:: RELAT_1 semantic presentation

{} is empty trivial set

the empty trivial set is empty trivial set

X is set

R is set

X is () set

bool X is set

R is Element of bool X

R is set

F

F

[:F

X is set

R is set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

X is () set

X is () set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is () set

R is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

z is set

c is set

[z,c] is non empty V4() set

{z,c} is non empty set

{z} is non empty trivial set

{{z,c},{z}} is non empty set

R is set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

R is set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is () set

R is set

X /\ R is set

X \ R is () Element of bool X

bool X is set

X is () set

R is () set

X \/ R is set

R is set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

c is set

x is set

[c,x] is non empty V4() set

{c,x} is non empty set

{c} is non empty trivial set

{{c,x},{c}} is non empty set

X is () set

R is () set

X \+\ R is set

X \ R is () set

R \ X is () set

(X \ R) \/ (R \ X) is () set

X is set

R is set

[X,R] is non empty V4() set

{X,R} is non empty set

{X} is non empty trivial set

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

{[X,R]} is non empty trivial set

R is set

[:X,R:] is set

R is set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is set

[X,R] is non empty V4() set

{X,R} is non empty set

{X} is non empty trivial set

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

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

{[X,R],[R,y]} is non empty set

{[X,R]} is non empty trivial () set

{[R,y]} is non empty trivial () set

{[X,R]} \/ {[R,y]} is non empty () set

X is () set

R is set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

R is set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is () set

R is () set

X \/ R is () set

proj1 (X \/ R) is set

proj1 X is set

proj1 R is set

(proj1 X) \/ (proj1 R) is set

X is () set

R is () set

X /\ R is () set

proj1 (X /\ R) is set

proj1 X is set

proj1 R is set

(proj1 X) /\ (proj1 R) is set

X is () set

proj1 X is set

R is () set

proj1 R is set

(proj1 X) \ (proj1 R) is Element of bool (proj1 X)

bool (proj1 X) is set

X \ R is () Element of bool X

bool X is set

proj1 (X \ R) is set

X is () set

proj1 X is set

proj2 X is set

[:(proj1 X),(proj2 X):] is () set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

X is () set

proj1 X is set

proj2 X is set

[:(proj1 X),(proj2 X):] is () set

X /\ [:(proj1 X),(proj2 X):] is () set

X is set

{X} is non empty trivial set

R is set

[X,R] is non empty V4() set

{X,R} is non empty set

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

{[X,R]} is non empty trivial () set

{R} is non empty trivial set

R is () set

proj1 R is set

proj2 R is set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

y is set

z is set

[z,y] is non empty V4() set

{z,y} is non empty set

{z} is non empty trivial set

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

[X,y] is non empty V4() set

{X,y} is non empty set

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

X is set

R is set

[X,R] is non empty V4() set

{X,R} is non empty set

{X} is non empty trivial set

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

R is set

{X,R} is non empty set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

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

{R,y} is non empty set

z is () set

proj1 z is set

proj2 z is set

c is set

x is set

[c,x] is non empty V4() set

{c,x} is non empty set

{c} is non empty trivial set

{{c,x},{c}} is non empty set

c is set

[c,R] is non empty V4() set

{c,R} is non empty set

{c} is non empty trivial set

{{c,R},{c}} is non empty set

[c,y] is non empty V4() set

{c,y} is non empty set

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

c is set

x is set

[x,c] is non empty V4() set

{x,c} is non empty set

{x} is non empty trivial set

{{x,c},{x}} is non empty set

c is set

[X,c] is non empty V4() set

{X,c} is non empty set

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

[R,c] is non empty V4() set

{R,c} is non empty set

{{R,c},{R}} is non empty set

X is () set

R is () set

proj1 X is set

proj1 R is set

proj2 X is set

proj2 R is set

X is () set

R is () set

X \/ R is () set

proj2 (X \/ R) is set

proj2 X is set

proj2 R is set

(proj2 X) \/ (proj2 R) is set

X is () set

R is () set

X /\ R is () set

proj2 (X /\ R) is set

proj2 X is set

proj2 R is set

(proj2 X) /\ (proj2 R) is set

X is () set

proj2 X is set

R is () set

proj2 R is set

(proj2 X) \ (proj2 R) is Element of bool (proj2 X)

bool (proj2 X) is set

X \ R is () Element of bool X

bool X is set

proj2 (X \ R) is set

X is () set

proj1 X is set

proj2 X is set

(proj1 X) \/ (proj2 X) is set

X is set

R is set

[X,R] is non empty V4() set

{X,R} is non empty set

{X} is non empty trivial set

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

R is () set

(R) is set

proj1 R is set

proj2 R is set

(proj1 R) \/ (proj2 R) is set

X is () set

(X) is set

proj1 X is set

proj2 X is set

(proj1 X) \/ (proj2 X) is set

R is () set

(R) is set

proj1 R is set

proj2 R is set

(proj1 R) \/ (proj2 R) is set

X is set

R is set

[X,R] is non empty V4() set

{X,R} is non empty set

{X} is non empty trivial set

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

{[X,R]} is non empty trivial () set

({[X,R]}) is set

proj1 {[X,R]} is set

proj2 {[X,R]} is set

(proj1 {[X,R]}) \/ (proj2 {[X,R]}) is set

{R} is non empty trivial set

X is () set

(X) is set

proj1 X is set

proj2 X is set

(proj1 X) \/ (proj2 X) is set

R is () set

X \/ R is () set

((X \/ R)) is set

proj1 (X \/ R) is set

proj2 (X \/ R) is set

(proj1 (X \/ R)) \/ (proj2 (X \/ R)) is set

(R) is set

proj1 R is set

proj2 R is set

(proj1 R) \/ (proj2 R) is set

(X) \/ (R) is set

(proj1 X) \/ (proj1 R) is set

((proj1 X) \/ (proj1 R)) \/ (proj2 (X \/ R)) is set

(proj2 X) \/ (proj2 R) is set

((proj1 X) \/ (proj1 R)) \/ ((proj2 X) \/ (proj2 R)) is set

((proj1 X) \/ (proj1 R)) \/ (proj2 X) is set

(((proj1 X) \/ (proj1 R)) \/ (proj2 X)) \/ (proj2 R) is set

(X) \/ (proj1 R) is set

((X) \/ (proj1 R)) \/ (proj2 R) is set

X is () set

(X) is set

proj1 X is set

proj2 X is set

(proj1 X) \/ (proj2 X) is set

R is () set

X /\ R is () set

((X /\ R)) is set

proj1 (X /\ R) is set

proj2 (X /\ R) is set

(proj1 (X /\ R)) \/ (proj2 (X /\ R)) is set

(R) is set

proj1 R is set

proj2 R is set

(proj1 R) \/ (proj2 R) is set

(X) /\ (R) is set

R is set

(proj1 X) /\ (proj1 R) is set

(proj2 X) /\ (proj2 R) is set

X is () set

proj2 X is set

proj1 X is set

R is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

R is () set

R is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

[z,y] is non empty V4() set

{z,y} is non empty set

{z} is non empty trivial set

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

R is () set

R is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

[z,y] is non empty V4() set

{z,y} is non empty set

{z} is non empty trivial set

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

x is set

c is set

[x,c] is non empty V4() set

{x,c} is non empty set

{x} is non empty trivial set

{{x,c},{x}} is non empty set

[c,x] is non empty V4() set

{c,x} is non empty set

{c} is non empty trivial set

{{c,x},{c}} is non empty set

X is () set

proj2 X is set

(X) is () set

proj1 (X) is set

proj1 X is set

proj2 (X) is set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

X is () set

(X) is set

proj1 X is set

proj2 X is set

(proj1 X) \/ (proj2 X) is set

(X) is () set

((X)) is set

proj1 (X) is set

proj2 (X) is set

(proj1 (X)) \/ (proj2 (X)) is set

(proj2 (X)) \/ (proj2 X) is set

X is () set

(X) is () set

R is () set

X /\ R is () set

((X /\ R)) is () set

(R) is () set

(X) /\ (R) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

X is () set

(X) is () set

R is () set

X \/ R is () set

((X \/ R)) is () set

(R) is () set

(X) \/ (R) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

X is () set

(X) is () set

R is () set

X \ R is () Element of bool X

bool X is set

((X \ R)) is () set

(R) is () set

(X) \ (R) is () Element of bool (X)

bool (X) is set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

X is set

R is set

proj1 X is set

proj2 R is set

R is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

R is () set

y is () set

z is set

c is set

[z,c] is non empty V4() set

{z,c} is non empty set

{z} is non empty trivial set

{{z,c},{z}} is non empty set

x is set

[z,x] is non empty V4() set

{z,x} is non empty set

{{z,x},{z}} is non empty set

[x,c] is non empty V4() set

{x,c} is non empty set

{x} is non empty trivial set

{{x,c},{x}} is non empty set

x is set

[z,x] is non empty V4() set

{z,x} is non empty set

{{z,x},{z}} is non empty set

[x,c] is non empty V4() set

{x,c} is non empty set

{x} is non empty trivial set

{{x,c},{x}} is non empty set

X is () set

proj1 X is set

R is () set

(X,R) is () set

proj1 (X,R) is set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

z is set

[R,z] is non empty V4() set

{R,z} is non empty set

{{R,z},{R}} is non empty set

[z,y] is non empty V4() set

{z,y} is non empty set

{z} is non empty trivial set

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

X is () set

R is () set

(X,R) is () set

proj2 (X,R) is set

proj2 R is set

R is set

y is set

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

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

[z,R] is non empty V4() set

{z,R} is non empty set

{z} is non empty trivial set

{{z,R},{z}} is non empty set

X is () set

proj2 X is set

proj1 X is set

R is () set

proj1 R is set

(X,R) is () set

proj1 (X,R) is set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

[R,z] is non empty V4() set

{R,z} is non empty set

{{R,z},{R}} is non empty set

X is () set

proj1 X is set

proj2 X is set

R is () set

proj2 R is set

(R,X) is () set

proj2 (R,X) is set

R is set

y is set

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

z is set

[z,y] is non empty V4() set

{z,y} is non empty set

{z} is non empty trivial set

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

[z,R] is non empty V4() set

{z,R} is non empty set

{{z,R},{z}} is non empty set

X is () set

R is () set

R is () set

(R,X) is () set

(R,R) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

X is () set

R is () set

R is () set

(X,R) is () set

(R,R) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

X is () set

R is () set

R is () set

(X,R) is () set

y is () set

(R,y) is () set

z is set

c is set

[z,c] is non empty V4() set

{z,c} is non empty set

{z} is non empty trivial set

{{z,c},{z}} is non empty set

x is set

[z,x] is non empty V4() set

{z,x} is non empty set

{{z,x},{z}} is non empty set

[x,c] is non empty V4() set

{x,c} is non empty set

{x} is non empty trivial set

{{x,c},{x}} is non empty set

X is () set

R is () set

(X,R) is () set

R is () set

R \/ R is () set

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

(X,R) is () set

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

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

X is () set

R is () set

(X,R) is () set

R is () set

R /\ R is () set

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

(X,R) is () set

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

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

X is () set

R is () set

(X,R) is () set

R is () set

(X,R) is () set

(X,R) \ (X,R) is () Element of bool (X,R)

bool (X,R) is set

R \ R is () Element of bool R

bool R is set

(X,(R \ R)) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

X is () set

(X) is () set

R is () set

(X,R) is () set

((X,R)) is () set

(R) is () set

((R),(X)) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

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

[z,R] is non empty V4() set

{z,R} is non empty set

{z} is non empty trivial set

{{z,R},{z}} is non empty set

[z,y] is non empty V4() set

{z,y} is non empty set

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

[R,z] is non empty V4() set

{R,z} is non empty set

{{R,z},{R}} is non empty set

z is set

[R,z] is non empty V4() set

{R,z} is non empty set

{{R,z},{R}} is non empty set

[z,y] is non empty V4() set

{z,y} is non empty set

{z} is non empty trivial set

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

[z,R] is non empty V4() set

{z,R} is non empty set

{{z,R},{z}} is non empty set

[y,z] is non empty V4() set

{y,z} is non empty set

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

X is () set

R is () set

(X,R) is () set

R is () set

((X,R),R) is () set

(R,R) is () set

(X,(R,R)) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

x is set

[y,x] is non empty V4() set

{y,x} is non empty set

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

[x,c] is non empty V4() set

{x,c} is non empty set

{x} is non empty trivial set

{{x,c},{x}} is non empty set

[x,z] is non empty V4() set

{x,z} is non empty set

{{x,z},{x}} is non empty set

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

x is set

[c,x] is non empty V4() set

{c,x} is non empty set

{{c,x},{c}} is non empty set

[x,z] is non empty V4() set

{x,z} is non empty set

{x} is non empty trivial set

{{x,z},{x}} is non empty set

[y,x] is non empty V4() set

{y,x} is non empty set

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

[{},{}] is non empty V4() set

{{},{}} is non empty set

{{}} is non empty trivial set

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

{[{},{}]} is non empty trivial () set

X is non empty () set

proj1 X is set

the Element of X is Element of X

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

proj2 X is set

the Element of X is Element of X

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

X is () set

the Element of X is Element of X

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

proj1 {} is empty trivial () set

proj2 {} is empty trivial () set

X is set

R is set

[X,R] is non empty V4() set

{X,R} is non empty set

{X} is non empty trivial set

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

R is set

[[X,R],R] is non empty V4() set

{[X,R],R} is non empty set

{[X,R]} is non empty trivial () set

{{[X,R],R},{[X,R]}} is non empty set

X is set

R is set

[X,R] is non empty V4() set

{X,R} is non empty set

{X} is non empty trivial set

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

R is set

[R,[X,R]] is non empty V4() set

{R,[X,R]} is non empty set

{R} is non empty trivial set

{{R,[X,R]},{R}} is non empty set

X is () set

({},X) is () set

(X,{}) is () set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

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

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

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

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

X is empty trivial () set

proj1 X is empty trivial () set

proj2 X is empty trivial () set

R is () set

(X,R) is () set

(R,X) is () set

({}) is set

(proj1 {}) \/ (proj2 {}) is () set

X is () set

proj1 X is set

proj2 X is set

X is () set

proj1 X is set

proj2 X is set

R is () set

proj2 R is set

proj1 R is set

X is empty trivial () set

(X) is () set

({}) is () set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

({}) is empty trivial () set

X is () set

proj2 X is set

R is () set

proj1 R is set

(X,R) is () set

(proj2 X) /\ (proj1 R) is set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

z is set

[R,z] is non empty V4() set

{R,z} is non empty set

{{R,z},{R}} is non empty set

[z,y] is non empty V4() set

{z,y} is non empty set

{z} is non empty trivial set

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

X is () set

R is () () set

(X,R) is () set

proj2 (X,R) is set

proj2 R is set

X is set

R is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

R is () set

R is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

(X) is () set

proj1 (X) is set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

proj2 (X) is set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

X is set

(X) is () set

proj1 (X) is set

R is set

(R) is () set

proj2 (R) is set

X is set

(X) is () set

((X)) is () set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

X is set

(X) is () set

((X)) is () set

X is set

(X) is () set

R is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

X is set

R is set

[X,R] is non empty V4() set

{X,R} is non empty set

{X} is non empty trivial set

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

R is set

(R) is () set

y is () set

((R),y) is () set

z is set

[X,z] is non empty V4() set

{X,z} is non empty set

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

[z,R] is non empty V4() set

{z,R} is non empty set

{z} is non empty trivial set

{{z,R},{z}} is non empty set

[X,X] is non empty V4() set

{X,X} is non empty set

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

X is set

R is set

[X,R] is non empty V4() set

{X,R} is non empty set

{X} is non empty trivial set

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

R is set

(R) is () set

y is () set

(y,(R)) is () set

z is set

[X,z] is non empty V4() set

{X,z} is non empty set

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

[z,R] is non empty V4() set

{z,R} is non empty set

{z} is non empty trivial set

{{z,R},{z}} is non empty set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

X is set

(X) is () set

R is () set

(R,(X)) is () set

((X),R) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

z is set

[R,z] is non empty V4() set

{R,z} is non empty set

{{R,z},{R}} is non empty set

[z,y] is non empty V4() set

{z,y} is non empty set

{z} is non empty trivial set

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

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

z is set

[R,z] is non empty V4() set

{R,z} is non empty set

{{R,z},{R}} is non empty set

[z,y] is non empty V4() set

{z,y} is non empty set

{z} is non empty trivial set

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

X is set

(X) is () set

R is () set

proj1 R is set

((X),R) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

[R,R] is non empty V4() set

{R,R} is non empty set

{{R,R},{R}} is non empty set

X is () set

proj1 X is set

((proj1 X)) is () set

(((proj1 X)),X) is () set

X is set

(X) is () set

R is () set

proj2 R is set

(R,(X)) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

[y,y] is non empty V4() set

{y,y} is non empty set

{y} is non empty trivial set

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

X is () set

proj2 X is set

((proj2 X)) is () set

(X,((proj2 X))) is () set

({}) is () set

proj1 ({}) is set

X is set

(X) is () set

R is () set

proj2 R is set

R is () set

(R,R) is () set

y is () set

proj1 y is set

((proj1 y)) is () set

(R,y) is () set

((R,R),y) is () set

(R,(R,y)) is () set

(((proj1 y)),y) is () set

R is set

X is () set

proj1 X is set

proj2 X is set

R is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

R is () set

y is () set

z is set

c is set

[z,c] is non empty V4() set

{z,c} is non empty set

{z} is non empty trivial set

{{z,c},{z}} is non empty set

X is () set

R is empty trivial () set

(X,R) is () set

(X,{}) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

X is set

R is set

R is () set

(R,R) is () set

proj1 (R,R) is set

proj1 R is set

y is set

[X,y] is non empty V4() set

{X,y} is non empty set

{X} is non empty trivial set

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

y is set

[X,y] is non empty V4() set

{X,y} is non empty set

{X} is non empty trivial set

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

X is set

R is () set

(R,X) is () set

proj1 (R,X) is set

R is set

X is set

R is () set

(R,X) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

X is set

R is () set

(R,X) is () set

proj1 (R,X) is set

proj1 R is set

R is set

X is set

R is () set

(R,X) is () set

proj1 (R,X) is set

proj1 R is set

(proj1 R) /\ X is set

R is set

X is set

R is () set

proj1 R is set

(R,X) is () set

proj1 (R,X) is set

(proj1 R) /\ X is set

R is () set

X is set

(R,X) is () set

R is () set

((R,X),R) is () set

(R,R) is () set

R is () set

R is () set

X is set

(R,X) is () set

(R,(R,X)) is () set

(R,R) is () set

X is set

(X) is () set

R is () set

(R,X) is () set

((X),R) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

X is set

R is () set

(R,X) is () set

proj1 R is set

(proj1 R) /\ X is set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

(proj1 R) /\ X is set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

X is set

R is () set

(R,X) is () set

proj2 R is set

[:X,(proj2 R):] is () set

R /\ [:X,(proj2 R):] is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is () set

proj1 R is set

(R,X) is () set

proj2 R is set

[:(proj1 R),(proj2 R):] is () set

[:X,(proj2 R):] is () set

R /\ [:X,(proj2 R):] is () set

X is () set

proj1 X is set

(X,(proj1 X)) is () set

X is () set

proj1 X is set

(X,(proj1 X)) is () set

X is set

R is () set

(R,X) is () set

proj2 (R,X) is set

proj2 R is set

X is set

R is set

X /\ R is set

R is () set

(R,X) is () set

((R,X),R) is () set

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

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is () set

R is set

(X,R) is () set

((X,R),R) is () set

R /\ R is set

R is () set

X is set

(R,X) is () set

((R,X),X) is () set

X is set

R is set

R is () set

(R,X) is () set

((R,X),R) is () set

X /\ R is set

X is set

R is set

R is () set

(R,R) is () set

((R,R),X) is () set

(R,X) is () set

R /\ X is set

X is set

R is set

R is () set

(R,X) is () set

(R,R) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is () set

(R,X) is () set

R is () set

(R,X) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is set

R is () set

(R,X) is () set

y is () set

(y,R) is () set

(y,X) is () set

X is set

R is set

X \/ R is set

R is () set

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

(R,X) is () set

(R,R) is () set

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

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is set

X /\ R is set

R is () set

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

(R,X) is () set

(R,R) is () set

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

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is set

X \ R is Element of bool X

bool X is set

R is () set

(R,(X \ R)) is () set

(R,X) is () set

(R,R) is () set

(R,X) \ (R,R) is () Element of bool (R,X)

bool (R,X) is set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is empty trivial () set

R is set

(X,R) is () set

({},R) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

X is () set

(X,{}) is empty trivial () set

X is set

({},X) is empty trivial () set

X is set

R is () set

(R,X) is () set

R is () set

(R,R) is () set

((R,R),X) is () set

((R,X),R) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

X is set

R is () set

proj1 R is set

proj2 R is set

R is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

R is () set

y is () set

z is set

c is set

[z,c] is non empty V4() set

{z,c} is non empty set

{z} is non empty trivial set

{{z,c},{z}} is non empty set

R is empty trivial () set

X is () set

(R,X) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

X is set

R is set

R is () set

(R,R) is () set

proj2 (R,R) is set

proj2 R is set

y is set

[y,X] is non empty V4() set

{y,X} is non empty set

{y} is non empty trivial set

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

y is set

[y,X] is non empty V4() set

{y,X} is non empty set

{y} is non empty trivial set

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

X is set

R is () set

(X,R) is () set

proj2 (X,R) is set

R is set

X is set

R is () set

(X,R) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

X is set

R is () set

(X,R) is () set

proj2 (X,R) is set

proj2 R is set

X is set

R is () set

(X,R) is () set

proj2 (X,R) is set

proj2 R is set

(proj2 R) /\ X is set

R is set

y is set

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

X is set

R is () set

proj2 R is set

(X,R) is () set

proj2 (X,R) is set

(proj2 R) /\ X is set

X is set

R is () set

(X,R) is () set

R is () set

((X,R),R) is () set

(R,R) is () set

R is () set

X is set

R is () set

(X,R) is () set

(R,(X,R)) is () set

(R,R) is () set

X is set

(X) is () set

R is () set

(X,R) is () set

(R,(X)) is () set

R is set

y is set

[R,y] is non empty V4() set

{R,y} is non empty set

{R} is non empty trivial set

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

X is set

R is () set

(X,R) is () set

proj1 R is set

[:(proj1 R),X:] is () set

R /\ [:(proj1 R),X:] is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is () set

proj2 R is set

(X,R) is () set

proj1 R is set

[:(proj1 R),(proj2 R):] is () set

[:(proj1 R),X:] is () set

R /\ [:(proj1 R),X:] is () set

X is () set

proj2 X is set

((proj2 X),X) is () set

X is () set

proj2 X is set

((proj2 X),X) is () set

X is set

R is set

X /\ R is set

R is () set

(R,R) is () set

(X,(R,R)) is () set

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

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is () set

(X,R) is () set

(X,(X,R)) is () set

X /\ X is set

X is set

R is () set

(X,R) is () set

(X,(X,R)) is () set

X is set

R is set

R is () set

(X,R) is () set

(R,(X,R)) is () set

R /\ X is set

X is set

R is set

R is () set

(R,R) is () set

(X,(R,R)) is () set

(X,R) is () set

X /\ R is set

X is set

R is set

R is () set

(X,R) is () set

(R,R) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is () set

(X,R) is () set

R is () set

(X,R) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is set

R is () set

(X,R) is () set

y is () set

(R,y) is () set

(X,y) is () set

X is set

R is set

X \/ R is set

R is () set

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

(X,R) is () set

(R,R) is () set

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

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is set

X /\ R is set

R is () set

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

(X,R) is () set

(R,R) is () set

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

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is set

R is set

X \ R is Element of bool X

bool X is set

R is () set

((X \ R),R) is () set

(X,R) is () set

(R,R) is () set

(X,R) \ (R,R) is () Element of bool (X,R)

bool (X,R) is set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is () set

({},X) is empty trivial () set

X is set

(X,{}) is () set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

X is set

R is () set

R is () set

(R,R) is () set

(X,(R,R)) is () set

(X,R) is () set

(R,(X,R)) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

c is set

[y,c] is non empty V4() set

{y,c} is non empty set

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

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

X is set

R is set

R is () set

(X,R) is () set

((X,R),R) is () set

(R,R) is () set

(X,(R,R)) is () set

y is set

z is set

[y,z] is non empty V4() set

{y,z} is non empty set

{y} is non empty trivial set

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

X is () set

R is set

proj2 X is set

R is set

y is set

z is set

[z,y] is non empty V4() set

{z,y} is non empty set

{z} is non empty trivial set

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

R is set

y is set

z is set

c is set

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

c is set

[c,z] is non empty V4() set

{c,z} is non empty set

{c} is non empty trivial set

{{c,z},{c}} is non empty set

X is set

R is set

R is () set

(R,R) is set

proj1 R is set

y is set

[y,X] is non empty V4() set

{y,X} is non empty set

{y} is non empty trivial set

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

y is set

[y,X] is non empty V4() set

{y,X} is non empty set

{y} is non empty trivial set

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

X is set

R is () set

(R,X) is set

proj2 R is set

R is set

y is set

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

X is set

R is () set

(R,X) is set

proj1 R is set

(proj1 R) /\ X is set

(R,((proj1 R) /\ X)) is set

R is set

y is set

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

y is set

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

X is () set

proj1 X is set

(X,(proj1 X)) is set

proj2 X is set

R is set

R is set

[R,R] is non empty V4() set

{R,R} is non empty set

{R} is non empty trivial set

{{R,R},{R}} is non empty set

X is set

R is () set

(R,X) is set

proj1 R is set

(R,(proj1 R)) is set

proj2 R is set

X is set

R is () set

(R,X) is () set

proj2 (R,X) is set

(R,X) is set

R is set

y is set

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

y is set

[y,R] is non empty V4() set

{y,R} is non empty set

{y} is non empty trivial set

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

X is () set

R is empty trivial () set

(X,R) is set

(X,{}) is set

the Element of (X,{}) is Element of (X,{})

y is set

[y, the Element of (X,{})] is non empty V4() set

{y, the Element of (X,{})} is non empty set

{y} is non empty trivial set

{{y, the Element of (X,{})},{y}} is non empty set

X is empty trivial () set

R is set

(X,R) is set

({},R) is set

the Element of ({},R) is