:: ORDINAL1 semantic presentation

X is set
Y is set
X is set
{X} is non empty set
X \/ {X} is non empty set
X is set
(X) is set
{X} is non empty set
X \/ {X} is non empty set
X is set
(X) is non empty set
{X} is non empty set
X \/ {X} is non empty set
X is set
(X) is non empty set
{X} is non empty set
X \/ {X} is non empty set
Y is set
(Y) is non empty set
{Y} is non empty set
Y \/ {Y} is non empty set
X is set
Y is set
(Y) is non empty set
{Y} is non empty set
Y \/ {Y} is non empty set
X is set
(X) is non empty set
{X} is non empty set
X \/ {X} is non empty set
X is set
X is set
Y is set
X is set
X is set
X is set
Y is set
x is () set
X is () set
Y is () () () set
Y \ X is Element of bool Y
bool Y is non empty set
the Element of Y \ X is Element of Y \ X
y is set
A2 is set
B is set
A2 is set
X is () set
Y is () () () set
x is () () () set
X is set
Y is () () () set
x is set
y is set
x \ X is Element of bool x
bool x is non empty set
A2 is set
x is set
y is set
X is () () () set
Y is () () () set
x is set
X \ Y is Element of bool X
bool X is non empty set
y is set
A2 is set
X is () () () set
Y is () () () set
x is () () () set
x is set
y is () () () set
x is () () () set
y is () () () set
A2 is () () () set
B is () () () set
X is () () () set
Y is () () () set
X is () () () set
Y is () () () set
X is set
X is set
(X) is non empty set
{X} is non empty set
X \/ {X} is non empty set
Y is set
Y is set
Y is set
x is set
X is set
union X is set
x is set
y is set
Y is () () () set
A2 is () () () set
x is set
y is set
A2 is set
Y is () () () set
B is set
A is () () () set
a is () () () set
({}) is non empty set
is non empty functional set
{} \/ is non empty set
X is () () () set
X is () () () set
(X) is non empty set
{X} is non empty set
X \/ {X} is non empty set
union X is set
X is set
Y is set
Y is set
x is set
X is set
Y is () () () set
the Element of X is Element of X
y is set
A2 is () () () set
B is () () () set
X is () () () set
(X) is non empty () () () set
{X} is non empty set
X \/ {X} is non empty set
Y is () () () set
x is set
X is () () () set
Y is () () () set
(Y) is non empty () () () set
{Y} is non empty set
Y \/ {Y} is non empty set
X is () () () set
X is () () () set
(X) is non empty () () () set
{X} is non empty set
X \/ {X} is non empty set
Y is set
x is set
x is () () () set
y is () () () set
y is () () () set
X is () () () set
(X) is non empty () () () set
{X} is non empty set
X \/ {X} is non empty set
x is set
(X) \ x is Element of bool (X)
bool (X) is non empty set
y is () () () set
A2 is () () () set
B is () () () set
y is () () () set
X is set
union X is set
Y is set
x is set
y is set
Y is set
x is set
y is set
A2 is set
X is set
union X is set
(()) is non empty set
{()} is non empty set
() \/ {()} is non empty set
Y is () () () set
x is set
y is () () () set
A2 is set
X is set
Y is set
x is set
Y is set
x is set
X is set
Y is set
x is set
x is set
y is set
X is set
Y is () () () set
(Y) is non empty () () () set
{Y} is non empty set
Y \/ {Y} is non empty set
x is set
y is set
y is () () () set
A2 is () () () set
X is () () () set
union X is () () () set
Y is () () () set
(Y) is non empty () () () set
{Y} is non empty set
Y \/ {Y} is non empty set
x is set
y is set
Y is set
(Y) is non empty set
{Y} is non empty set
Y \/ {Y} is non empty set
union X is () () () set
Y is set
x is set
X is () () () set
Y is () () () set
(Y) is non empty () () () set
{Y} is non empty set
Y \/ {Y} is non empty set
Y is () () () set
(Y) is non empty () () () set
{Y} is non empty set
Y \/ {Y} is non empty set
X is set
proj1 X is set
X is set

proj2 Y is set
X is set

proj2 Y is set

proj1 X is set
proj2 X is set

proj1 X is set
X is set
Y is set

proj2 x is set

proj2 X is set
Y is () () () set

proj2 (X | Y) is set
proj1 X is () () () set
proj1 (X | Y) is set
X is set

x is () () () set

proj2 Y is set
X is set
union X is set
Y is set
x is set

A2 is set
Y is set
x is set
[Y,x] is V14() set
{Y,x} is non empty set
{Y} is non empty set
{{Y,x},{Y}} is non empty set
y is set
[Y,y] is V14() set
{Y,y} is non empty set
{{Y,y},{Y}} is non empty set
A2 is set
a is set

x is set
y is set
A2 is set

proj1 B is () () () set

y is set
A2 is set
[y,A2] is V14() set
{y,A2} is non empty set
{y} is non empty set
{{y,A2},{y}} is non empty set

proj1 B is () () () set
proj2 x is set
y is set
proj1 x is set
A2 is set
x . A2 is set
[A2,y] is V14() set
{A2,y} is non empty set
{A2} is non empty set
{{A2,y},{A2}} is non empty set
y is () () () set
A2 is () () () set
A2 is () () () set

proj1 Y is set
B is set
a is set
[B,a] is V14() set
{B,a} is non empty set
{B} is non empty set
{{B,a},{B}} is non empty set
A is set

proj1 L is () () () set

proj1 B is () () () set
[L,()] is V14() set
{L,()} is non empty set
{L} is non empty functional set
{{L,()},{L}} is non empty set
proj1 x is set
x . L is set
B is set
a is () () () set
A is () () () set
proj1 x is set
L is set
x . L is set
[L,A] is V14() set
{L,A} is non empty set
{L} is non empty set
{{L,A},{L}} is non empty set

proj1 B is () () () set

proj1 A is () () () set

proj1 A is () () () set
L is set
[B,L] is V14() set
{B,L} is non empty set
{B} is non empty set
{{B,L},{B}} is non empty set
F3() is Relation-like Function-like () set
proj1 F3() is () () () set
F1() is () () () set
F4() is Relation-like Function-like () set
proj1 F4() is () () () set
X is set
Y is set
Y is set
F3() . Y is set
F4() . Y is set
Y is () () () set
F3() | Y is Relation-like proj2 F3() -valued Function-like () set
proj2 F3() is set
proj1 (F3() | Y) is () () () set
F4() | Y is Relation-like proj2 F4() -valued Function-like () set
proj2 F4() is set
proj1 (F4() | Y) is () () () set
x is () () () set
F3() . x is set
F4() . x is set
x is set
y is () () () set
F3() . y is set
F4() . y is set
(F3() | Y) . x is set
F3() . x is set
(F4() | Y) . x is set
F3() . Y is set
F2((F3() | Y)) is set
F4() . Y is set
F2((F4() | Y)) is set
F1() is () () () set
X is () () () set
Y is set
x is set
y is set

proj1 A2 is () () () set
B is () () () set
a is () () () set

proj2 A2 is set
A2 . a is set
F2(A) is set

proj1 a is () () () set
A is () () () set

proj2 a is set
a . A is set
F2(L) is set

proj1 Y is set
x is set
y is set
[x,y] is V14() set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
x is set
y is () () () set

proj1 A2 is () () () set
B is () () () set

proj1 a is () () () set
A is () () () set
a . A is set

proj2 a is set
F2((a | A)) is set
[y,A2] is V14() set
{y,A2} is non empty set
{y} is non empty set
{{y,A2},{y}} is non empty set
x is set
Y . x is set
y is set
[x,y] is V14() set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set

F2(A2) is set
x is set

Y . x is set
y is set
F2(B) is set

A2 is set
F2(a) is set

proj1 x is set

proj1 y is () () () set
A2 is () () () set
y . A2 is set

proj2 y is set
F2((y | A2)) is set
Y . A2 is set
x . A2 is set

F2(B) is set
[A2,B] is V14() set
{A2,B} is non empty set
{A2} is non empty set
{{A2,B},{A2}} is non empty set
proj1 B is () () () set
a is () () () set
A is () () () set

proj2 B is set
proj1 L is () () () set
B is () () () set

proj2 L is set
B . B is set
F2((B | B)) is set
L . B is set
F2((L | B)) is set
[a,(B | a)] is V14() set
{a,(B | a)} is non empty set
{a} is non empty set
{{a,(B | a)},{a}} is non empty set
Y . a is set
a is set
A is () () () set
Y . A is set

(y | A2) . A is set
y . A is set
x . A is set
(y | A2) . a is set
B . a is set

F2(L) is set
proj1 (y | A2) is () () () set

proj1 X is () () () set
Y is () () () set

proj2 X is set
X . Y is set

F2(x) is set
F1() is Relation-like Function-like () set
proj1 F1() is () () () set
F2((proj1 F1())) is set

F3(X) is set
proj1 X is () () () set
Y is set
proj2 X is set
x is () () () set

F3((X | x)) is set

F3(y) is set
proj1 y is () () () set
A2 is () () () set

proj2 y is set
y . A2 is set
X . A2 is set
F3((y | A2)) is set
F2(x) is set
X . x is set

F3(y) is set
proj1 y is () () () set
F1() . Y is set
X . Y is set
Y is () () () set
F1() . Y is set
F1() | Y is Relation-like proj2 F1() -valued Function-like () set
proj2 F1() is set
F3((F1() | Y)) is set
X is () () () set
Y is () () () set
X is set
Y is set
x is set
Y is set
x is set
X is () () () set
Y is set
(Y) is set
x is set
y is () () () set
A2 is set
B is () () () set
x is () () () set
y is () () () set
(y) is non empty () () () set
{y} is non empty set
y \/ {y} is non empty set
bool y is non empty set
A2 is set
X is () () () set
X is set
Y is set
() is set
the Element of () is Element of ()
X is Element of ()
X is () set
X is () () () set
Y is Element of X
X is set
Y is () () () Element of ()
F1() is non empty set
X is set
Y is Element of F1()
x is () () () set
y is set
A2 is () () () set
X is set
Y is set
x is set
y is () () () set
A2 is () () () set

proj1 X is set
Y is Element of F1()
X . Y is set
X is set
(X) is non empty set
{X} is non empty set
X \/ {X} is non empty set
(X) \ {X} is Element of bool (X)
bool (X) is non empty set
Y is set
Y is set
X is set
X is () () () Element of ()
({}) is non empty () () () set
is non empty functional set
{} \/ is non empty set
X is () () () () set
(X) is non empty () () () set
{X} is non empty set
X \/ {X} is non empty set
X is set
Y is set
x is set
X is () set
bool X is non empty set
Y is Element of bool X
x is set
y is set