:: TOLER_1 semantic presentation

{} is Relation-like non-empty empty-yielding empty set

X 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

field {} is set

dom {} is Relation-like non-empty empty-yielding empty set

rng {} is Relation-like non-empty empty-yielding empty set

(dom {}) \/ (rng {}) 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

X is Relation-like set

T is set

X |_2 T is Relation-like set

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

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

bool [:T,T:] is non empty set

X is set

nabla X is Relation-like X -defined X -valued reflexive symmetric transitive total Element of bool [:X,X:]

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

bool [:X,X:] is non empty set

rng (nabla X) 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

nabla X is Relation-like X -defined X -valued reflexive symmetric transitive total Element of bool [:X,X:]

[: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

nabla X is Relation-like X -defined X -valued reflexive symmetric transitive total Element of bool [:X,X:]

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

bool [:X,X:] is non empty set

field (nabla X) is set

dom (nabla X) is set

rng (nabla X) is set

(dom (nabla X)) \/ (rng (nabla X)) 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

nabla X is Relation-like X -defined X -valued reflexive symmetric transitive total Element of bool [:X,X:]

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

bool [:X,X:] is non empty set

T is set

field (nabla X) is set

dom (nabla X) is set

rng (nabla X) is set

(dom (nabla X)) \/ (rng (nabla 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

X is set

nabla X is Relation-like X -defined X -valued reflexive symmetric transitive total Element of bool [:X,X:]

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

bool [:X,X:] is non empty set

T is set

field (nabla X) is set

dom (nabla X) is set

rng (nabla X) is set

(dom (nabla X)) \/ (rng (nabla 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

X is set

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

bool [:X,X:] is non empty set

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

x is Relation-like X -defined X -valued reflexive total Element of bool [:X,X:]

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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 is Relation-like X -defined T -valued Element of bool [:X,T:]

(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

y /\ [:x,x:] is Relation-like X -defined T -valued 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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

x is Element of bool X

T |_2 x is Relation-like set

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

T /\ [:x,x:] is Relation-like X -defined X -valued 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 is Relation-like T -defined T -valued reflexive symmetric total Element of bool [:T,T:]

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

x /\ [:X,X:] is Relation-like T -defined T -valued set

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 /\ [:y,y:] is Relation-like T -defined T -valued set

X is set

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

bool [:X,X:] is non empty set

T is Relation-like X -defined X -valued reflexive symmetric total 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

X is set

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

bool [:X,X:] is non empty set

T is Relation-like X -defined X -valued reflexive symmetric total 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

X is set

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

bool [:X,X:] is non empty set

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

X is set

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

bool [:X,X:] is non empty set

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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)

c

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

c

y is set

[c

{c

{c

{{c

[y,c

{y,c

{y} is non empty set

{{y,c

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

[:{},{}:] is Relation-like set

bool [:{},{}:] is non empty set

X is set

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

bool [:X,X:] is non empty set

T is Relation-like X -defined X -valued reflexive symmetric total 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 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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

x is Relation-like T -defined T -valued reflexive symmetric total Element of bool [:T,T:]

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

c

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

T is Relation-like X -defined X -valued reflexive symmetric total 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 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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

nabla X is Relation-like X -defined X -valued reflexive symmetric transitive total Element of bool [:X,X:]

T is Relation-like X -defined X -valued reflexive symmetric total 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

X is set

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

bool [:X,X:] is non empty set

id X is Relation-like X -defined X -valued reflexive symmetric antisymmetric transitive total Element of bool [:X,X:]

T is Relation-like X -defined X -valued reflexive symmetric total 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

F

[:F

bool [:F

X is set

T is set

T is Relation-like F

field T is set

dom T is set

rng T is set

(dom T) \/ (rng T) is set

F

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 F

bool F

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 F

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

[:(union X),(union X):] is Relation-like set

bool [:(union X),(union X):] is non empty set

T is set

x is set

T is set

x is set

y is set

T is Relation-like union X -defined union X -valued reflexive symmetric total Element of bool [:(union X),(union 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 set

union X is set

[:(union X),(union X):] is Relation-like set

bool [:(union X),(union X):] is non empty set

T is Relation-like union X -defined union X -valued reflexive symmetric total Element of bool [:(union X),(union X):]

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

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

x is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

x is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

x is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

x is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

(X,T) is set

x is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

(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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

(X,T) is set

x is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

(X,x) is set

y is set

X is set

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

bool [:X,X:] is non empty set

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

(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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

(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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

(X,T) is set

x is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

(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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

(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

T is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

x is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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 is Relation-like X -defined X -valued reflexive symmetric total Element of bool [:X,X:]

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