:: AFPROJ semantic presentation

K139() is Element of bool K135()

K135() is set

bool K135() is non empty set

K134() is set

bool K134() is non empty set

bool K139() is non empty set

{} is empty set

1 is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

a is Element of the carrier of AS

b is Element of the carrier of AS

c is Element of the carrier of AS

Line (a,b) is Element of bool the carrier of AS

Line (a,c) is Element of bool the carrier of AS

Plane ((Line (a,c)),(Line (a,b))) is Element of bool the carrier of AS

c9 is set

L1 is Element of the carrier of AS

L1 * (Line (a,c)) is Element of bool the carrier of AS

R1 is Element of the carrier of AS

{ b

( b

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

a is Element of bool the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

a is Element of bool the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

a is Element of the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

a is Element of bool the carrier of AS

b is Element of bool the carrier of AS

c is Element of bool the carrier of AS

the Element of c is Element of c

the Element of b is Element of b

b9 is Element of the carrier of AS

b9 * a is Element of bool the carrier of AS

b9 * XX is Element of bool the carrier of AS

b9 + b is Element of bool the carrier of AS

c9 is Element of the carrier of AS

c9 * a is Element of bool the carrier of AS

c9 * XX is Element of bool the carrier of AS

c9 + c is Element of bool the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

a is Element of bool the carrier of AS

b is Element of bool the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

{ b

bool (bool the carrier of AS) is non empty set

a is set

b is Element of bool the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

{ b

bool (bool the carrier of AS) is non empty set

a is set

b is Element of bool the carrier of AS

a is non empty non trivial AffinSpace-like AffinStruct

the carrier of a is non empty non trivial set

bool the carrier of a is non empty set

XX is set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

b is set

c is Element of bool the carrier of a

(a) is Element of bool (bool the carrier of a)

bool (bool the carrier of a) is non empty set

{ b

a is non empty non trivial AffinSpace-like AffinStruct

the carrier of a is non empty non trivial set

bool the carrier of a is non empty set

XX is set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

b is set

c is Element of bool the carrier of a

(a) is Element of bool (bool the carrier of a)

bool (bool the carrier of a) is non empty set

{ b

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

{ [b

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

[:(AS),(AS):] is Relation-like bool the carrier of AS -defined bool the carrier of AS -valued Element of bool [:(bool the carrier of AS),(bool the carrier of AS):]

[:(bool the carrier of AS),(bool the carrier of AS):] is non empty set

bool [:(bool the carrier of AS),(bool the carrier of AS):] is non empty set

c is set

d is Element of bool the carrier of AS

a9 is Element of bool the carrier of AS

[d,a9] is V1() Element of [:(bool the carrier of AS),(bool the carrier of AS):]

{d,a9} is non empty set

{d} is non empty set

{{d,a9},{d}} is non empty set

d is set

a9 is Element of bool the carrier of AS

[d,d] is V1() set

{d,d} is non empty set

{d} is non empty set

{{d,d},{d}} is non empty set

c is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

field c is set

d is Element of bool the carrier of AS

a9 is Element of bool the carrier of AS

[d,a9] is V1() Element of [:(bool the carrier of AS),(bool the carrier of AS):]

{d,a9} is non empty set

{d} is non empty set

{{d,a9},{d}} is non empty set

b9 is Element of bool the carrier of AS

c9 is Element of bool the carrier of AS

[b9,c9] is V1() Element of [:(bool the carrier of AS),(bool the carrier of AS):]

{b9,c9} is non empty set

{b9} is non empty set

{{b9,c9},{b9}} is non empty set

d is set

a9 is set

b9 is set

[d,a9] is V1() set

{d,a9} is non empty set

{d} is non empty set

{{d,a9},{d}} is non empty set

[a9,b9] is V1() set

{a9,b9} is non empty set

{a9} is non empty set

{{a9,b9},{a9}} is non empty set

c9 is Element of bool the carrier of AS

L1 is Element of bool the carrier of AS

Q1 is Element of bool the carrier of AS

[d,b9] is V1() set

{d,b9} is non empty set

{{d,b9},{d}} is non empty set

d is set

a9 is set

[d,a9] is V1() set

{d,a9} is non empty set

{d} is non empty set

{{d,a9},{d}} is non empty set

b9 is Element of bool the carrier of AS

c9 is Element of bool the carrier of AS

[a9,d] is V1() set

{a9,d} is non empty set

{a9} is non empty set

{{a9,d},{a9}} is non empty set

dom c is set

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

{ [b

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

[:(AS),(AS):] is Relation-like bool the carrier of AS -defined bool the carrier of AS -valued Element of bool [:(bool the carrier of AS),(bool the carrier of AS):]

[:(bool the carrier of AS),(bool the carrier of AS):] is non empty set

bool [:(bool the carrier of AS),(bool the carrier of AS):] is non empty set

c is set

d is Element of bool the carrier of AS

a9 is Element of bool the carrier of AS

[d,a9] is V1() Element of [:(bool the carrier of AS),(bool the carrier of AS):]

{d,a9} is non empty set

{d} is non empty set

{{d,a9},{d}} is non empty set

d is set

a9 is Element of bool the carrier of AS

[d,d] is V1() set

{d,d} is non empty set

{d} is non empty set

{{d,d},{d}} is non empty set

c is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

field c is set

d is Element of bool the carrier of AS

a9 is Element of bool the carrier of AS

[d,a9] is V1() Element of [:(bool the carrier of AS),(bool the carrier of AS):]

{d,a9} is non empty set

{d} is non empty set

{{d,a9},{d}} is non empty set

b9 is Element of bool the carrier of AS

c9 is Element of bool the carrier of AS

[b9,c9] is V1() Element of [:(bool the carrier of AS),(bool the carrier of AS):]

{b9,c9} is non empty set

{b9} is non empty set

{{b9,c9},{b9}} is non empty set

d is set

a9 is set

b9 is set

[d,a9] is V1() set

{d,a9} is non empty set

{d} is non empty set

{{d,a9},{d}} is non empty set

[a9,b9] is V1() set

{a9,b9} is non empty set

{a9} is non empty set

{{a9,b9},{a9}} is non empty set

c9 is Element of bool the carrier of AS

L1 is Element of bool the carrier of AS

Q1 is Element of bool the carrier of AS

[d,b9] is V1() set

{d,b9} is non empty set

{{d,b9},{d}} is non empty set

d is set

a9 is set

[d,a9] is V1() set

{d,a9} is non empty set

{d} is non empty set

{{d,a9},{d}} is non empty set

b9 is Element of bool the carrier of AS

c9 is Element of bool the carrier of AS

[a9,d] is V1() set

{a9,d} is non empty set

{a9} is non empty set

{{a9,d},{a9}} is non empty set

dom c is set

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

XX is Element of bool the carrier of AS

Class ((AS),XX) is Element of bool (AS)

bool (AS) is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

XX is Element of bool the carrier of AS

Class ((AS),XX) is Element of bool (AS)

bool (AS) is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

(AS,XX) is Element of bool (AS)

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

bool (AS) is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class ((AS),XX) is Element of bool (AS)

a is set

[a,XX] is V1() set

{a,XX} is non empty set

{a} is non empty set

{{a,XX},{a}} is non empty set

b is Element of bool the carrier of AS

c is Element of bool the carrier of AS

[b,c] is V1() Element of [:(bool the carrier of AS),(bool the carrier of AS):]

[:(bool the carrier of AS),(bool the carrier of AS):] is non empty set

{b,c} is non empty set

{b} is non empty set

{{b,c},{b}} is non empty set

d is Element of bool the carrier of AS

b is Element of bool the carrier of AS

[b,XX] is V1() Element of [:(bool the carrier of AS),(bool the carrier of AS):]

{b,XX} is non empty set

{b} is non empty set

{{b,XX},{b}} is non empty set

b is Element of bool the carrier of AS

c is Element of bool the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

(AS,XX) is Element of bool (AS)

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

bool (AS) is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class ((AS),XX) is Element of bool (AS)

a is set

[a,XX] is V1() set

{a,XX} is non empty set

{a} is non empty set

{{a,XX},{a}} is non empty set

b is Element of bool the carrier of AS

c is Element of bool the carrier of AS

[b,c] is V1() Element of [:(bool the carrier of AS),(bool the carrier of AS):]

[:(bool the carrier of AS),(bool the carrier of AS):] is non empty set

{b,c} is non empty set

{b} is non empty set

{{b,c},{b}} is non empty set

d is Element of bool the carrier of AS

b is Element of bool the carrier of AS

[b,XX] is V1() Element of [:(bool the carrier of AS),(bool the carrier of AS):]

{b,XX} is non empty set

{b} is non empty set

{{b,XX},{b}} is non empty set

b is Element of bool the carrier of AS

c is Element of bool the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

(AS,XX) is Element of bool (AS)

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

bool (AS) is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class ((AS),XX) is Element of bool (AS)

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

b is Element of bool the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

(AS,XX) is Element of bool (AS)

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

bool (AS) is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class ((AS),XX) is Element of bool (AS)

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

XX is Element of bool the carrier of AS

(AS,XX) is Element of bool (AS)

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

bool (AS) is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class ((AS),XX) is Element of bool (AS)

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

b is Element of bool the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

XX is Element of the carrier of AS

a is Element of the carrier of AS

Line (XX,a) is Element of bool the carrier of AS

Class ((AS),(Line (XX,a))) is Element of bool (AS)

bool (AS) is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

the Element of the carrier of AS is Element of the carrier of AS

a is Element of bool the carrier of AS

Class ((AS),a) is Element of bool (AS)

bool (AS) is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

XX is set

bool (AS) is non empty set

a is Element of bool (AS)

b is set

Class ((AS),b) is Element of bool (AS)

c is Element of bool the carrier of AS

d is Element of bool the carrier of AS

(AS,d) is Element of bool (AS)

Class ((AS),d) is Element of bool (AS)

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

b is Element of bool the carrier of AS

(AS,b) is Element of bool (AS)

Class ((AS),b) is Element of bool (AS)

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

XX is set

bool (AS) is non empty set

a is Element of bool (AS)

b is set

Class ((AS),b) is Element of bool (AS)

c is Element of bool the carrier of AS

d is Element of bool the carrier of AS

(AS,d) is Element of bool (AS)

Class ((AS),d) is Element of bool (AS)

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

b is Element of bool the carrier of AS

(AS,b) is Element of bool (AS)

Class ((AS),b) is Element of bool (AS)

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

XX is set

b is Element of bool the carrier of AS

(AS,b) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),b) is Element of bool (AS)

a is Element of the carrier of AS

a * b is Element of bool the carrier of AS

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

XX is Element of bool the carrier of AS

a is set

b is Element of bool the carrier of AS

c is Element of bool the carrier of AS

(AS,c) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),c) is Element of bool (AS)

d is Element of the carrier of AS

a9 is Element of the carrier of AS

b9 is Element of bool the carrier of AS

{1} is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

[:(AS),{1}:] is set

XX is set

a is set

b is set

[a,b] is V1() set

{a,b} is non empty set

{a} is non empty set

{{a,b},{a}} is non empty set

c is Element of bool the carrier of AS

d is Element of bool the carrier of AS

[d,1] is V1() set

{d,1} is non empty set

{d} is non empty set

{{d,1},{d}} is non empty set

a is Element of bool the carrier of AS

[a,1] is V1() set

{a,1} is non empty set

{a} is non empty set

{{a,1},{a}} is non empty set

a is Element of bool the carrier of AS

[a,1] is V1() set

{a,1} is non empty set

{a} is non empty set

{{a,1},{a}} is non empty set

b is Element of bool the carrier of AS

[b,1] is V1() set

{b,1} is non empty set

{b} is non empty set

{{b,1},{b}} is non empty set

2 is non empty set

{2} is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

[:(AS),{2}:] is non empty set

XX is set

a is set

b is set

[a,b] is V1() set

{a,b} is non empty set

{a} is non empty set

{{a,b},{a}} is non empty set

c is Element of bool the carrier of AS

(AS,c) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),c) is Element of bool (AS)

d is Element of bool the carrier of AS

(AS,d) is Element of bool (AS)

Class ((AS),d) is Element of bool (AS)

[(AS,d),2] is V1() set

{(AS,d),2} is non empty set

{(AS,d)} is non empty set

{{(AS,d),2},{(AS,d)}} is non empty set

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

[(AS,a),2] is V1() set

{(AS,a),2} is non empty set

{(AS,a)} is non empty set

{{(AS,a),2},{(AS,a)}} is non empty set

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

[(AS,a),2] is V1() set

{(AS,a),2} is non empty set

{(AS,a)} is non empty set

{{(AS,a),2},{(AS,a)}} is non empty set

b is Element of bool the carrier of AS

(AS,b) is Element of bool (AS)

Class ((AS),b) is Element of bool (AS)

[(AS,b),2] is V1() set

{(AS,b),2} is non empty set

{(AS,b)} is non empty set

{{(AS,b),2},{(AS,b)}} is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

the carrier of AS \/ (AS) is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

[:(AS),{1}:] is set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

[:(AS),{2}:] is non empty set

[:(AS),{1}:] \/ [:(AS),{2}:] is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is non empty set

the carrier of AS is non empty non trivial set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

the carrier of AS \/ (AS) is non empty set

(AS) is non empty set

[:(AS),{1}:] is set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

[:(AS),{2}:] is non empty set

[:(AS),{1}:] \/ [:(AS),{2}:] is non empty set

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

b is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

c is set

d is set

[c,d] is V1() set

{c,d} is non empty set

{c} is non empty set

{{c,d},{c}} is non empty set

a9 is Element of bool the carrier of AS

[a9,1] is V1() set

{a9,1} is non empty set

{a9} is non empty set

{{a9,1},{a9}} is non empty set

(AS,a9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a9) is Element of bool (AS)

a9 is Element of bool the carrier of AS

b9 is Element of bool the carrier of AS

(AS,a9) is Element of bool (AS)

Class ((AS),a9) is Element of bool (AS)

(AS,b9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),b9) is Element of bool (AS)

[(AS,b9),2] is V1() set

{(AS,b9),2} is non empty set

{(AS,b9)} is non empty set

{{(AS,b9),2},{(AS,b9)}} is non empty set

a9 is Element of bool the carrier of AS

[a9,1] is V1() set

{a9,1} is non empty set

{a9} is non empty set

{{a9,1},{a9}} is non empty set

(AS,a9) is Element of bool (AS)

Class ((AS),a9) is Element of bool (AS)

b9 is Element of bool the carrier of AS

c9 is Element of bool the carrier of AS

(AS,b9) is Element of bool (AS)

Class ((AS),b9) is Element of bool (AS)

(AS,c9) is Element of bool (AS)

Class ((AS),c9) is Element of bool (AS)

[(AS,c9),2] is V1() set

{(AS,c9),2} is non empty set

{(AS,c9)} is non empty set

{{(AS,c9),2},{(AS,c9)}} is non empty set

a9 is Element of bool the carrier of AS

[a9,1] is V1() set

{a9,1} is non empty set

{a9} is non empty set

{{a9,1},{a9}} is non empty set

(AS,a9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a9) is Element of bool (AS)

b9 is Element of bool the carrier of AS

c9 is Element of bool the carrier of AS

(AS,b9) is Element of bool (AS)

Class ((AS),b9) is Element of bool (AS)

(AS,c9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),c9) is Element of bool (AS)

[(AS,c9),2] is V1() set

{(AS,c9),2} is non empty set

{(AS,c9)} is non empty set

{{(AS,c9),2},{(AS,c9)}} is non empty set

XX is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

a is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

b is set

c is set

[b,c] is V1() set

{b,c} is non empty set

{b} is non empty set

{{b,c},{b}} is non empty set

d is Element of bool the carrier of AS

[d,1] is V1() set

{d,1} is non empty set

{d} is non empty set

{{d,1},{d}} is non empty set

(AS,d) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),d) is Element of bool (AS)

a9 is Element of bool the carrier of AS

b9 is Element of bool the carrier of AS

(AS,a9) is Element of bool (AS)

Class ((AS),a9) is Element of bool (AS)

(AS,b9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),b9) is Element of bool (AS)

[(AS,b9),2] is V1() set

{(AS,b9),2} is non empty set

{(AS,b9)} is non empty set

{{(AS,b9),2},{(AS,b9)}} is non empty set

d is Element of bool the carrier of AS

[d,1] is V1() set

{d,1} is non empty set

{d} is non empty set

{{d,1},{d}} is non empty set

(AS,d) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),d) is Element of bool (AS)

a9 is Element of bool the carrier of AS

b9 is Element of bool the carrier of AS

(AS,a9) is Element of bool (AS)

Class ((AS),a9) is Element of bool (AS)

(AS,b9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),b9) is Element of bool (AS)

[(AS,b9),2] is V1() set

{(AS,b9),2} is non empty set

{(AS,b9)} is non empty set

{{(AS,b9),2},{(AS,b9)}} is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

b is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

c is set

d is set

[c,d] is V1() set

{c,d} is non empty set

{c} is non empty set

{{c,d},{c}} is non empty set

a9 is Element of bool the carrier of AS

(AS,a9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a9) is Element of bool (AS)

b9 is Element of bool the carrier of AS

(AS,b9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),b9) is Element of bool (AS)

a9 is Element of bool the carrier of AS

(AS,a9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a9) is Element of bool (AS)

b9 is Element of bool the carrier of AS

(AS,b9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),b9) is Element of bool (AS)

a9 is Element of bool the carrier of AS

(AS,a9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a9) is Element of bool (AS)

b9 is Element of bool the carrier of AS

(AS,b9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),b9) is Element of bool (AS)

XX is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

a is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

b is set

c is set

[b,c] is V1() set

{b,c} is non empty set

{b} is non empty set

{{b,c},{b}} is non empty set

d is Element of bool the carrier of AS

(AS,d) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),d) is Element of bool (AS)

a9 is Element of bool the carrier of AS

(AS,a9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a9) is Element of bool (AS)

d is Element of bool the carrier of AS

(AS,d) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),d) is Element of bool (AS)

a9 is Element of bool the carrier of AS

(AS,a9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a9) is Element of bool (AS)

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is non empty set

the carrier of AS is non empty non trivial set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

the carrier of AS \/ (AS) is non empty set

(AS) is non empty set

[:(AS),{1}:] is set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

[:(AS),{2}:] is non empty set

[:(AS),{1}:] \/ [:(AS),{2}:] is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is strict IncProjStr

(AS) is non empty set

the carrier of AS is non empty non trivial set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

the carrier of AS \/ (AS) is non empty set

(AS) is non empty set

[:(AS),{1}:] is set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

[:(AS),{2}:] is non empty set

[:(AS),{1}:] \/ [:(AS),{2}:] is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Points of (AS) is non empty set

XX is set

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a) is Element of bool (AS)

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

b is Element of bool the carrier of AS

(AS,b) is Element of bool (AS)

Class ((AS),b) is Element of bool (AS)

a is non empty non trivial AffinSpace-like AffinStruct

the carrier of a is non empty non trivial set

bool the carrier of a is non empty set

XX is set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is strict IncProjStr

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Points of (AS) is non empty set

b is set

c is Element of bool the carrier of a

(a,c) is Element of bool (a)

(a) is Element of bool (bool the carrier of a)

bool (bool the carrier of a) is non empty set

{ b

bool (a) is non empty set

(a) is Relation-like (a) -defined (a) -valued symmetric transitive V28((a)) Element of bool [:(a),(a):]

[:(a),(a):] is set

bool [:(a),(a):] is non empty set

{ [b

Class ((a),c) is Element of bool (a)

(a) is strict IncProjStr

(a) is non empty set

Class (a) is a_partition of (a)

(a) is non empty set

(a) is Element of bool (bool the carrier of a)

{ b

(a) is Relation-like (a) -defined (a) -valued symmetric transitive V28((a)) Element of bool [:(a),(a):]

[:(a),(a):] is set

bool [:(a),(a):] is non empty set

{ [b

Class (a) is a_partition of (a)

(a) is Relation-like (a) -defined (a) -valued Element of bool [:(a),(a):]

[:(a),(a):] is non empty set

bool [:(a),(a):] is non empty set

IncProjStr(# (a),(a),(a) #) is strict IncProjStr

the Points of (a) is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is strict IncProjStr

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Points of (AS) is non empty set

(AS) is strict IncProjStr

(AS) is non empty set

the carrier of AS \/ (AS) is non empty set

(AS) is non empty set

[:(AS),{1}:] is set

[:(AS),{2}:] is non empty set

[:(AS),{1}:] \/ [:(AS),{2}:] is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Points of (AS) is non empty set

XX is set

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a) is Element of bool (AS)

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is strict IncProjStr

(AS) is non empty set

the carrier of AS is non empty non trivial set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

the carrier of AS \/ (AS) is non empty set

(AS) is non empty set

[:(AS),{1}:] is set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

[:(AS),{2}:] is non empty set

[:(AS),{1}:] \/ [:(AS),{2}:] is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Lines of (AS) is non empty set

XX is set

a is Element of bool the carrier of AS

[a,1] is V1() set

{a,1} is non empty set

{a} is non empty set

{{a,1},{a}} is non empty set

(AS,a) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a) is Element of bool (AS)

[(AS,a),2] is V1() set

{(AS,a),2} is non empty set

{(AS,a)} is non empty set

{{(AS,a),2},{(AS,a)}} is non empty set

a is Element of bool the carrier of AS

[a,1] is V1() set

{a,1} is non empty set

{a} is non empty set

{{a,1},{a}} is non empty set

b is Element of bool the carrier of AS

(AS,b) is Element of bool (AS)

Class ((AS),b) is Element of bool (AS)

[(AS,b),2] is V1() set

{(AS,b),2} is non empty set

{(AS,b)} is non empty set

{{(AS,b),2},{(AS,b)}} is non empty set

c is Element of bool the carrier of AS

[c,1] is V1() set

{c,1} is non empty set

{c} is non empty set

{{c,1},{c}} is non empty set

d is Element of bool the carrier of AS

(AS,d) is Element of bool (AS)

Class ((AS),d) is Element of bool (AS)

[(AS,d),2] is V1() set

{(AS,d),2} is non empty set

{(AS,d)} is non empty set

{{(AS,d),2},{(AS,d)}} is non empty set

a is Element of bool the carrier of AS

[a,1] is V1() set

{a,1} is non empty set

{a} is non empty set

{{a,1},{a}} is non empty set

b is Element of bool the carrier of AS

(AS,b) is Element of bool (AS)

Class ((AS),b) is Element of bool (AS)

[(AS,b),2] is V1() set

{(AS,b),2} is non empty set

{(AS,b)} is non empty set

{{(AS,b),2},{(AS,b)}} is non empty set

c is Element of bool the carrier of AS

[c,1] is V1() set

{c,1} is non empty set

{c} is non empty set

{{c,1},{c}} is non empty set

d is Element of bool the carrier of AS

(AS,d) is Element of bool (AS)

Class ((AS),d) is Element of bool (AS)

[(AS,d),2] is V1() set

{(AS,d),2} is non empty set

{(AS,d)} is non empty set

{{(AS,d),2},{(AS,d)}} is non empty set

a is non empty non trivial AffinSpace-like AffinStruct

the carrier of a is non empty non trivial set

bool the carrier of a is non empty set

XX is set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is strict IncProjStr

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Lines of (AS) is non empty set

b is set

c is Element of bool the carrier of a

(a,c) is Element of bool (a)

(a) is Element of bool (bool the carrier of a)

bool (bool the carrier of a) is non empty set

{ b

bool (a) is non empty set

(a) is Relation-like (a) -defined (a) -valued symmetric transitive V28((a)) Element of bool [:(a),(a):]

[:(a),(a):] is set

bool [:(a),(a):] is non empty set

{ [b

Class ((a),c) is Element of bool (a)

(a) is strict IncProjStr

(a) is non empty set

(a) is Element of bool (bool the carrier of a)

{ b

(a) is Relation-like (a) -defined (a) -valued symmetric transitive V28((a)) Element of bool [:(a),(a):]

[:(a),(a):] is set

bool [:(a),(a):] is non empty set

{ [b

Class (a) is a_partition of (a)

(a) is non empty set

Class (a) is a_partition of (a)

(a) is Relation-like (a) -defined (a) -valued Element of bool [:(a),(a):]

[:(a),(a):] is non empty set

bool [:(a),(a):] is non empty set

IncProjStr(# (a),(a),(a) #) is strict IncProjStr

the Lines of (a) is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

(AS) is strict IncProjStr

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Lines of (AS) is non empty set

(AS) is strict IncProjStr

(AS) is non empty set

the carrier of AS \/ (AS) is non empty set

(AS) is non empty set

[:(AS),{1}:] is set

[:(AS),{2}:] is non empty set

[:(AS),{1}:] \/ [:(AS),{2}:] is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Lines of (AS) is non empty set

XX is set

[XX,2] is V1() set

{XX,2} is non empty set

{XX} is non empty set

{{XX,2},{XX}} is non empty set

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a) is Element of bool (AS)

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

(AS) is strict IncProjStr

(AS) is non empty set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

the carrier of AS \/ (AS) is non empty set

(AS) is non empty set

[:(AS),{1}:] is set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

[:(AS),{2}:] is non empty set

[:(AS),{1}:] \/ [:(AS),{2}:] is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Points of (AS) is non empty set

the Lines of (AS) is non empty set

XX is Element of the carrier of AS

a is Element of bool the carrier of AS

[a,1] is V1() set

{a,1} is non empty set

{a} is non empty set

{{a,1},{a}} is non empty set

b is Element of the Points of (AS)

c is Element of the Lines of (AS)

d is Element of bool the carrier of AS

[d,1] is V1() set

{d,1} is non empty set

{d} is non empty set

{{d,1},{d}} is non empty set

(AS,d) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),d) is Element of bool (AS)

the carrier of AS /\ (AS) is set

[d,1] `1 is set

[b,c] is V1() Element of [: the Points of (AS), the Lines of (AS):]

[: the Points of (AS), the Lines of (AS):] is non empty set

{b,c} is non empty set

{b} is non empty set

{{b,c},{b}} is non empty set

the Inc of (AS) is Relation-like the Points of (AS) -defined the Lines of (AS) -valued Element of bool [: the Points of (AS), the Lines of (AS):]

bool [: the Points of (AS), the Lines of (AS):] is non empty set

d is Element of bool the carrier of AS

a9 is Element of bool the carrier of AS

(AS,d) is Element of bool (AS)

Class ((AS),d) is Element of bool (AS)

(AS,a9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a9) is Element of bool (AS)

[(AS,a9),2] is V1() set

{(AS,a9),2} is non empty set

{(AS,a9)} is non empty set

{{(AS,a9),2},{(AS,a9)}} is non empty set

[XX,[a,1]] is V1() set

{XX,[a,1]} is non empty set

{XX} is non empty set

{{XX,[a,1]},{XX}} is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

(AS) is strict IncProjStr

(AS) is non empty set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

the carrier of AS \/ (AS) is non empty set

(AS) is non empty set

[:(AS),{1}:] is set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

[:(AS),{2}:] is non empty set

[:(AS),{1}:] \/ [:(AS),{2}:] is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Points of (AS) is non empty set

the Lines of (AS) is non empty set

XX is Element of the carrier of AS

a is Element of bool the carrier of AS

(AS,a) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a) is Element of bool (AS)

[(AS,a),2] is V1() set

{(AS,a),2} is non empty set

{(AS,a)} is non empty set

{{(AS,a),2},{(AS,a)}} is non empty set

b is Element of the Points of (AS)

c is Element of the Lines of (AS)

d is Element of bool the carrier of AS

[d,1] is V1() set

{d,1} is non empty set

{d} is non empty set

{{d,1},{d}} is non empty set

(AS,d) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),d) is Element of bool (AS)

[d,1] `2 is set

d is Element of bool the carrier of AS

a9 is Element of bool the carrier of AS

(AS,d) is Element of bool (AS)

Class ((AS),d) is Element of bool (AS)

(AS,a9) is Element of bool (AS)

Class ((AS),a9) is Element of bool (AS)

[(AS,a9),2] is V1() set

{(AS,a9),2} is non empty set

{(AS,a9)} is non empty set

{{(AS,a9),2},{(AS,a9)}} is non empty set

the carrier of AS /\ (AS) is set

[b,c] is V1() Element of [: the Points of (AS), the Lines of (AS):]

[: the Points of (AS), the Lines of (AS):] is non empty set

{b,c} is non empty set

{b} is non empty set

{{b,c},{b}} is non empty set

the Inc of (AS) is Relation-like the Points of (AS) -defined the Lines of (AS) -valued Element of bool [: the Points of (AS), the Lines of (AS):]

bool [: the Points of (AS), the Lines of (AS):] is non empty set

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

(AS) is strict IncProjStr

(AS) is non empty set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool (bool the carrier of AS) is non empty set

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

the carrier of AS \/ (AS) is non empty set

(AS) is non empty set

[:(AS),{1}:] is set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

{ b

(AS) is Relation-like (AS) -defined (AS) -valued symmetric transitive V28((AS)) Element of bool [:(AS),(AS):]

[:(AS),(AS):] is set

bool [:(AS),(AS):] is non empty set

{ [b

Class (AS) is a_partition of (AS)

[:(AS),{2}:] is non empty set

[:(AS),{1}:] \/ [:(AS),{2}:] is non empty set

(AS) is Relation-like (AS) -defined (AS) -valued Element of bool [:(AS),(AS):]

[:(AS),(AS):] is non empty set

bool [:(AS),(AS):] is non empty set

IncProjStr(# (AS),(AS),(AS) #) is strict IncProjStr

the Points of (AS) is non empty set

the Lines of (AS) is non empty set

XX is Element of bool the carrier of AS

(AS,XX) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),XX) is Element of bool (AS)

a is Element of bool the carrier of AS

[a,1] is V1() set

{a,1} is non empty set

{a} is non empty set

{{a,1},{a}} is non empty set

b is Element of the Points of (AS)

c is Element of the Lines of (AS)

d is Element of bool the carrier of AS

[d,1] is V1() set

{d,1} is non empty set

{d} is non empty set

{{d,1},{d}} is non empty set

(AS,d) is Element of bool (AS)

Class ((AS),d) is Element of bool (AS)

a9 is Element of bool the carrier of AS

the carrier of AS /\ (AS) is set

[b,c] is V1() Element of [: the Points of (AS), the Lines of (AS):]

[: the Points of (AS), the Lines of (AS):] is non empty set

{b,c} is non empty set

{b} is non empty set

{{b,c},{b}} is non empty set

the Inc of (AS) is Relation-like the Points of (AS) -defined the Lines of (AS) -valued Element of bool [: the Points of (AS), the Lines of (AS):]

bool [: the Points of (AS), the Lines of (AS):] is non empty set

d is Element of bool the carrier of AS

a9 is Element of bool the carrier of AS

(AS,d) is Element of bool (AS)

Class ((AS),d) is Element of bool (AS)

(AS,a9) is Element of bool (AS)

bool (AS) is non empty set

Class ((AS),a9) is Element of bool (AS)

[(AS,a9),2] is V1() set

{(AS,a9),2} is non empty set

{(AS,a9)} is non empty set

{{(AS,a9),2},{(AS,a9)}} is non empty set

(AS,a) is Element of bool (AS)

Class ((AS),a) is Element of bool (AS)

AS is non empty non trivial AffinSpace-like AffinStruct

the carrier of AS is non empty non trivial set

bool the carrier of AS is non empty set

(AS) is strict IncProjStr

(AS) is non empty set

(AS) is non empty set

(AS) is Element of bool (bool the carrier of AS)

bool (bool the