:: ORDINAL1 semantic presentation

{} is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional set
the empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional set is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional set
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
((union X)) is non empty set
{(union X)} is non empty set
(union X) \/ {(union X)} 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
Y is Relation-like Function-like () set
proj2 {} is empty trivial Relation-like non-empty empty-yielding Function-like one-to-one constant functional () () () () set
proj2 Y is set
X is set
Y is Relation-like Function-like () set
proj2 Y is set
X is Relation-like Function-like set
proj1 X is set
proj2 X is set
X is Relation-like Function-like () set
proj1 X is set
X is set
Y is set
x is Relation-like X -valued Function-like () set
proj2 x is set
X is Relation-like Function-like () set
proj2 X is set
Y is () () () set
X | Y is Relation-like Function-like set
proj2 (X | Y) is set
proj1 X is () () () set
proj1 (X | Y) is set
X is set
Y is Relation-like X -valued Function-like () set
x is () () () set
Y | x is Relation-like X -valued proj2 Y -valued Function-like () set
proj2 Y is set
X is set
union X is set
Y is set
x is set
y is Relation-like Function-like () 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
A is Relation-like Function-like () set
B is Relation-like Function-like () set
x is set
y is set
A2 is set
B is Relation-like Function-like () set
proj1 B is () () () set
x is Relation-like Function-like 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
B is Relation-like Function-like () 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
Y is Relation-like Function-like 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
L is Relation-like Function-like () set
proj1 L is () () () set
B is Relation-like Function-like () set
proj1 B is () () () set
[L,(proj1 L)] is V14() set
{L,(proj1 L)} is non empty set
{L} is non empty functional set
{{L,(proj1 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
B is Relation-like Function-like () set
proj1 B is () () () set
A is Relation-like Function-like () set
proj1 A is () () () set
A is Relation-like Function-like () 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
A2 is Relation-like Function-like () set
proj1 A2 is () () () set
B is () () () set
a is () () () set
A is Relation-like Function-like () set
A2 | a is Relation-like proj2 A2 -valued Function-like () set
proj2 A2 is set
A2 . a is set
F₂(A) is set
a is Relation-like Function-like () set
proj1 a is () () () set
A is () () () set
L is Relation-like Function-like () set
a | A is Relation-like proj2 a -valued Function-like () set
proj2 a is set
a . A is set
F₂(L) is set
Y is Relation-like Function-like 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
A2 is Relation-like Function-like () set
proj1 A2 is () () () set
B is () () () set
a is Relation-like Function-like () set
proj1 a is () () () set
A is () () () set
a . A is set
a | A is Relation-like proj2 a -valued Function-like () 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
A2 is Relation-like Function-like () set
F₂(A2) is set
x is set
B is Relation-like Function-like () set
Y . x is set
y is set
F₂(B) is set
a is Relation-like Function-like () set
A2 is set
F₂(a) is set
x is Relation-like Function-like set
proj1 x is set
y is Relation-like Function-like () set
proj1 y is () () () set
A2 is () () () set
y . A2 is set
y | A2 is Relation-like proj2 y -valued Function-like () set
proj2 y is set
F₂((y | A2)) is set
Y . A2 is set
x . A2 is set
B is Relation-like Function-like () 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
L is Relation-like Function-like () set
B | a is Relation-like proj2 B -valued Function-like () set
proj2 B is set
proj1 L is () () () set
B is () () () set
B | B is Relation-like proj2 B -valued Function-like () set
L | B is Relation-like proj2 L -valued Function-like () 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
B | A is Relation-like proj2 B -valued Function-like () set
(y | A2) . A is set
y . A is set
x . A is set
(y | A2) . a is set
B . a is set
L is Relation-like Function-like () set
F₂(L) is set
proj1 (y | A2) is () () () set
X is Relation-like Function-like () set
proj1 X is () () () set
Y is () () () set
X | Y is Relation-like proj2 X -valued Function-like () set
proj2 X is set
X . Y is set
x is Relation-like Function-like () set
F₂(x) is set
F₁() is Relation-like Function-like () set
proj1 F₁() is () () () set
F₂((proj1 F₁())) is set
X is Relation-like Function-like () set
F₃(X) is set
proj1 X is () () () set
Y is set
proj2 X is set
x is () () () set
X | x is Relation-like proj2 X -valued Function-like () set
F₃((X | x)) is set
y is Relation-like proj2 X -valued Function-like () set
F₃(y) is set
proj1 y is () () () set
A2 is () () () set
X | A2 is Relation-like proj2 X -valued Function-like () set
y | A2 is Relation-like proj2 X -valued proj2 y -valued Function-like () 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
y is Relation-like proj2 X -valued Function-like () 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
X is Relation-like Function-like 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