:: TOLER_1 semantic presentation

T is set
[T,T] is set
{T,T} is non empty set
{T} is non empty set
{{T,T},{T}} is non empty set

() \/ () is Relation-like set
T is set
[T,T] is set
{T,T} is non empty set
{T} is non empty set
{{T,T},{T}} is non empty set
T is set
field X is set
dom X is set
rng X is set
(dom X) \/ (rng X) is set
x is set
[T,x] is set
{T,x} is non empty set
{T} is non empty set
{{T,x},{T}} is non empty set
[x,T] is set
{x,T} is non empty set
{x} is non empty set
{{x,T},{x}} is non empty set
T is set
x is set
[T,x] is set
{T,x} is non empty set
{T} is non empty set
{{T,x},{T}} is non empty set
[x,T] is set
{x,T} is non empty set
{x} is non empty set
{{x,T},{x}} is non empty set
T is set
x is set
[T,x] is set
{T,x} is non empty set
{T} is non empty set
{{T,x},{T}} is non empty set
[x,T] is set
{x,T} is non empty set
{x} is non empty set
{{x,T},{x}} is non empty set
T is set
x is set
[T,x] is set
{T,x} is non empty set
{T} is non empty set
{{T,x},{T}} is non empty set
[x,T] is set
{x,T} is non empty set
{x} is non empty set
{{x,T},{x}} is non empty set
T is set
x is set
[T,x] is set
{T,x} is non empty set
{T} is non empty set
{{T,x},{T}} is non empty set
[x,T] is set
{x,T} is non empty set
{x} is non empty set
{{x,T},{x}} is non empty set
T is set
x is set
[T,x] is set
{T,x} is non empty set
{T} is non empty set
{{T,x},{T}} is non empty set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
[T,y] is set
{T,y} is non empty set
{{T,y},{T}} is non empty set

T is set

[:T,T:] is Relation-like set
X /\ [:T,T:] is Relation-like set
bool [:T,T:] is non empty set
X is set

[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
rng () is Element of bool X
bool X is non empty set
T is set
[T,T] is set
{T,T} is non empty set
{T} is non empty set
{{T,T},{T}} is non empty set
x is set
[x,T] is set
{x,T} is non empty set
{x} is non empty set
{{x,T},{x}} is non empty set
X is set

[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
T is set
x is set
[T,x] is set
{T,x} is non empty set
{T} is non empty set
{{T,x},{T}} is non empty set
X is set

[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
field () is set
dom () is set
rng () is set
(dom ()) \/ (rng ()) is set
T is set
x is set
[T,x] is set
{T,x} is non empty set
{T} is non empty set
{{T,x},{T}} is non empty set
X is set

[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
T is set
field () is set
dom () is set
rng () is set
(dom ()) \/ (rng ()) is set
x is set
[T,x] is set
{T,x} is non empty set
{T} is non empty set
{{T,x},{T}} is non empty set
[x,T] is set
{x,T} is non empty set
{x} is non empty set
{{x,T},{x}} is non empty set
X is set

[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
T is set
field () is set
dom () is set
rng () is set
(dom ()) \/ (rng ()) is set
x is set
[T,x] is set
{T,x} is non empty set
{T} is non empty set
{{T,x},{T}} is non empty set
[x,T] is set
{x,T} is non empty set
{x} is non empty set
{{x,T},{x}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

rng T is Element of bool X
bool X is non empty set
x is set
field T is set
dom T is set
rng T is set
(dom T) \/ (rng T) is set
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
T is set
[T,T] is set
{T,T} is non empty set
{T} is non empty set
{{T,T},{T}} is non empty set

field x is set
dom x is set
rng x is set
(dom x) \/ (rng x) is set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

field T is set
dom T is set
rng T is set
(dom T) \/ (rng T) is set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

field T is set
dom T is set
rng T is set
(dom T) \/ (rng T) is set
X is set
T is set
[:X,T:] is Relation-like set
bool [:X,T:] is non empty set
x is set

(y,x) is Relation-like x -defined x -valued Element of bool [:x,x:]
[:x,x:] is Relation-like set
bool [:x,x:] is non empty set

field y is set
dom y is set
rng y is set
(dom y) \/ (rng y) is set
y is set
field (y,x) is set
dom (y,x) is set
rng (y,x) is set
(dom (y,x)) \/ (rng (y,x)) is set
x is set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
bool X is non empty set

x is Element of bool X

[:x,x:] is Relation-like set

bool [:x,x:] is non empty set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
(T,x) is Relation-like x -defined x -valued Element of bool [:x,x:]
dom (T,x) is Element of bool x
bool x is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
T is set
[:T,T:] is Relation-like set
bool [:T,T:] is non empty set

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

bool T is non empty set
y is Element of bool T
(T,x,y) is Relation-like y -defined y -valued reflexive symmetric total Element of bool [:y,y:]
[:y,y:] is Relation-like set
bool [:y,y:] is non empty set

X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

bool X is non empty set
x is set
y is set
y is set
union y is set
y is set
x is set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
y is set
y is set
z is (X,T)
c8 is (X,T)
union (bool X) is set
y is set
y is set
y is (X,T)
x is set
{x} is non empty set
y \/ {x} is non empty set
c8 is set
y is set
[c8,y] is set
{c8,y} is non empty set
{c8} is non empty set
{{c8,y},{c8}} is non empty set
[y,c8] is set
{y,c8} is non empty set
{y} is non empty set
{{y,c8},{y}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

y is set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
x is (X,T) (X,T)
x is set
[y,x] is set
{y,x} is non empty set
{{y,x},{y}} is non empty set

bool is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
y is set
x is set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
{x} is non empty set
[x,x] is set
{x,x} is non empty set
{{x,x},{x}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
y is set
x /\ y is set
y is set
x is set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
X is set
T is set
[:T,T:] is Relation-like set
bool [:T,T:] is non empty set

y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is (X,T)
bool X is non empty set
y is set
y is set
x is set
y is set
y is set
union y is set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
c8 is set
z is set
Zx is (X,T)
y is (X,T)
the Element of y is Element of y
y is set
union (bool X) is set
x is set
the Element of y is Element of y
y is set
x is set
y is set
y is set
x is (X,T)
y is set
{y} is non empty set
x \/ {y} is non empty set
y is set
z is set
[y,z] is set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
[z,y] is set
{z,y} is non empty set
{z} is non empty set
{{z,y},{z}} is non empty set
y is (X,T) (X,T)
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
y is set
x is set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
y is (X,T)
x is (X,T) (X,T)
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
y is (X,T) (X,T)
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
F1() is set
[:F1(),F1():] is Relation-like set
bool [:F1(),F1():] is non empty set
X is set
T is set
T is Relation-like F1() -defined F1() -valued Element of bool [:F1(),F1():]
field T is set
dom T is set
rng T is set
(dom T) \/ (rng T) is set
F1() \/ F1() is set
x is set
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
y is set
x is set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
dom T is Element of bool F1()
bool F1() is non empty set
x is set
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
x is Relation-like F1() -defined F1() -valued reflexive symmetric total Element of bool [:F1(),F1():]
y is set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
X is set
union X is set
[:(),():] is Relation-like set
bool [:(),():] is non empty set
T is set
x is set
T is set
x is set
y is set

x is set
y is set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
X is set
union X is set
[:(),():] is Relation-like set
bool [:(),():] is non empty set

y is set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
x is set
x is set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

y is set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
x is (X,T) (X,T)
y is (X,x) (X,x)
x is (X,x) (X,x)
y is (X,T) (X,T)
X is set
T is set
[:X,T:] is Relation-like set
bool [:X,T:] is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
T is set

Im (x,T) is set
{T} is non empty set
x .: {T} is set
y is set
[T,y] is set
{T,y} is non empty set
{{T,y},{T}} is non empty set
[y,T] is set
{y,T} is non empty set
{y} is non empty set
{{y,T},{y}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
T is set

Im (x,T) is set
{T} is non empty set
x .: {T} is set
y is set
union y is set
y is set
[T,y] is set
{T,y} is non empty set
{{T,y},{T}} is non empty set
x is (X,x) (X,x)
x is set
y is (X,x) (X,x)
[T,y] is set
{T,y} is non empty set
{{T,y},{T}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
T is set

Im (x,T) is set
{T} is non empty set
x .: {T} is set
y is set
union y is set
y is set
[T,y] is set
{T,y} is non empty set
{{T,y},{T}} is non empty set
x is (X,x) (X,x)
x is set
y is (X,x)
[T,y] is set
{T,y} is non empty set
{{T,y},{T}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

bool X is non empty set
x is set
y is set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
x is set
y is set
bool X is non empty set
x is set
y is set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
x is set
y is set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

(X,T) is set

(X,x) is set
y is set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
x is (X,T) (X,T)
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

(X,T) is set

(X,x) is set
y is set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

(X,T) is set
union (X,T) is set
x is set
y is set
y is (X,T) (X,T)
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

(X,T) is set
union (X,T) is set
x is set
y is set
y is (X,T) (X,T)
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

field T is set
dom T is set
rng T is set
(dom T) \/ (rng T) is set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
[x,y] is set
{x,y} is non empty set
{{x,y},{x}} is non empty set
Im (T,y) is set
T .: {y} is set
[y,x] is set
{y,x} is non empty set
{{y,x},{y}} is non empty set
x is (X,T)
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
Im (T,x) is set
{x} is non empty set
T .: {x} is set
Class (T,x) is Element of bool X
bool X is non empty set
field T is set
dom T is set
rng T is set
(dom T) \/ (rng T) is set
y is set
x is set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
[x,y] is set
{x,y} is non empty set
{{x,y},{x}} is non empty set
[y,x] is set
{y,x} is non empty set
{{y,x},{y}} is non empty set
[x,x] is set
{x,x} is non empty set
{{x,x},{x}} is non empty set
y is (X,T)
x is set
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
[x,x] is set
{x,x} is non empty set
{{x,x},{x}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

x is set
Im (T,x) is set
{x} is non empty set
T .: {x} is set
y is (X,T) (X,T)
y is set
[x,y] is set
{x,y} is non empty set
{{x,y},{x}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

(X,T) is set

(X,x) is set
y is set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
x is (X,T) (X,T)
y is set
y is (X,T)
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

(X,T) is set
(X,T) is set
x is set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

y is set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
Im (T,y) is set
T .: {y} is set
Im (x,y) is set
x .: {y} is set
X is set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set

T * T is Relation-like X -defined X -valued Element of bool [:X,X:]
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set