeg (|[0,0]|,|[0,1]|)) /\ {|[1,1]|} is functional Element of K19( the carrier of (TOP-REAL 2))
f `1 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
|[(R `1),(R `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (P,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
|[(S `1),(S `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
P `1 is V28() ext-real V110() Element of REAL
LSeg (|[1,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[1,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `1 is V28() ext-real V110() Element of REAL
(LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (P,|[0,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
|[(P `1),0]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
p2 is set
P1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
P1 `1 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
P1 `2 is V28() ext-real V110() Element of REAL
|[(f `1),0]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
the Relation-like Function-like Element of (LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f)) is Relation-like Function-like Element of (LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))
P1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
P1 `1 is V28() ext-real V110() Element of REAL
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f)))) \/ {|[1,0]|} is non empty set
(LSeg (P,|[0,0]|)) /\ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,P)) \/ (LSeg (P,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,P)) \/ (LSeg (P,f))) \/ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,P)) \/ (LSeg (P,f))) \/ (LSeg (f,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,P)) \/ (LSeg (P,f))) \/ (LSeg (f,|[1,0]|))) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (P,|[0,0]|))) \/ ((LSeg (P,f)) /\ ((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[1,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
{P} \/ (((LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
{P} \/ ((((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
{P} \/ (((((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f}) is non empty set
((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f} is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f})) is non empty set
{P} \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ {f}) is non empty set
LSeg (|[0,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
|[(f `1),0]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (P,|[1,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
f `1 is V28() ext-real V110() Element of REAL
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
P `1 is V28() ext-real V110() Element of REAL
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
|[(P `1),0]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
the Relation-like Function-like Element of (LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)) is Relation-like Function-like Element of (LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
(((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (LSeg (|[0,0]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ {|[0,0]|} is non empty set
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (f,P)) \/ (LSeg (P,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (f,P)) \/ (LSeg (P,|[1,0]|))) \/ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) \/ ((LSeg (f,P)) \/ (LSeg (P,|[1,0]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,f)) \/ ((LSeg (f,P)) \/ (LSeg (P,|[1,0]|)))) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,f)) /\ ((((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is non empty set
(LSeg (P,f)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
{P} \/ (((LSeg (P,f)) /\ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
{P} \/ ((((LSeg (P,f)) /\ ((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
{P} \/ (((((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f} is non empty set
((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f})) is non empty set
{P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|))) is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[1,0]|,|[1,1]|)))) \/ {f} is non empty set
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
P `1 is V28() ext-real V110() Element of REAL
f `2 is V28() ext-real V110() Element of REAL
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
LSeg (f,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
LSeg (|[1,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ (LSeg (P,|[0,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[1,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (P,|[0,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
(LSeg (|[1,1]|,f)) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[0,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) \/ ((LSeg (P,|[1,0]|)) \/ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,1]|,f))) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (LSeg (P,|[0,0]|))) \/ ((LSeg (P,|[1,0]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,0]|)) /\ (LSeg (P,|[0,0]|))) \/ ((LSeg (P,|[1,0]|)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
({P} \/ (((LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is non empty set
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,0]|,P)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,0]|,P)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,0]|,P)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
({P} \/ ((((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,0]|,P)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[0,0]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is non empty set
((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
(LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,0]|))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ (((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,0]|))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))))) is non empty set
(LSeg (|[1,0]|,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,0]|))) \/ (((LSeg (|[1,0]|,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,0]|))) \/ (((LSeg (|[1,0]|,f)) /\ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f})) is non empty set
(LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f} is non empty set
((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,0]|))) \/ ((((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,0]|))) \/ ((((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f})) is non empty set
((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f} is non empty set
((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,0]|))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[0,0]|))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f})) is non empty set
(LSeg (|[1,0]|,f)) /\ {|[0,0]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{|[1,0]|} /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
{P} \/ ({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) is non empty set
({P} \/ ({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{|[1,0]|} /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} \/ {f} is non empty set
{P} \/ ({f} \/ {f}) is non empty set
(LSeg (P,|[1,0]|)) /\ {|[1,1]|} is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
{P,f} is functional non empty set
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (P,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (P,|[1,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,0]|,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,P)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
R is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
R `1 is V28() ext-real V110() Element of REAL
R `2 is V28() ext-real V110() Element of REAL
LSeg (|[0,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[0,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[0,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (LSeg (P,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,f)) \/ (LSeg (|[0,1]|,f))) \/ (LSeg (|[0,1]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,f)) \/ (LSeg (|[0,1]|,f))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) \/ (LSeg (|[0,1]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,f)) \/ ((LSeg (|[0,1]|,f)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,f)) \/ ((LSeg (|[0,1]|,f)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f))) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f))) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ ((LSeg (P,|[1,0]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f))) \/ ((LSeg (P,|[1,1]|)) \/ ((LSeg (P,|[1,0]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,f))))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f))) \/ ((LSeg (P,|[1,1]|)) \/ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) \/ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,1]|,f)))) \/ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
((LSeg (P,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) \/ ((LSeg (|[0,1]|,f)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f} is non empty set
(((LSeg (P,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f}) is non empty set
(LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f} is non empty set
(((LSeg (P,|[1,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) \/ ((((LSeg (|[0,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f}) is non empty set
(LSeg (P,|[1,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f} is non empty set
(((LSeg (P,|[1,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
(LSeg (|[0,1]|,|[1,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,|[1,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,|[1,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) \/ ((((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) /\ (((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[0,0]|,f)))) \/ ((((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
(LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
(({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
(LSeg (|[0,1]|,|[1,1]|)) /\ {|[1,0]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{|[1,1]|} /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
P `2 is V28() ext-real V110() Element of REAL
{P} \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[0,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
(LSeg (|[0,1]|,|[1,1]|)) /\ {|[0,0]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{|[0,1]|} /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} \/ {f} is non empty set
{P} \/ ({f} \/ {f}) is non empty set
f `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
f `1 is V28() ext-real V110() Element of REAL
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
LSeg (|[0,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (LSeg (P,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
(LSeg (P,|[1,1]|)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[0,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
(LSeg (|[1,1]|,f)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,f)) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[1,0]|,P)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) \/ ((LSeg (P,|[1,1]|)) \/ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) \/ (((LSeg (|[1,0]|,|[1,1]|)) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,f))) \/ (LSeg (|[1,1]|,f))) \/ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))))) \/ ((LSeg (|[1,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))))) \/ ((LSeg (|[1,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) is non empty set
({P} \/ (((LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))))) \/ ((LSeg (|[1,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))))) is non empty set
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) is non empty set
({P} \/ ((((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))))) \/ ((LSeg (|[1,1]|,f)) /\ ((LSeg (P,|[1,0]|)) \/ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))))) is non empty set
((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) is non empty set
(LSeg (|[1,1]|,f)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,1]|,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[1,1]|,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ (((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((LSeg (|[1,1]|,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,f))))) is non empty set
(LSeg (|[1,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ (((LSeg (|[1,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ (((LSeg (|[1,1]|,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f})) is non empty set
(LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ ((((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f})) is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f} is non empty set
((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f})) is non empty set
(LSeg (|[1,1]|,f)) /\ {|[1,0]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (P,|[1,0]|))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f})) is non empty set
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{|[1,1]|} /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
{P} \/ ({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) is non empty set
({P} \/ ({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,f)))) \/ (((LSeg (|[1,1]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
(LSeg (P,|[1,1]|)) /\ {|[0,1]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{|[1,1]|} /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} \/ {f} is non empty set
{P} \/ ({f} \/ {f}) is non empty set
LSeg (f,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
f `1 is V28() ext-real V110() Element of REAL
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
LSeg (|[0,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
(LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
LSeg (|[1,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ (LSeg (P,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[1,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (P,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
(LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
LSeg (f,|[0,0]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
(LSeg (|[0,0]|,f)) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) \/ ((LSeg (P,|[1,0]|)) \/ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) \/ ((LSeg (|[1,0]|,|[1,1]|)) \/ (((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,f))) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (LSeg (P,|[1,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,0]|)) /\ (LSeg (P,|[1,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
({P} \/ (((LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))))) is non empty set
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,P)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,P)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,P)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
({P} \/ ((((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,P)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))))) \/ ((LSeg (|[1,0]|,f)) /\ ((LSeg (P,|[1,1]|)) \/ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))))) is non empty set
((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
(LSeg (|[1,0]|,f)) /\ (LSeg (P,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[1,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f)))) is functional Element of K19( the carrier of (TOP-REAL 2))
({P} \/ (((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[1,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,f))))) is non empty set
(LSeg (|[1,0]|,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[1,1]|))) \/ (((LSeg (|[1,0]|,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[1,1]|))) \/ (((LSeg (|[1,0]|,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f})) is non empty set
(LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f} is non empty set
((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[1,1]|))) \/ ((((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[1,1]|))) \/ ((((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ {f})) is non empty set
((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f} is non empty set
((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[1,1]|))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
({P} \/ (((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (P,|[1,1]|))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f})) is non empty set
{|[1,0]|} /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
{P} \/ ({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) is non empty set
({P} \/ ({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
(LSeg (|[1,0]|,f)) /\ {|[1,1]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ {P} is non empty set
({P} \/ {P}) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
(({P} \/ {P}) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
{P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f))) is non empty set
({P} \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,f)))) \/ (((LSeg (|[1,0]|,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) \/ {f}) is non empty set
(LSeg (P,|[1,0]|)) /\ {|[0,0]|} is functional Element of K19( the carrier of (TOP-REAL 2))
{|[1,0]|} /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} \/ {f} is non empty set
{P} \/ ({f} \/ {f}) is non empty set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
|[(R `1),(R `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (P,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S `1 is V28() ext-real V110() Element of REAL
S `2 is V28() ext-real V110() Element of REAL
|[(S `1),(S `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (|[1,1]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (f,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
f `1 is V28() ext-real V110() Element of REAL
|[1,(f `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
the Relation-like Function-like Element of (LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f)) is Relation-like Function-like Element of (LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
LSeg (f,|[1,1]|) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (P,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
f `1 is V28() ext-real V110() Element of REAL
|[1,(P `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (LSeg (|[1,1]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (LSeg (|[1,1]|,f))) \/ ((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,1]|,f)))) \/ {|[1,1]|} is non empty set
(LSeg (P,|[1,0]|)) /\ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,|[1,0]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,0]|)) \/ (LSeg (P,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) \/ ((LSeg (P,|[1,0]|)) \/ (LSeg (P,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,P)) \/ (LSeg (P,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[1,0]|,P)) \/ (LSeg (P,f))) \/ (LSeg (f,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (((LSeg (|[1,0]|,P)) \/ (LSeg (P,f))) \/ (LSeg (f,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[1,0]|)) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) \/ ((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,f)) /\ ((((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[1,1]|,f)))) is non empty set
(LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f} is non empty set
{P} \/ (((LSeg (P,f)) /\ (((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f} is non empty set
{P} \/ ((((LSeg (P,f)) /\ ((LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f} is non empty set
{P} \/ (((((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ {f}) is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f} is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f})) is non empty set
{P} \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ {f}) is non empty set
LSeg (|[1,0]|,f) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
{f} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
|[1,(f `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
the Relation-like Function-like Element of (LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f)) is Relation-like Function-like Element of (LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f `2 is V28() ext-real V110() Element of REAL
p1 `2 is V28() ext-real V110() Element of REAL
P `2 is V28() ext-real V110() Element of REAL
(LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (P,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} is functional non empty set
x is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() ext-real V110() Element of REAL
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
f `1 is V28() ext-real V110() Element of REAL
p1 `1 is V28() ext-real V110() Element of REAL
P `1 is V28() ext-real V110() Element of REAL
|[1,(P `2)]| is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
(LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ ((((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (LSeg (|[1,0]|,f)) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) /\ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[0,0]|,|[1,0]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) \/ ((LSeg (|[0,0]|,|[0,1]|)) /\ (LSeg (|[1,0]|,f)))) \/ {|[1,0]|} is non empty set
(LSeg (P,|[1,1]|)) /\ ((((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,|[1,1]|)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,|[1,1]|)) \/ (LSeg (P,f)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) \/ ((LSeg (P,|[1,1]|)) \/ (LSeg (P,f))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) \/ (LSeg (P,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(LSeg (|[1,0]|,f)) \/ ((LSeg (P,f)) \/ (LSeg (P,|[1,1]|))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ ((LSeg (|[1,0]|,f)) \/ ((LSeg (P,f)) \/ (LSeg (P,|[1,1]|)))) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ ((((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f))) is functional Element of K19( the carrier of (TOP-REAL 2))
{P} \/ ((LSeg (P,f)) /\ ((((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) \/ (LSeg (|[1,0]|,f)))) is non empty set
(LSeg (P,f)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f} is non empty set
{P} \/ (((LSeg (P,f)) /\ (((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) \/ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f} is non empty set
{P} \/ ((((LSeg (P,f)) /\ ((LSeg (|[0,1]|,|[1,1]|)) \/ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f}) is non empty set
(LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)) is functional Element of K19( the carrier of (TOP-REAL 2))
((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
(((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) is functional Element of K19( the carrier of (TOP-REAL 2))
((((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f} is non empty set
{P} \/ (((((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[0,1]|)))) \/ ((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|)))) \/ {f}) is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f} is non empty set
((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f})) is non empty set
{P} \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|))) is non empty set
({P} \/ ((LSeg (P,f)) /\ (LSeg (|[0,1]|,|[1,1]|)))) \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
{P} \/ (((LSeg (P,f)) /\ (LSeg (|[0,0]|,|[1,0]|))) \/ {f}) is non empty set
LSeg (f,P) is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty V210( TOP-REAL 2) Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
P is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
{P,f} is functional non empty set
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is functional non empty Element of K19( the carrier of (TOP-REAL 2))
P is functional non empty Element of K19( the carrier of (TOP-REAL 2))
f is functional non empty Element of K19( the carrier of (TOP-REAL 2))
P \/ f is functional non empty Element of K19( the carrier of (TOP-REAL 2))
P /\ f is functional Element of K19( the carrier of (TOP-REAL 2))
P is functional non empty Element of K19( the carrier of (TOP-REAL 2))
f is functional non empty Element of K19( the carrier of (TOP-REAL 2))
P \/ f is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | P is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | P) is non empty set
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | P)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | P))) is set
R is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | P) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | P)))
rng R is Element of K19( the carrier of ((TOP-REAL 2) | P))
K19( the carrier of ((TOP-REAL 2) | P)) is set
[#] ((TOP-REAL 2) | P) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | P))
(TOP-REAL 2) | f is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is non empty set
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | f)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | f))) is set
S is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | f) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | f)))
rng S is Element of K19( the carrier of ((TOP-REAL 2) | f))
K19( the carrier of ((TOP-REAL 2) | f)) is set
[#] ((TOP-REAL 2) | f) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | f))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | x is non empty strict TopSpace-like SubSpace of TOP-REAL 2
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p1 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
P is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
R is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | R is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | R) is non empty set
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | S is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | S) is non empty set
K20( the carrier of ((TOP-REAL 2) | R), the carrier of ((TOP-REAL 2) | S)) is set
K19(K20( the carrier of ((TOP-REAL 2) | R), the carrier of ((TOP-REAL 2) | S))) is set
x is Relation-like the carrier of ((TOP-REAL 2) | R) -defined the carrier of ((TOP-REAL 2) | S) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R), the carrier of ((TOP-REAL 2) | S)))
x . P is set
x . f is set
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | R)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | R))) is set
P2 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | R) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | R)))
P2 . 0 is set
P2 . 1 is set
P1 is Relation-like the carrier of ((TOP-REAL 2) | R) -defined the carrier of ((TOP-REAL 2) | S) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R), the carrier of ((TOP-REAL 2) | S)))
P1 * P2 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | S) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | S)))
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | S)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | S))) is set
dom P2 is Element of K19( the carrier of I[01])
K19( the carrier of I[01]) is set
(P1 * P2) . 0 is set
(P1 * P2) . 1 is set
(TOP-REAL 2) | R^2-unit_square is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | R^2-unit_square) is non empty set
K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | R^2-unit_square)) is set
K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | R^2-unit_square))) is set
id ((TOP-REAL 2) | R^2-unit_square) is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | R^2-unit_square) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | R^2-unit_square)))
id the carrier of ((TOP-REAL 2) | R^2-unit_square) is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | R^2-unit_square) -valued Function-like one-to-one non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | R^2-unit_square)))
f is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | R^2-unit_square) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | R^2-unit_square)))
dom f is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
K19( the carrier of ((TOP-REAL 2) | R^2-unit_square)) is set
[#] ((TOP-REAL 2) | R^2-unit_square) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
rng f is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
f " is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | R^2-unit_square) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | R^2-unit_square)))
f " is Relation-like Function-like set
R is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
f " R is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
f is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | f) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | f))
the carrier of ((TOP-REAL 2) | f) is non empty set
K19( the carrier of ((TOP-REAL 2) | f)) is set
[#] (TOP-REAL 2) is functional non empty non proper closed Element of K19( the carrier of (TOP-REAL 2))
K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | f)) is set
K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | f))) is set
R is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | f) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | f)))
rng R is Element of K19( the carrier of ((TOP-REAL 2) | f))
P is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | P is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | P) is non empty set
K20( the carrier of ((TOP-REAL 2) | P), the carrier of ((TOP-REAL 2) | f)) is set
K19(K20( the carrier of ((TOP-REAL 2) | P), the carrier of ((TOP-REAL 2) | f))) is set
S is Relation-like the carrier of ((TOP-REAL 2) | P) -defined the carrier of ((TOP-REAL 2) | f) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | P), the carrier of ((TOP-REAL 2) | f)))
dom S is Element of K19( the carrier of ((TOP-REAL 2) | P))
K19( the carrier of ((TOP-REAL 2) | P)) is set
[#] ((TOP-REAL 2) | P) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | P))
S . |[0,0]| is set
S . |[1,1]| is set
rng S is Element of K19( the carrier of ((TOP-REAL 2) | f))
p2 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
P1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
{P,f} is functional non empty set
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x \/ p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | x is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | x) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | x))
the carrier of ((TOP-REAL 2) | x) is non empty set
K19( the carrier of ((TOP-REAL 2) | x)) is set
q2 is Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like FinSequence-like FinSequence of the carrier of (TOP-REAL 2)
Q1 is Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like FinSequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ q2 is functional Element of K19( the carrier of (TOP-REAL 2))
L~ Q1 is functional Element of K19( the carrier of (TOP-REAL 2))
(L~ q2) \/ (L~ Q1) is functional Element of K19( the carrier of (TOP-REAL 2))
(L~ q2) /\ (L~ Q1) is functional Element of K19( the carrier of (TOP-REAL 2))
q2 /. 1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
len q2 is V27() V28() ext-real V110() V114() V115() V162() V163() V164() V165() V166() V167() Element of NAT
q2 /. (len q2) is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
Q1 /. 1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
len Q1 is V27() V28() ext-real V110() V114() V115() V162() V163() V164() V165() V166() V167() Element of NAT
Q1 /. (len Q1) is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
q2 is Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like FinSequence-like FinSequence of the carrier of (TOP-REAL 2)
Q1 is Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like FinSequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ q2 is functional Element of K19( the carrier of (TOP-REAL 2))
L~ Q1 is functional Element of K19( the carrier of (TOP-REAL 2))
(L~ q2) \/ (L~ Q1) is functional Element of K19( the carrier of (TOP-REAL 2))
(L~ q2) /\ (L~ Q1) is functional Element of K19( the carrier of (TOP-REAL 2))
q2 /. 1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
len q2 is V27() V28() ext-real V110() V114() V115() V162() V163() V164() V165() V166() V167() Element of NAT
q2 /. (len q2) is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
Q1 /. 1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
len Q1 is V27() V28() ext-real V110() V114() V115() V162() V163() V164() V165() V166() V167() Element of NAT
Q1 /. (len Q1) is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
Q2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | Q2 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
P1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | P1 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
R is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | R is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | R) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | R))
the carrier of ((TOP-REAL 2) | R) is non empty set
K19( the carrier of ((TOP-REAL 2) | R)) is set
[#] ((TOP-REAL 2) | P1) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | P1))
the carrier of ((TOP-REAL 2) | P1) is non empty set
K19( the carrier of ((TOP-REAL 2) | P1)) is set
[#] ((TOP-REAL 2) | Q2) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | Q2))
the carrier of ((TOP-REAL 2) | Q2) is non empty set
K19( the carrier of ((TOP-REAL 2) | Q2)) is set
(TOP-REAL 2) | S is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | S) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | S))
the carrier of ((TOP-REAL 2) | S) is non empty set
K19( the carrier of ((TOP-REAL 2) | S)) is set
(TOP-REAL 2) | p1 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | p1) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p1))
the carrier of ((TOP-REAL 2) | p1) is non empty set
K19( the carrier of ((TOP-REAL 2) | p1)) is set
P2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | P2 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
p2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | p1))) is set
F1 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | p1)))
F1 . 0 is set
F1 . 1 is set
dom F1 is Element of K19( the carrier of I[01])
K19( the carrier of I[01]) is set
rng F1 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
the carrier of ((TOP-REAL 2) | p2) is non empty set
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | p2)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | p2))) is set
Q19 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | p2)))
dom Q19 is Element of K19( the carrier of I[01])
P1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | P1 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | x)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | x))) is set
Q29 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | x) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | x)))
Q29 . 0 is set
Q29 . 1 is set
dom Q29 is Element of K19( the carrier of I[01])
rng Q29 is Element of K19( the carrier of ((TOP-REAL 2) | x))
ff is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | p2)))
F2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | F2 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | F2) is non empty set
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | F2)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | F2))) is set
S1 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | F2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | F2)))
S1 . 0 is set
S1 . 1 is set
ff is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | ff is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | ff) is non empty set
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | ff)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | ff))) is set
S2 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | ff) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | ff)))
S2 . 0 is set
S2 . 1 is set
S1 " is Relation-like the carrier of ((TOP-REAL 2) | F2) -defined the carrier of I[01] -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | F2), the carrier of I[01]))
K20( the carrier of ((TOP-REAL 2) | F2), the carrier of I[01]) is set
K19(K20( the carrier of ((TOP-REAL 2) | F2), the carrier of I[01])) is set
ff * (S1 ") is Relation-like the carrier of ((TOP-REAL 2) | F2) -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | F2), the carrier of ((TOP-REAL 2) | p2)))
K20( the carrier of ((TOP-REAL 2) | F2), the carrier of ((TOP-REAL 2) | p2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | F2), the carrier of ((TOP-REAL 2) | p2))) is set
S2 " is Relation-like the carrier of ((TOP-REAL 2) | ff) -defined the carrier of I[01] -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | ff), the carrier of I[01]))
K20( the carrier of ((TOP-REAL 2) | ff), the carrier of I[01]) is set
K19(K20( the carrier of ((TOP-REAL 2) | ff), the carrier of I[01])) is set
Q19 * (S2 ") is Relation-like the carrier of ((TOP-REAL 2) | ff) -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | ff), the carrier of ((TOP-REAL 2) | p2)))
K20( the carrier of ((TOP-REAL 2) | ff), the carrier of ((TOP-REAL 2) | p2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | ff), the carrier of ((TOP-REAL 2) | p2))) is set
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | Q2)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | Q2))) is set
g1 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | Q2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | Q2)))
dom g1 is Element of K19( the carrier of I[01])
rng g1 is Element of K19( the carrier of ((TOP-REAL 2) | Q2))
g1 " is Relation-like the carrier of ((TOP-REAL 2) | Q2) -defined the carrier of I[01] -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | Q2), the carrier of I[01]))
K20( the carrier of ((TOP-REAL 2) | Q2), the carrier of I[01]) is set
K19(K20( the carrier of ((TOP-REAL 2) | Q2), the carrier of I[01])) is set
g1 " is Relation-like Function-like set
rng (g1 ") is Element of K19( the carrier of I[01])
rng (ff * (S1 ")) is Element of K19( the carrier of ((TOP-REAL 2) | p2))
K19( the carrier of ((TOP-REAL 2) | p2)) is set
p00 is Element of the carrier of ((TOP-REAL 2) | R)
(g1 ") . p00 is set
dom (g1 ") is Element of K19( the carrier of ((TOP-REAL 2) | Q2))
p11 is Element of the carrier of ((TOP-REAL 2) | R)
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | P1)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | P1))) is set
g2 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | P1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | P1)))
rng g2 is Element of K19( the carrier of ((TOP-REAL 2) | P1))
g2 " is Relation-like the carrier of ((TOP-REAL 2) | P1) -defined the carrier of I[01] -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | P1), the carrier of I[01]))
K20( the carrier of ((TOP-REAL 2) | P1), the carrier of I[01]) is set
K19(K20( the carrier of ((TOP-REAL 2) | P1), the carrier of I[01])) is set
g2 " is Relation-like Function-like set
dom g2 is Element of K19( the carrier of I[01])
dom (g2 ") is Element of K19( the carrier of ((TOP-REAL 2) | P1))
(g2 ") . p00 is set
Q19 * (g2 ") is Relation-like the carrier of ((TOP-REAL 2) | P1) -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | P1), the carrier of ((TOP-REAL 2) | p2)))
K20( the carrier of ((TOP-REAL 2) | P1), the carrier of ((TOP-REAL 2) | p2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | P1), the carrier of ((TOP-REAL 2) | p2))) is set
dom (Q19 * (g2 ")) is Element of K19( the carrier of ((TOP-REAL 2) | P1))
dom ff is Element of K19( the carrier of I[01])
ff * (g1 ") is Relation-like the carrier of ((TOP-REAL 2) | Q2) -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | Q2), the carrier of ((TOP-REAL 2) | p2)))
K20( the carrier of ((TOP-REAL 2) | Q2), the carrier of ((TOP-REAL 2) | p2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | Q2), the carrier of ((TOP-REAL 2) | p2))) is set
dom (ff * (g1 ")) is Element of K19( the carrier of ((TOP-REAL 2) | Q2))
(ff * (S1 ")) . p00 is set
ff . ((g1 ") . p00) is set
Q19 . ((g2 ") . p00) is set
(Q19 * (S2 ")) . p00 is set
(g2 ") . p11 is set
(g1 ") . p11 is set
(ff * (S1 ")) . p11 is set
ff . ((g1 ") . p11) is set
Q19 . ((g2 ") . p11) is set
(Q19 * (S2 ")) . p11 is set
K20( the carrier of ((TOP-REAL 2) | R), the carrier of ((TOP-REAL 2) | S)) is set
K19(K20( the carrier of ((TOP-REAL 2) | R), the carrier of ((TOP-REAL 2) | S))) is set
(ff * (S1 ")) +* (Q19 * (S2 ")) is Relation-like Function-like set
rng (g2 ") is Element of K19( the carrier of I[01])
rng (Q19 * (S2 ")) is Element of K19( the carrier of ((TOP-REAL 2) | p2))
h is set
dom (Q19 * (S2 ")) is Element of K19( the carrier of ((TOP-REAL 2) | ff))
K19( the carrier of ((TOP-REAL 2) | ff)) is set
c₄₂ is set
dom (ff * (S1 ")) is Element of K19( the carrier of ((TOP-REAL 2) | F2))
K19( the carrier of ((TOP-REAL 2) | F2)) is set
(dom (ff * (S1 "))) \ (dom (Q19 * (S2 "))) is Element of K19( the carrier of ((TOP-REAL 2) | F2))
(Q19 * (S2 ")) . h is set
(ff * (S1 ")) . c₄₂ is set
(g1 ") . c₄₂ is set
ff . ((g1 ") . c₄₂) is set
(g2 ") . h is set
Q19 . ((g2 ") . h) is set
(g1 ") . c₄₂ is set
ff . ((g1 ") . c₄₂) is set
(g2 ") . h is set
Q19 . ((g2 ") . h) is set
h is Relation-like the carrier of ((TOP-REAL 2) | R) -defined the carrier of ((TOP-REAL 2) | S) -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | R), the carrier of ((TOP-REAL 2) | S)))
(dom (ff * (S1 "))) /\ (dom (Q19 * (S2 "))) is Element of K19( the carrier of ((TOP-REAL 2) | ff))
(ff * (S1 ")) .: ((dom (ff * (S1 "))) /\ (dom (Q19 * (S2 ")))) is Element of K19( the carrier of ((TOP-REAL 2) | p2))
h is set
c₄₂ is set
(ff * (S1 ")) . c₄₂ is set
rng h is Element of K19( the carrier of ((TOP-REAL 2) | S))
[#] ((TOP-REAL 2) | p2) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p2))
dom h is Element of K19( the carrier of ((TOP-REAL 2) | R))
K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | S)) is set
K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | S))) is set
h is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | S) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | S)))
P is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | P is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | P) is non empty set
K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | P)) is set
K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | P))) is set
f is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | P) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | P)))
dom f is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
K19( the carrier of ((TOP-REAL 2) | R^2-unit_square)) is set
[#] ((TOP-REAL 2) | R^2-unit_square) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
[#] ((TOP-REAL 2) | P) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | P))
K19( the carrier of ((TOP-REAL 2) | P)) is set
[#] (TOP-REAL 2) is functional non empty non proper closed Element of K19( the carrier of (TOP-REAL 2))
S is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
x is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
{S,x} is functional non empty set
f " is Relation-like the carrier of ((TOP-REAL 2) | P) -defined the carrier of ((TOP-REAL 2) | R^2-unit_square) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | P), the carrier of ((TOP-REAL 2) | R^2-unit_square)))
K20( the carrier of ((TOP-REAL 2) | P), the carrier of ((TOP-REAL 2) | R^2-unit_square)) is set
K19(K20( the carrier of ((TOP-REAL 2) | P), the carrier of ((TOP-REAL 2) | R^2-unit_square))) is set
(f ") . S is set
(f ") . x is set
rng f is Element of K19( the carrier of ((TOP-REAL 2) | P))
f " is Relation-like Function-like set
rng (f ") is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
dom (f ") is Element of K19( the carrier of ((TOP-REAL 2) | P))
P1 is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | P) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | P)))
P1 " is Relation-like the carrier of ((TOP-REAL 2) | P) -defined the carrier of ((TOP-REAL 2) | R^2-unit_square) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | P), the carrier of ((TOP-REAL 2) | R^2-unit_square)))
rng (P1 ") is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
P2 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
q2 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
dom P1 is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
P1 . P2 is set
{P2,q2} is functional non empty set
Q1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
Q2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
Q1 \/ Q2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
Q1 /\ Q2 is functional Element of K19( the carrier of (TOP-REAL 2))
P1 .: Q1 is Element of K19( the carrier of ((TOP-REAL 2) | P))
P1 .: Q2 is Element of K19( the carrier of ((TOP-REAL 2) | P))
P1 | Q1 is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | P) -valued Function-like Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | P)))
rng (P1 | Q1) is Element of K19( the carrier of ((TOP-REAL 2) | P))
P1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | P1 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | P1) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | P1))
the carrier of ((TOP-REAL 2) | P1) is non empty set
K19( the carrier of ((TOP-REAL 2) | P1)) is set
dom (P1 | Q1) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
R^2-unit_square /\ Q1 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | Q1 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | Q1) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | Q1))
the carrier of ((TOP-REAL 2) | Q1) is non empty set
K19( the carrier of ((TOP-REAL 2) | Q1)) is set
K20( the carrier of ((TOP-REAL 2) | Q1), the carrier of ((TOP-REAL 2) | P1)) is set
K19(K20( the carrier of ((TOP-REAL 2) | Q1), the carrier of ((TOP-REAL 2) | P1))) is set
P1 " P1 is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
F1 is Relation-like the carrier of ((TOP-REAL 2) | Q1) -defined the carrier of ((TOP-REAL 2) | P1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | Q1), the carrier of ((TOP-REAL 2) | P1)))
Q19 is Element of K19( the carrier of ((TOP-REAL 2) | P1))
F1 " Q19 is Element of K19( the carrier of ((TOP-REAL 2) | Q1))
Q29 is functional Element of K19( the carrier of (TOP-REAL 2))
Q29 /\ ([#] ((TOP-REAL 2) | P1)) is Element of K19( the carrier of ((TOP-REAL 2) | P1))
rng P1 is Element of K19( the carrier of ((TOP-REAL 2) | P))
Q29 /\ (rng P1) is Element of K19( the carrier of ((TOP-REAL 2) | P))
(rng P1) /\ Q29 is functional Element of K19( the carrier of (TOP-REAL 2))
ff is Element of K19( the carrier of ((TOP-REAL 2) | P))
P1 " ff is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
P1 " Q19 is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
Q1 /\ (P1 " Q19) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
P1 " Q29 is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
P1 " ([#] ((TOP-REAL 2) | P1)) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
(P1 " Q29) /\ (P1 " ([#] ((TOP-REAL 2) | P1))) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
Q1 /\ ((P1 " Q29) /\ (P1 " ([#] ((TOP-REAL 2) | P1)))) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
(P1 " Q29) /\ Q1 is functional Element of K19( the carrier of (TOP-REAL 2))
((P1 " Q29) /\ Q1) /\ Q1 is functional Element of K19( the carrier of (TOP-REAL 2))
Q1 /\ Q1 is functional Element of K19( the carrier of (TOP-REAL 2))
(P1 " Q29) /\ (Q1 /\ Q1) is functional Element of K19( the carrier of (TOP-REAL 2))
(P1 " Q29) /\ ([#] ((TOP-REAL 2) | Q1)) is Element of K19( the carrier of ((TOP-REAL 2) | Q1))
P1 " ((rng P1) /\ Q29) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
(P1 " ((rng P1) /\ Q29)) /\ ([#] ((TOP-REAL 2) | Q1)) is Element of K19( the carrier of ((TOP-REAL 2) | Q1))
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | Q1)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | Q1))) is set
ff is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | Q1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | Q1)))
ff . 0 is set
ff . 1 is set
rng ff is Element of K19( the carrier of ((TOP-REAL 2) | Q1))
P1 | Q2 is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | P) -valued Function-like Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | P)))
rng (P1 | Q2) is Element of K19( the carrier of ((TOP-REAL 2) | P))
P2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | P2 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | P2) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | P2))
the carrier of ((TOP-REAL 2) | P2) is non empty set
K19( the carrier of ((TOP-REAL 2) | P2)) is set
P1 . q2 is set
dom (P1 | Q2) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
R^2-unit_square /\ Q2 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | Q2 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | Q2) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | Q2))
the carrier of ((TOP-REAL 2) | Q2) is non empty set
K19( the carrier of ((TOP-REAL 2) | Q2)) is set
K20( the carrier of ((TOP-REAL 2) | Q2), the carrier of ((TOP-REAL 2) | P2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | Q2), the carrier of ((TOP-REAL 2) | P2))) is set
P1 " P2 is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
F2 is Relation-like the carrier of ((TOP-REAL 2) | Q2) -defined the carrier of ((TOP-REAL 2) | P2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | Q2), the carrier of ((TOP-REAL 2) | P2)))
ff is Element of K19( the carrier of ((TOP-REAL 2) | P2))
F2 " ff is Element of K19( the carrier of ((TOP-REAL 2) | Q2))
S1 is functional Element of K19( the carrier of (TOP-REAL 2))
S1 /\ ([#] ((TOP-REAL 2) | P2)) is Element of K19( the carrier of ((TOP-REAL 2) | P2))
rng P1 is Element of K19( the carrier of ((TOP-REAL 2) | P))
S1 /\ (rng P1) is Element of K19( the carrier of ((TOP-REAL 2) | P))
(rng P1) /\ S1 is functional Element of K19( the carrier of (TOP-REAL 2))
S2 is Element of K19( the carrier of ((TOP-REAL 2) | P))
P1 " S2 is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
P1 " ff is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
Q2 /\ (P1 " ff) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
P1 " S1 is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
P1 " ([#] ((TOP-REAL 2) | P2)) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
(P1 " S1) /\ (P1 " ([#] ((TOP-REAL 2) | P2))) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
Q2 /\ ((P1 " S1) /\ (P1 " ([#] ((TOP-REAL 2) | P2)))) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
(P1 " S1) /\ Q2 is functional Element of K19( the carrier of (TOP-REAL 2))
((P1 " S1) /\ Q2) /\ Q2 is functional Element of K19( the carrier of (TOP-REAL 2))
Q2 /\ Q2 is functional Element of K19( the carrier of (TOP-REAL 2))
(P1 " S1) /\ (Q2 /\ Q2) is functional Element of K19( the carrier of (TOP-REAL 2))
(P1 " S1) /\ ([#] ((TOP-REAL 2) | Q2)) is Element of K19( the carrier of ((TOP-REAL 2) | Q2))
P1 " ((rng P1) /\ S1) is Element of K19( the carrier of ((TOP-REAL 2) | R^2-unit_square))
(P1 " ((rng P1) /\ S1)) /\ ([#] ((TOP-REAL 2) | Q2)) is Element of K19( the carrier of ((TOP-REAL 2) | Q2))
(dom P1) /\ Q1 is functional Element of K19( the carrier of (TOP-REAL 2))
P1 \/ P2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
P1 /\ P2 is functional Element of K19( the carrier of (TOP-REAL 2))
F1 . q2 is set
rng F1 is Element of K19( the carrier of ((TOP-REAL 2) | P1))
Q19 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | Q19 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
F1 . P2 is set
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | Q2)) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | Q2))) is set
ff is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | Q2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | Q2)))
ff . 0 is set
ff . 1 is set
rng ff is Element of K19( the carrier of ((TOP-REAL 2) | Q2))
(dom P1) /\ Q2 is functional Element of K19( the carrier of (TOP-REAL 2))
F2 . P2 is set
F2 . q2 is set
Q29 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | Q29 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
rng F2 is Element of K19( the carrier of ((TOP-REAL 2) | P2))
P1 .: (Q1 \/ Q2) is Element of K19( the carrier of ((TOP-REAL 2) | P))
P1 .: (Q1 /\ Q2) is Element of K19( the carrier of ((TOP-REAL 2) | P))
{P2} is functional non empty set
{q2} is functional non empty set
{P2} \/ {q2} is non empty set
P1 .: ({P2} \/ {q2}) is Element of K19( the carrier of ((TOP-REAL 2) | P))
Im (P1,P2) is set
P1 .: {P2} is set
Im (P1,q2) is set
P1 .: {q2} is set
(Im (P1,P2)) \/ (Im (P1,q2)) is set
{S} is functional non empty set
{S} \/ (Im (P1,q2)) is non empty set
{x} is functional non empty set
{S} \/ {x} is non empty set
f is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
R is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
{f,R} is functional non empty set
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
P is functional non empty Element of K19( the carrier of (TOP-REAL 2))
f is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
R is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
{f,R} is functional non empty set
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
P1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
P2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
P1 \/ P2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
P1 /\ P2 is functional Element of K19( the carrier of (TOP-REAL 2))
{p1,p2} is functional non empty set
f is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
R is Relation-like Function-like V42(2) FinSequence-like V154() Element of the carrier of (TOP-REAL 2)
S is functional non empty Element of K19( the carrier of (TOP-REAL 2))
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S \/ x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
S /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
{f,R} is functional non empty set
P is 1-sorted
the carrier of P is set
f is 1-sorted
the carrier of f is set
K20( the carrier of P, the carrier of f) is set
K19(K20( the carrier of P, the carrier of f)) is set
[#] f is non proper Element of K19( the carrier of f)
K19( the carrier of f) is set
R is Relation-like the carrier of P -defined the carrier of f -valued Function-like quasi_total Element of K19(K20( the carrier of P, the carrier of f))
rng R is Element of K19( the carrier of f)
S is non empty 1-sorted
the carrier of S is non empty set
x is set
dom R is Element of K19( the carrier of P)
K19( the carrier of P) is set
p1 is set
R . p1 is set
P is 1-sorted
the carrier of P is set
[#] P is non proper Element of K19( the carrier of P)
K19( the carrier of P) is set
f is 1-sorted
the carrier of f is set
K20( the carrier of P, the carrier of f) is set
K19(K20( the carrier of P, the carrier of f)) is set
R is Relation-like the carrier of P -defined the carrier of f -valued Function-like quasi_total Element of K19(K20( the carrier of P, the carrier of f))
dom R is Element of K19( the carrier of P)
S is non empty 1-sorted
the carrier of S is non empty set
x is set
R . x is set
rng R is Element of K19( the carrier of f)
K19( the carrier of f) is set
P is TopStruct
the carrier of P is set
f is TopStruct
the carrier of f is set
K20( the carrier of P, the carrier of f) is set
K19(K20( the carrier of P, the carrier of f)) is set
R is Relation-like the carrier of P -defined the carrier of f -valued Function-like quasi_total Element of K19(K20( the carrier of P, the carrier of f))
dom R is Element of K19( the carrier of P)
K19( the carrier of P) is set
[#] P is non proper Element of K19( the carrier of P)
rng R is Element of K19( the carrier of f)
K19( the carrier of f) is set
[#] f is non proper Element of K19( the carrier of f)
P is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | P is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | P) is set
K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | P)) is set
K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | P))) is set
f is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | P) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | P)))
rng f is Element of K19( the carrier of ((TOP-REAL 2) | P))
K19( the carrier of ((TOP-REAL 2) | P)) is set
[#] ((TOP-REAL 2) | P) is non proper closed Element of K19( the carrier of ((TOP-REAL 2) | P))
R is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | R is non empty strict TopSpace-like SubSpace of TOP-REAL 2