:: RELSET_1 semantic presentation

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

the empty Relation-like non-empty empty-yielding set is empty Relation-like non-empty empty-yielding set

X is set

Y is set

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

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

X is Relation-like Element of bool [:X,Y:]

X is set

Y is set

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

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

X is Relation-like Element of bool [:X,Y:]

dom X is set

P is set

b is set

[P,b] is set

{P,b} is non empty set

{P} is non empty set

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

P is set

rng X is set

b is set

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

X is set

Y is set

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

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

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

P is set

b is Element of X

y is Element of Y

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

b is set

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

b is Element of X

c

[b,c

{b,c

{b} is non empty set

{{b,c

X is set

Y is set

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

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

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

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

b is Element of X

y is Element of Y

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

b is Element of X

c

[b,c

{b,c

{b} is non empty set

{{b,c

b is set

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

b is Element of X

c

[b,c

{b,c

{b} is non empty set

{{b,c

b is Element of X

c

[b,c

{b,c

{b} is non empty set

{{b,c

Y is set

X is set

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

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

X is set

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

X is set

Y is set

X is set

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

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

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

b is set

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

X is set

Y 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,X]} is non empty Relation-like set

P is set

[:Y,P:] is Relation-like set

bool [:Y,P:] is non empty set

X is set

Y is set

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

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

X is Relation-like set

dom X is set

rng X is set

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

X is set

Y is set

X is set

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

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

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

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

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

dom P is set

rng P is set

[:(dom P),(rng P):] is Relation-like set

X is set

Y is set

X is set

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

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

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

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

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

rng P is set

dom P is set

[:(dom P),(rng P):] is Relation-like set

X is set

Y is set

X is set

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

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

P is set

[:Y,P:] is Relation-like set

bool [:Y,P:] is non empty set

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

X is set

Y is Relation-like X -defined set

X is Relation-like X -defined set

Y \/ X is Relation-like set

dom (Y \/ X) is set

dom Y is set

dom X is set

(dom Y) \/ (dom X) is set

X is set

Y is Relation-like X -defined set

X is Relation-like set

Y /\ X is Relation-like set

dom Y is set

dom (Y /\ X) is set

Y \ X is Relation-like X -defined Element of bool Y

bool Y is non empty set

X is set

Y is Relation-like X -valued set

X is Relation-like X -valued set

Y \/ X is Relation-like set

rng (Y \/ X) is set

rng Y is set

rng X is set

(rng Y) \/ (rng X) is set

X is set

Y is Relation-like X -valued set

X is Relation-like set

Y /\ X is Relation-like set

rng Y is set

rng (Y /\ X) is set

Y \ X is Relation-like X -valued Element of bool Y

bool Y is non empty set

X is set

Y is Relation-like X -defined set

dom Y is set

bool X is non empty set

X is set

Y is Relation-like X -valued set

rng Y is set

bool X is non empty set

X is set

Y is set

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

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

X \/ Y is set

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

field X is set

dom X is set

rng X is set

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

(X,X) is Element of bool X

bool X is non empty set

(Y,X) is Element of bool Y

bool Y is non empty set

(X,X) \/ (Y,X) is set

X is set

Y is set

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

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

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

(Y,X) is Element of bool Y

bool Y is non empty set

P is set

b is set

[P,b] is set

{P,b} is non empty set

{P} is non empty set

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

P is set

X is set

Y is set

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

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

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

(Y,X) is Element of bool Y

bool Y is non empty set

P is set

b is set

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

P is set

X is set

Y is set

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

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

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

X ~ is Relation-like set

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

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

P is set

b is set

[P,b] is set

{P,b} is non empty set

{P} is non empty set

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

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

X is set

Y is set

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

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

X is set

P is set

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

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

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

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

b * y is Relation-like X -defined P -valued set

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

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

b is set

c

[b,c

{b,c

{b} is non empty set

{{b,c

a is set

[b,a] is set

{b,a} is non empty set

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

[a,c

{a,c

{a} is non empty set

{{a,c

X is set

Y is set

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

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

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

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

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

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

(Y,(X,Y,X)) is Element of bool Y

bool Y is non empty set

(Y,X) is Element of bool Y

(X,(X,Y,X)) is Element of bool X

bool X is non empty set

(X,X) is Element of bool X

P is set

b is set

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

[P,b] is set

{P,b} is non empty set

{P} is non empty set

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

b is set

[P,b] is set

{P,b} is non empty set

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

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

P is set

b is set

[P,b] is set

{P,b} is non empty set

{P} is non empty set

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

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

b is set

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

[P,b] is set

{P,b} is non empty set

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

X is set

Y is set

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

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

X is empty Relation-like non-empty empty-yielding set

Y is set

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

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

X is empty Relation-like non-empty empty-yielding X -defined Y -valued Element of bool [:X,Y:]

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

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

X is empty Relation-like non-empty empty-yielding Y -defined X -valued Element of bool [:Y,X:]

X is set

id X is Relation-like X -defined X -valued set

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

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

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

X is set

P is set

[X,P] is set

{X,P} is non empty set

{X} is non empty set

{{X,P},{X}} is non empty set

X is set

id X is Relation-like X -defined X -valued set

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

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

X is set

Y is set

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

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

X is set

id X is Relation-like X -defined X -valued set

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

(X,P) is Element of bool X

bool X is non empty set

(Y,P) is Element of bool Y

bool Y is non empty set

b is set

[b,b] is set

{b,b} is non empty set

{b} is non empty set

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

b is set

[b,b] is set

{b,b} is non empty set

{b} is non empty set

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

X is set

Y is set

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

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

id Y is Relation-like Y -defined Y -valued set

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

(Y,X) is Element of bool Y

bool Y is non empty set

(X,X) is Element of bool X

bool X is non empty set

X is set

Y is set

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

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

id Y is Relation-like Y -defined Y -valued set

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

(X,X) is Element of bool X

bool X is non empty set

(Y,X) is Element of bool Y

bool Y is non empty set

X is set

Y is set

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

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

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

P is set

X | P is Relation-like P -defined X -defined Y -valued set

b is set

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

X is set

Y is set

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

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

X is set

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

X |` P is Relation-like X -defined X -valued Y -valued set

b is set

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

{{b,y},{b}} 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

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

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

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

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

b is set

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

X is set

Y is set

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

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

X is set

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

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

b is set

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

{{b,y},{b}} 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,Y:] is Relation-like set

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

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

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

b is set

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

X is set

Y is set

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

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

X is set

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

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

b is set

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

X is set

Y is set

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

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

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

P is set

X .: P is set

bool Y is non empty set

(Y,X) is Element of bool Y

X " P is set

bool X is non empty set

(X,X) is Element of bool X

X is set

Y is set

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

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

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

(X,Y,X,X) is Element of bool Y

bool Y is non empty set

(Y,X) is Element of bool Y

(X,Y,X,Y) is Element of bool X

bool X is non empty set

(X,X) is Element of bool X

P is set

b is set

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

b is set

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

P is set

b is set

[P,b] is set

{P,b} is non empty set

{P} is non empty set

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

b is set

[P,b] is set

{P,b} is non empty set

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

X is set

Y is set

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

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

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

(Y,X,X,X) is Element of bool Y

bool Y is non empty set

(Y,X,X,(Y,X,X,X)) is Element of bool X

bool X is non empty set

(X,X) is Element of bool X

(Y,X,X,Y) is Element of bool X

(Y,X,X,(Y,X,X,Y)) is Element of bool Y

(Y,X) is Element of bool Y

F

F

[:F

bool [:F

X is Relation-like 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 Relation-like F

X is set

P is set

[X,P] is set

{X,P} is non empty set

{X} is non empty set

{{X,P},{X}} is non empty set

b is set

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

X is non empty set

id X is Relation-like X -defined X -valued set

the Element of X is Element of X

[ the Element of X, the Element of X] is set

{ the Element of X, the Element of X} is non empty set

{ the Element of X} is non empty set

{{ the Element of X, the Element of X},{ the Element of X}} is non empty set

X is non empty set

Y is non empty set

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

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

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

(X,X) is Element of bool X

bool X is non empty set

P is Element of X

b is set

[P,b] is set

{P,b} is non empty set

{P} is non empty set

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

y is Element of Y

[P,y] is set

{P,y} is non empty set

{{P,y},{P}} is non empty set

b is Element of Y

[P,b] is set

{P,b} is non empty set

{P} is non empty set

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

X is non empty set

Y is non empty set

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

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

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

(X,X) is Element of bool X

bool X is non empty set

P is set

b is set

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

y is Element of Y

[y,P] is set

{y,P} is non empty set

{y} is non empty set

{{y,P},{y}} is non empty set

b is Element of Y

[b,P] is set

{b,P} is non empty set

{b} is non empty set

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

X is non empty set

Y is non empty set

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

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

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

(X,X) is Element of bool X

bool X is non empty set

(Y,X) is Element of bool Y

bool Y is non empty set

P is set

X is non empty set

Y is non empty set

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

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

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

(X,X) is Element of bool X

bool X is non empty set

(Y,X) is Element of bool Y

bool Y is non empty set

P is set

X is non empty set

Y is non empty set

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

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

X is non empty set

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

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

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

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

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

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

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

y is set

b is set

[y,b] is set

{y,b} is non empty set

{y} is non empty set

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

c

[y,c

{y,c

{{y,c

[c

{c

{c

{{c

a is Element of Y

[y,a] is set

{y,a} is non empty set

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

[a,b] is set

{a,b} is non empty set

{a} is non empty set

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

c

[y,c

{y,c

{{y,c

[c

{c

{c

{{c

X is non empty set

Y is non empty set

X is non empty set

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

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

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

(X,X,P,Y) is Element of bool X

bool X is non empty set

b is Element of X

y is set

[y,b] is set

{y,b} is non empty set

{y} is non empty set

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

b is Element of X

[b,b] is set

{b,b} is non empty set

{b} is non empty set

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

y is Element of X

[y,b] is set

{y,b} is non empty set

{y} is non empty set

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

X is non empty set

Y is non empty set

X is non empty set

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

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

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

(X,X,P,Y) is Element of bool X

bool X is non empty set

b is Element of X

y is set

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

b is Element of X

[b,b] is set

{b,b} is non empty set

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

y is Element of X

[b,y] is set

{b,y} is non empty set

{b} is non empty set

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

F

F

[:F

bool [:F

X is Relation-like F

Y is Element of F

X is Element of F

[Y,X] is set

{Y,X} is non empty set

{Y} is non empty set

{{Y,X},{Y}} is non empty set

P is Element of F

b is Element of F

[P,b] is set

{P,b} is non empty set

{P} is non empty set

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

F

bool F

F

[:F

bool [:F

X is Relation-like F

Y is Element of F

Im (X,Y) is set

{Y} is non empty set

X .: {Y} is set

F

X is set

P is set

[P,X] is set

{P,X} is non empty set

{P} is non empty set

{{P,X},{P}} is non empty set

X is set

[Y,X] is set

{Y,X} 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

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

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

P is Element of X

b is Element of X

[P,b] is set

{P,b} is non empty set

{P} is non empty set

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

(X,Y) is Element of bool X

bool X is non empty set

Im (Y,P) is set

Y .: {P} is set

Im (X,P) is set

X .: {P} is set

y is set

[y,b] is set

{y,b} is non empty set

{y} is non empty set

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

(X,X) is Element of bool X

bool X is non empty set

Im (X,P) is set

X .: {P} is set

Im (Y,P) is set

Y .: {P} is set

y is set

[y,b] is set

{y,b} is non empty set

{y} is non empty set

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

F

F

[:F

bool [:F

F

F

X is Element of F

Y is Element of F

[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

Y is set

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

X is set

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

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

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

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

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

X is set

Y is set

X is set

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

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

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

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

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

bool [:Y,X:] 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

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

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

(X,P) is Element of bool X

bool X is non empty set

X is non empty Relation-like set

dom X is non empty set

bool (dom X) is non empty set

Y is non empty Element of bool (dom X)

X | Y is Relation-like set

dom (X | Y) is set

X is non empty Relation-like set

dom X is non empty set

bool (dom X) is non empty set

Y is non empty Element of bool (dom X)

X .: Y is set

X | Y is non empty Relation-like set

rng (X | Y) is non empty set

X is set

Y is set

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

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