:: FUNCT_4 semantic presentation

f is set
g is set
[f,g] is non empty set
{f,g} is non empty set
{f} is non empty trivial set
{{f,g},{f}} is non empty set
h is set
x is set
[h,x] is non empty set
{h,x} is non empty set
{h} is non empty trivial set
{{h,x},{h}} is non empty set
[[f,g],[h,x]] is non empty set
{[f,g],[h,x]} is Relation-like non empty set

{{[f,g],[h,x]},{[f,g]}} is non empty set
y is set
b is set
[y,b] is non empty set
{y,b} is non empty set
{y} is non empty trivial set
{{y,b},{y}} is non empty set
z is set
nm is set
[z,nm] is non empty set
{z,nm} is non empty set
{z} is non empty trivial set
{{z,nm},{z}} is non empty set
[[y,b],[z,nm]] is non empty set
{[y,b],[z,nm]} is Relation-like non empty set

{{[y,b],[z,nm]},{[y,b]}} is non empty set
f is set
union f is set
union () is set
g is set
h is set
[:g,h:] is Relation-like set
x is set
y is set
b is set
[y,b] is non empty set
{y,b} is non empty set
{y} is non empty trivial set
{{y,b},{y}} is non empty set

rng g is set

g * (f | (rng g)) is Relation-like Function-like set
dom (g * f) is set
dom (g * (f | (rng g))) is set
h is set
dom (f | (rng g)) is set
dom f is set
(dom f) /\ (rng g) is set
dom g is set
g . h is set
g . h is set
dom g is set
h is set
(g * f) . h is set
(g * (f | (rng g))) . h is set
dom g is set
g . h is set
f . (g . h) is set
(f | (rng g)) . (g . h) is set
f is set

[:f,f:] is Relation-like set
bool [:f,f:] is set
g is set

[:g,g:] is Relation-like set
bool [:g,g:] is set
h is set
[h,h] is non empty set
{h,h} is non empty set
{h} is non empty trivial set
{{h,h},{h}} is non empty set
h is set
x is set
y is set
[x,y] is non empty set
{x,y} is non empty set
{x} is non empty trivial set
{{x,y},{x}} is non empty set
f is set
g is set
h is set
{h} is non empty trivial set

bool [:f,{h}:] is set

bool [:g,{h}:] is set
dom (f --> h) is Element of bool f
bool f is set
x is set
(f --> h) . x is set
(g --> h) . x is set
dom (g --> h) is Element of bool g
bool g is set
f is set
g is set
{g} is non empty trivial set

bool [:f,{g}:] is set
h is set
x is set

{x} is non empty trivial set

bool [:h,{x}:] is set
dom (f --> g) is Element of bool f
bool f is set
dom (h --> x) is Element of bool h
bool h is set
f is set
g is set
{g} is non empty trivial set

bool [:f,{g}:] is set
h is set
x is set

{x} is non empty trivial set

bool [:h,{x}:] is set
the Element of f is Element of f
(h --> x) . the Element of f is set
dom (f --> g) is Element of bool f
bool f is set
(f --> g) . the Element of f is set
f is set

dom g is set
g . f is set

{f} is non empty trivial set
{f} --> (g . f) is Relation-like {f} -defined {(g . f)} -valued Function-like constant non empty total quasi_total Element of bool [:{f},{(g . f)}:]
{(g . f)} is non empty trivial set
[:{f},{(g . f)}:] is Relation-like set
bool [:{f},{(g . f)}:] is set
h is set
dom (f .--> (g . f)) is Element of bool {f}
bool {f} is set
(f .--> (g . f)) . h is set
g . h is set
h is set
f is set
g is set

(f |` h) | g is Relation-like Function-like set
f is set
g is set

(f |` h) | g is Relation-like Function-like set

(f |` x) | g is Relation-like Function-like set

dom f is set

dom g is set
(dom f) \/ (dom g) is set

dom h is set

dom x is set
y is set
h . y is set
x . y is set
f . y is set
g . y is set

dom h is set
(dom h) \/ (dom h) is set
y is set

dom x is set
(dom x) \/ (dom x) is set
x . y is set

dom f is set

(f,g) is Relation-like Function-like set
dom (f,g) is set
dom g is set
(dom f) \/ (dom g) is set
f is set

dom g is set

(h,g) is Relation-like Function-like set
(h,g) . f is set
h . f is set
dom h is set
(dom h) \/ (dom g) is set
dom h is set
(dom h) \/ (dom g) is set
dom (h,g) is set
dom h is set
f is set

dom g is set

(g,h) is Relation-like Function-like set
dom (g,h) is set
dom h is set
(dom g) \/ (dom h) is set
f is set

dom g is set
g . f is set

(h,g) is Relation-like Function-like set
(h,g) . f is set
dom h is set
(dom h) \/ (dom g) is set

(f,g) is Relation-like Function-like set

((f,g),h) is Relation-like Function-like set
(g,h) is Relation-like Function-like set
(f,(g,h)) is Relation-like Function-like set
x is set
dom f is set
dom (g,h) is set
(dom f) \/ (dom (g,h)) is set
dom g is set
dom h is set
((f,g),h) . x is set
(f,g) . x is set
g . x is set
(g,h) . x is set
dom h is set
((f,g),h) . x is set
h . x is set
(g,h) . x is set
dom g is set
dom h is set
((f,g),h) . x is set
(g,h) . x is set
((f,g),h) . x is set
(g,h) . x is set
dom g is set
dom h is set
(f,g) . x is set
f . x is set
dom ((f,g),h) is set
dom (f,g) is set
(dom (f,g)) \/ (dom h) is set
(dom f) \/ (dom g) is set
((dom f) \/ (dom g)) \/ (dom h) is set
(dom g) \/ (dom h) is set
(dom f) \/ ((dom g) \/ (dom h)) is set
f is set

dom g is set
g . f is set

(g,h) is Relation-like Function-like set
(g,h) . f is set
dom h is set
(dom g) /\ (dom h) is set
h . f is set
dom h is set
dom h is set
f is set

dom g is set
g . f is set

dom h is set
(g,h) is Relation-like Function-like set
(g,h) . f is set
(dom g) /\ (dom h) is set

rng f is set

(f,g) is Relation-like Function-like set
rng (f,g) is set
rng g is set
(rng f) \/ (rng g) is set
h is set
dom (f,g) is set
x is set
(f,g) . x is set
dom f is set
dom g is set
f . x is set
g . x is set

rng f is set

(g,f) is Relation-like Function-like set
rng (g,f) is set
h is set
dom f is set
x is set
f . x is set
dom (g,f) is set
(g,f) . x is set

dom f is set

dom g is set
(f,g) is Relation-like Function-like set
(dom f) \/ (dom g) is set
dom (f,g) is set
h is set
(f,g) . h is set
g . h is set

(g,f) is Relation-like Function-like set

dom f is set
(f,g) is Relation-like Function-like set
dom f is set
h is set
(f,g) . h is set
f . h is set

(dom f) \ (dom g) is Element of bool (dom f)
bool (dom f) is set

(dom f) \/ (dom g) is set
dom (f,g) is set

f is set

[:f,f:] is Relation-like set
bool [:f,f:] is set
g is set

[:g,g:] is Relation-like set
bool [:g,g:] is set
((id f),(id g)) is Relation-like Function-like set
f \/ g is set
id (f \/ g) is Relation-like f \/ g -defined f \/ g -valued Function-like one-to-one total Element of bool [:(f \/ g),(f \/ g):]
[:(f \/ g),(f \/ g):] is Relation-like set
bool [:(f \/ g),(f \/ g):] is set
dom (id (f \/ g)) is Element of bool (f \/ g)
bool (f \/ g) is set
h is set
((id f),(id g)) . h is set
(id (f \/ g)) . h is set
dom (id g) is Element of bool g
bool g is set
(id g) . h is set
dom (id g) is Element of bool g
bool g is set
(id f) . h is set
dom ((id f),(id g)) is set
dom (id f) is Element of bool f
bool f is set
dom (id g) is Element of bool g
bool g is set
(dom (id f)) \/ (dom (id g)) is set
f \/ (dom (id g)) is set

(f,g) is Relation-like Function-like set
dom g is set
(f,g) | (dom g) is Relation-like Function-like set
dom f is set
(dom f) \/ (dom g) is set
dom (f,g) is set
dom ((f,g) | (dom g)) is set
h is set
((f,g) | (dom g)) . h is set
g . h is set
(f,g) . h is set

dom f is set

(f,g) is Relation-like Function-like set
dom g is set
(dom f) \ (dom g) is Element of bool (dom f)
bool (dom f) is set
(f,g) | ((dom f) \ (dom g)) is Relation-like Function-like set
dom ((f,g) | ((dom f) \ (dom g))) is set
h is set
((f,g) | ((dom f) \ (dom g))) . h is set
f . h is set
(f,g) . h is set

(g,f) is Relation-like Function-like set
dom (g,f) is set
dom g is set
dom f is set
(dom g) \/ (dom f) is set
h is set
(g,f) . h is set
f . h is set

dom f is set

(g,h) is Relation-like Function-like set
dom h is set
(dom f) \ (dom h) is Element of bool (dom f)
bool (dom f) is set
f | ((dom f) \ (dom h)) is Relation-like Function-like set
x is set
dom (f | ((dom f) \ (dom h))) is set
dom g is set
(dom (f | ((dom f) \ (dom h)))) /\ (dom g) is set
(f | ((dom f) \ (dom h))) . x is set
g . x is set
dom (g,h) is set
(dom f) /\ (dom (g,h)) is set
(g,h) . x is set
f . x is set

(g,h) is Relation-like Function-like set
x is set
dom f is set
dom h is set
(dom f) /\ (dom h) is set
f . x is set
h . x is set
dom (g,h) is set
(dom f) /\ (dom (g,h)) is set
(g,h) . x is set

(f,g) is Relation-like Function-like set
dom f is set
dom g is set
(dom f) \/ (dom g) is set
dom (f,g) is set
h is set
(f,g) . h is set
f . h is set

(f,g) is Relation-like Function-like set

h is set
x is set
y is set
[x,y] is non empty set
{x,y} is non empty set
{x} is non empty trivial set
{{x,y},{x}} is non empty set
dom (f,g) is set
dom f is set
dom g is set
(f,g) . x is set
f . x is set
g . x is set

(f,g) is Relation-like Function-like set

dom f is set

dom g is set

(f,g) is Relation-like Function-like set

dom f is set

dom g is set
(f,g) is Relation-like Function-like set

dom f is set

dom g is set
(f,g) is Relation-like Function-like set
(f,g) | (dom f) is Relation-like Function-like set
(dom f) \ (dom g) is Element of bool (dom f)
bool (dom f) is set
dom ((f,g) | (dom f)) is set
dom (f,g) is set
(dom (f,g)) /\ (dom f) is set
(dom f) \/ (dom g) is set
((dom f) \/ (dom g)) /\ (dom f) is set

(f,g) is Relation-like Function-like set
(g,f) is Relation-like Function-like set
dom (f,g) is set
h is set
(f,g) . h is set
(g,f) . h is set
dom f is set
dom g is set
(dom f) \/ (dom g) is set
f . h is set
(dom f) /\ (dom g) is set
g . h is set
f . h is set
g . h is set
dom g is set
dom f is set
(dom g) \/ (dom f) is set
dom (g,f) is set
h is set
dom f is set
dom g is set
(dom f) /\ (dom g) is set
f . h is set
g . h is set
(f,g) . h is set

dom f is set

dom g is set
(f,g) is Relation-like Function-like set
(g,f) is Relation-like Function-like set
f is set
g is set
[:f,g:] is Relation-like set
bool [:f,g:] is set

(h,x) is Relation-like Function-like set
dom x is Element of bool f
bool f is set
dom h is Element of bool f
f is set
g is set
[:f,g:] is Relation-like set
bool [:f,g:] is set

(h,x) is Relation-like Function-like set
dom h is Element of bool f
bool f is set
dom x is Element of bool f
f is set
[:f,f:] is Relation-like set
bool [:f,f:] is set

(g,h) is Relation-like Function-like set
f is set
g is non empty set
[:f,g:] is Relation-like set
bool [:f,g:] is set

(h,x) is Relation-like Function-like set
f is set
g is set
[:f,g:] is Relation-like set
bool [:f,g:] is set

(h,x) is Relation-like Function-like set
rng (h,x) is set
rng h is Element of bool g
bool g is set
rng x is Element of bool g
(rng h) \/ (rng x) is Element of bool g
dom (h,x) is set
dom h is Element of bool f
bool f is set
dom x is Element of bool f
(dom h) \/ (dom x) is Element of bool f

dom f is set
union (dom f) is set
union (union (dom f)) is set
g is set
h is set
[:h,g:] is Relation-like set
x is set
y is set
b is set
z is set
R is set
nm is set
[R,nm] is non empty set
{R,nm} is non empty set
{R} is non empty trivial set
{{R,nm},{R}} is non empty set
[nm,R] is non empty set
{nm,R} is non empty set
{nm} is non empty trivial set
{{nm,R},{nm}} is non empty set
f . [nm,R] is set
y9 is set
y is set
[y9,y] is non empty set
{y9,y} is non empty set
{y9} is non empty trivial set
{{y9,y},{y9}} is non empty set
[y,y9] is non empty set
{y,y9} is non empty set
{y} is non empty trivial set
{{y,y9},{y}} is non empty set
f . [y,y9] is set
y is set
z is set
b is set
[z,b] is non empty set
{z,b} is non empty set
{z} is non empty trivial set
{{z,b},{z}} is non empty set
[b,z] is non empty set
{b,z} is non empty set
{b} is non empty trivial set
{{b,z},{b}} is non empty set
f . [b,z] is set

dom y is set
b is set
nm is set
z is set
[nm,z] is non empty set
{nm,z} is non empty set
{nm} is non empty trivial set
{{nm,z},{nm}} is non empty set
[z,nm] is non empty set
{z,nm} is non empty set
{z} is non empty trivial set
{{z,nm},{z}} is non empty set
b is set
z is set
[b,z] is non empty set
{b,z} is non empty set
{b} is non empty trivial set
{{b,z},{b}} is non empty set
y . (z,b) is set
[z,b] is non empty set
{z,b} is non empty set
{z} is non empty trivial set
{{z,b},{z}} is non empty set
y . [z,b] is set
f . (b,z) is set
f . [b,z] is set
R is set
nm is set
[R,nm] is non empty set
{R,nm} is non empty set
{R} is non empty trivial set
{{R,nm},{R}} is non empty set
[nm,R] is non empty set
{nm,R} is non empty set
{nm} is non empty trivial set
{{nm,R},{nm}} is non empty set
f . [nm,R] is set

dom g is set

dom h is set
x is set
g . x is set
h . x is set
b is set
y is set
[b,y] is non empty set
{b,y} is non empty set
{b} is non empty trivial set
{{b,y},{b}} is non empty set
[y,b] is non empty set
{y,b} is non empty set
{y} is non empty trivial set
{{y,b},{y}} is non empty set
g . (b,y) is set
g . [b,y] is set
f . (y,b) is set
f . [y,b] is set
h . (b,y) is set
h . [b,y] is set
x is set
b is set
y is set
[b,y] is non empty set
{b,y} is non empty set
{b} is non empty trivial set
{{b,y},{b}} is non empty set
[y,b] is non empty set
{y,b} is non empty set
{y} is non empty trivial set
{{y,b},{y}} is non empty set
b is set
y is set
[b,y] is non empty set
{b,y} is non empty set
{b} is non empty trivial set
{{b,y},{b}} is non empty set
[y,b] is non empty set
{y,b} is non empty set
{y} is non empty trivial set
{{y,b},{y}} is non empty set

rng (f) is set
rng f is set
g is set
dom (f) is set
h is set
(f) . h is set
dom f is set
y is set
x is set
[y,x] is non empty set
{y,x} is non empty set
{y} is non empty trivial set
{{y,x},{y}} is non empty set
[x,y] is non empty set
{x,y} is non empty set
{x} is non empty trivial set
{{x,y},{x}} is non empty set
(f) . (y,x) is set
(f) . [y,x] is set
f . (x,y) is set
f . [x,y] is set
f is set
g is set
[f,g] is non empty set
{f,g} is non empty set
{f} is non empty trivial set
{{f,g},{f}} is non empty set
[g,f] is non empty set
{g,f} is non empty set
{g} is non empty trivial set
{{g,f},{g}} is non empty set

dom h is set

dom (h) is set
y is set
x is set
[y,x] is non empty set
{y,x} is non empty set
{y} is non empty trivial set
{{y,x},{y}} is non empty set
[x,y] is non empty set
{x,y} is non empty set
{x} is non empty trivial set
{{x,y},{x}} is non empty set
f is set
g is set
[f,g] is non empty set
{f,g} is non empty set
{f} is non empty trivial set
{{f,g},{f}} is non empty set

dom (h) is set
(h) . (f,g) is set
(h) . [f,g] is set
h . (g,f) is set
[g,f] is non empty set
{g,f} is non empty set
{g} is non empty trivial set
{{g,f},{g}} is non empty set
h . [g,f] is set
dom h is set

dom (f) is set
g is set
dom f is set
x is set
h is set
[x,h] is non empty set
{x,h} is non empty set
{x} is non empty trivial set
{{x,h},{x}} is non empty set
[h,x] is non empty set
{h,x} is non empty set
{h} is non empty trivial set
{{h,x},{h}} is non empty set
f is set
g is set
[:f,g:] is Relation-like set
[:g,f:] is Relation-like set

dom h is set

dom (h) is set
x is set
b is set
y is set
[b,y] is non empty set
{b,y} is non empty set
{b} is non empty trivial set
{{b,y},{b}} is non empty set
[y,b] is non empty set
{y,b} is non empty set
{y} is non empty trivial set
{{y,b},{y}} is non empty set
f is set
g is set
[:f,g:] is Relation-like set
[:g,f:] is Relation-like set

dom h is set

dom (h) is set
x is set
y is set
b is set
[y,b] is non empty set
{y,b} is non empty set
{y} is non empty trivial set
{{y,b},{y}} is non empty set
[b,y] is non empty set
{b,y} is non empty set
{b} is non empty trivial set
{{b,y},{b}} is non empty set
f is set
g is set
[:f,g:] is Relation-like set

dom h is set

rng (h) is set
rng h is set
x is set
y is set
h . y is set
b is set
z is set
[b,z] is non empty set
{b,z} is non empty set
{b} is non empty trivial set
{{b,z},{b}} is non empty set
[z,b] is non empty set
{z,b} is non empty set
{z} is non empty trivial set
{{z,b},{z}} is non empty set
dom (h) is set
h . (b,z) is set
h . [b,z] is set
(h) . (z,b) is set
(h) . [z,b] is set
f is set
g is set
[:f,g:] is Relation-like set
[:g,f:] is Relation-like set
h is set
[:[:f,g:],h:] is Relation-like set
bool [:[:f,g:],h:] is set
[:[:g,f:],h:] is Relation-like set
bool [:[:g,f:],h:] is set

bool [:f,g:] is set
dom (x) is set
rng x is Element of bool h
bool h is set
rng (x) is set
f is set
g is set
[:f,g:] is Relation-like set
[:g,f:] is Relation-like set
h is set
[:[:f,g:],h:] is Relation-like set
bool [:[:f,g:],h:] is set
[:[:g,f:],h:] is Relation-like set
bool [:[:g,f:],h:] is set

bool [:f,g:] is set
dom (x) is set
rng x is Element of bool h
bool h is set
rng (x) is set
y is Relation-like [:g,f:] -defined h -valued Element of bool [:[:g,f:],h:]

bool [:g,f:] is set
f is set
g is set
[:f,g:] is Relation-like set
h is non empty set
[:[:f,g:],h:] is Relation-like set
bool [:[:f,g:],h:] is set

[:g,f:] is Relation-like set
[:[:g,f:],h:] is Relation-like set
bool [:[:g,f:],h:] is set

((f)) is Relation-like Function-like set
g is set
dom ((f)) is set
dom (f) is set
x is set
h is set
[x,h] is non empty set
{x,h} is non empty set
{x} is non empty trivial set
{{x,h},{x}} is non empty set
[h,x] is non empty set
{h,x} is non empty set
{h} is non empty trivial set
{{h,x},{h}} is non empty set
b is set
y is set
[b,y] is non empty set
{b,y} is non empty set
{b} is non empty trivial set
{{b,y},{b}} is non empty set
[y,b] is non empty set
{y,b} is non empty set
{y} is non empty trivial set
{{y,b},{y}} is non empty set
dom f is set
g is set
((f)) . g is set
f . g is set
x is set
h is set
[x,h] is non empty set
{x,h} is non empty set
{x} is non empty trivial set
{{x,h},{x}} is non empty set
[h,x] is non empty set
{h,x} is non empty set
{h} is non empty trivial set
{{h,x},{h}} is non empty set
((f)) . (x,h) is set
((f)) . [x,h] is set
(f) . (h,x) is set
(f) . [h,x] is set
f . (x,h) is set
f . [x,h] is set
g is set
x is set
h is set
[x,h] is non empty set
{x,h} is non empty set
{x} is non empty trivial set
{{x,h},{x}} is non empty set
[h,x] is non empty set
{h,x} is non empty set
{h} is non empty trivial set
{{h,x},{h}} is non empty set
f is set
g is set
[:f,g:] is Relation-like set

dom h is set

((h)) is Relation-like Function-like set
dom ((h)) is set
x is set
y is set
b is set
[y,b] is non empty set
{y,b} is non empty set
{y} is non empty trivial set
{{y,b},{y}} is non empty set
[b,y] is non empty set
{b,y} is non empty set
{b} is non empty trivial set
{{b,y},{b}} is non empty set
dom (h) is set
f is set
g is set
[:f,g:] is Relation-like set
h is set
[:[:f,g:],h:] is Relation-like set
bool [:[:f,g:],h:] is set

((x)) is Relation-like Function-like set

bool [:f,g:] is set

dom f is set

dom g is set
union (dom f) is set
union (union (dom f)) is set
h is set
x is set
union (dom g) is set
union (union (dom g)) is set
y is set
b is set
[:h,y:] is Relation-like set
[:x,b:] is Relation-like set
[:[:h,y:],[:x,b:]:] is Relation-like set
z is set
nm is set
R is set
y is set
y9 is set
x9 is set
[y9,x9] is non empty set
{y9,x9} is non empty set
{y9} is non empty trivial set
{{y9,x9},{y9}} is non empty set
x is set
y1 is set
[x,y1] is non empty set
{x,y1} is non empty set
{x} is non empty trivial set
{{x,y1},{x}} is non empty set
[[y9,x9],[x,y1]] is non empty set
{[y9,x9],[x,y1]} is Relation-like non empty set

{{[y9,x9],[x,y1]},{[y9,x9]}} is non empty set
[y9,x] is non empty set
{y9,x} is non empty set
{{y9,x},{y9}} is non empty set
f . [y9,x] is set
[x9,y1] is non empty set
{x9,y1} is non empty set
{x9} is non empty trivial set
{{x9,y1},{x9}} is non empty set
g . [x9,y1] is set
[(f . [y9,x]),(g . [x9,y1])] is non empty set
{(f . [y9,x]),(g . [x9,y1])} is non empty set
{(f . [y9,x])} is non empty trivial set
{{(f . [y9,x]),(g . [x9,y1])},{(f . [y9,x])}} is non empty set
x19 is set
x19 is set
[x19,x19] is non empty set
{x19,x19} is non empty set
{x19} is non empty trivial set
{{x19,x19},{x19}} is non empty set
y19 is set
y19 is set
[y19,y19] is non empty set
{y19,y19} is non empty set
{y19} is non empty trivial set
{{y19,y19},{y19}} is non empty set
[[x19,x19],[y19,y19]] is non empty set
{[x19,x19],[y19,y19]} is Relation-like non empty set

{{[x19,x19],[y19,y19]},{[x19,x19]}} is non empty set
[x19,y19] is non empty set
{x19,y19} is non empty set
{{x19,y19},{x19}} is non empty set
f . [x19,y19] is set
[x19,y19] is non empty set
{x19,y19} is non empty set
{x19} is non empty trivial set
{{x19,y19},{x19}} is non empty set
g . [x19,y19] is set
[(f . [x19,y19]),(g . [x19,y19])] is non empty set
{(f . [x19,y19]),(g . [x19,y19])} is non empty set
{(f . [x19,y19])} is non empty trivial set
{{(f . [x19,y19]),(g . [x19,y19])},{(f . [x19,y19])}} is non empty set
nm is set
R is set
y9 is set
[R,y9] is non empty set
{R,y9} is non empty set
{R} is non empty trivial set
{{R,y9},{R}} is non empty set
y is set
x is set
[y,x] is non empty set
{y,x} is non empty set
{y} is non empty trivial set
{{y,x},{y}} is non empty set
[[R,y9],[y,x]] is non empty set
{[R,y9],[y,x]} is Relation-like non empty set

{{[R,y9],[y,x]},{[R,y9]}} is non empty set
[R,y] is non empty set
{R,y} is non empty set
{{R,y},{R}} is non empty set
[y9,x] is non empty set
{y9,x} is non empty set
{y9} is non empty trivial set
{{y9,x},{y9}} is non empty set
f . [R,y] is set
g . [y9,x] is set
[(f . [R,y]),(g . [y9,x])] is non empty set
{(f . [R,y]),(g . [y9,x])} is non empty set
{(f . [R,y])} is non empty trivial set
{{(f . [R,y]),(g . [y9,x])},{(f . [R,y])}} is non empty set

dom nm is set
R is set
y is set
x is set
[y,x] is non empty set
{y,x} is non empty set
{y} is non empty trivial set
{{y,x},{y}} is non empty set
y9 is set
x9 is set
[y9,x9] is non empty set
{y9,x9} is non empty set
{y9} is non empty trivial set
{{y9,x9},{y9}} is non empty set
[[y,x],[y9,x9]] is non empty set
{[y,x],[y9,x9]} is Relation-like non empty set

{{[y,x],[y9,x9]},{[y,x]}} is non empty set
[y,y9] is non empty set
{y,y9} is non empty set
{{y,y9},{y}} is non empty set
[x,x9] is non empty set
{x,x9} is non empty set
{x} is non empty trivial set
{{x,x9},{x}} is non empty set
R is set
y is set
[R,y] is non empty set
{R,y} is non empty set
{R} is non empty trivial set
{{R,y},{R}} is non empty set
f . (R,y) is set
f . [R,y] is set
y9 is set
[R,y9] is non empty set
{R,y9} is non empty set
{{R,y9},{R}} is non empty set
x is set
[y9,x] is non empty set
{y9,x} is non empty set
{y9} is non empty trivial set
{{y9,x},{y9}} is non empty set
[y,x] is non empty set
{y,x} is non empty set
{y} is non empty trivial set
{{y,x},{y}} is non empty set
nm . ([R,y9],[y,x]) is set
[[R,y9],[y,x]] is non empty set
{[R,y9],[y,x]} is Relation-like non empty set

{{[R,y9],[y,x]},{[R,y9]}} is non empty set
nm . [[R,y9],[y,x]] is set
g . (y9,x) is set
g . [y9,x] is set
[(f . (R,y)),(g . (y9,x))] is non empty set
{(f . (R,y)),(g . (y9,x))} is non empty set
{(f . (R,y))} is non empty trivial set
{{(f . (R,y)),(g . (y9,x))},{(f . (R,y))}} is non empty set
x9 is set
x19 is set
[x9,x19] is non empty set
{x9,x19} is non empty set
{x9} is non empty trivial set
{{x9,x19},{x9}} is non empty set
y1 is set
y19 is set
[y1,y19] is non empty set
{y1,y19} is non empty set
{y1} is non empty trivial set
{{y1,y19},{y1}} is non empty set
[[x9,x19],[y1,y19]] is non empty set
{[x9,x19],[y1,y19]} is Relation-like non empty set

{{[x9,x19],[y1,y19]},{[x9,x19]}} is non empty set
[x9,y1] is non empty set
{x9,y1} is non empty set
{{x9,y1},{x9}} is non empty set
f . [x9,y1] is set
[x19,y19] is non empty set
{x19,y19} is non empty set
{x19} is non empty trivial set
{{x19,y19},{x19}} is non empty set
g . [x19,y19] is set
[(f . [x9,y1]),(g . [x19,y19])] is non empty set
{(f . [x9,y1]),(g . [x19,y19])} is non empty set
{(f . [x9,y1])} is non empty trivial set
{{(f . [x9,y1]),(g . [x19,y19])},{(f . [x9,y1])}} is non empty set

dom h is set

dom x is set
y is set
h . y is set
x . y is set
b is set
nm is set
[b,nm] is non empty set
{b,nm} is non empty set
{b} is non empty trivial set
{{b,nm},{b}} is non empty set
z is set
R is set
[z,R] is non empty set
{z,R} is non empty set
{z} is non empty trivial set
{{z,R},{z}} is non empty set
[[b,nm],[z,R]] is non empty set
{[b,nm],[z,R]} is Relation-like non empty set

{{[b,nm],[z,R]},{[b,nm]}} is non empty set
[b,z] is non empty set
{b,z} is non empty set
{{b,z},{b}} is non empty set
[nm,R] is non empty set
{nm,R} is non empty set
{nm} is non empty trivial set
{{nm,R},{nm}} is non empty set
h . ([b,nm],[z,R]) is set
h . [[b,nm],[z,R]] is set
f . (b,z) is set
f . [b,z] is set
g . (nm,R) is set
g . [nm,R] is set
[(f . (b,z)),(g . (nm,R))] is non empty set
{(f . (b,z)),(g . (nm,R))} is non empty set
{(f . (b,z))} is non empty trivial set
{{(f . (b,z)),(g . (nm,R))},{(f . (b,z))}} is non empty set
x . ([b,nm],[z,R]) is set
x . [[b,nm],[z,R]] is set
y is set
b is set
nm is set
[b,nm] is non empty set
{b,nm} is non empty set
{b} is non empty trivial set
{{b,nm},{b}} is non empty set
z is set
R is set
[z,R] is non empty set
{z,R} is non empty set
{z} is non empty trivial set
{{z,R},{z}} is non empty set
[[b,nm],[z,R]] is non empty set
{[b,nm],[z,R]} is Relation-like non empty set

{{[b,nm],[z,R]},{[b,nm]}} is non empty set
[b,z] is non empty set
{b,z} is non empty set
{{b,z},{b}} is non empty set
[nm,R] is non empty set
{nm,R} is non empty set
{nm} is non empty trivial set
{{nm,R},{nm}} is non empty set
b is set
nm is set
[b,nm] is non empty set
{b,nm} is non empty set
{b} is non empty trivial set
{{b,nm},{b}} is non empty set
z is set
R is set
[z,R] is non empty set
{z,R} is non empty set
{z} is non empty trivial set
{{z,R},{z}} is non empty set
[[b,nm],[z,R]] is non empty set
{[b,nm],[z,R]} is Relation-like non empty set

{{[b,nm],[z,R]},{[b,nm]}} is non empty set
[b,z] is non empty set
{b,z} is non empty set
{{b,z},{b}} is non empty set
[nm,R] is non empty set
{nm,R} is non empty set
{nm} is non empty trivial set
{{nm,R},{nm}} is non empty set
f is set
g is set
[f,g] is non empty set
{f,g} is non empty set
{f} is non empty trivial set
{{f,g},{f}} is non empty set
h is set
[f,h] is non empty set
{f,h} is non empty set
{{f,h},{f}} is non empty set
x is set
[h,x] is non empty set
{h,x} is non empty set
{h} is non empty trivial set
{{h,x},{h}} is non empty set
[[f,g],[h,x]] is non empty set
{[f,g],[h,x]} is Relation-like non empty set

{{[f,g],[h,x]},{[f,g]}} is non empty set
[g,x] is non empty set
{g,x} is non empty set
{g} is non empty trivial set
{{g,x},{g}} is non empty set

dom y is set

(y,b) is Relation-like Function-like set
dom (y,b) is set
dom b is set
z is set
R is set
[z,R] is non empty set
{z,R} is non empty set
{z} is non empty trivial set
{{z,R},{z}} is non empty set
nm is set
y is set
[nm,y] is non empty set
{nm,y} is non empty set
{nm} is non empty trivial set
{{nm,y},{nm}} is non empty set
[[z,R],[nm,y]] is non empty set
{[z,R],[nm,y]} is Relation-like non empty set

{{[z,R],[nm,y]},{[z,R]}} is non empty set
[z,nm] is non empty set
{z,nm} is non empty set
{{z,nm},{z}} is non empty set
[R,y] is non empty set
{R,y} is non empty set
{R} is non empty trivial set
{{R,y},{R}} is non empty set
f is set
g is set
[f,g] is non empty set
{f,g} is non empty set
{f} is non empty trivial set
{{f,g},{f}} is non empty set
h is set
x is set
[h,x] is non empty set
{h,x} is non empty set
{h} is non empty trivial set
{{h,x},{h}} is non empty set
[[f,g],[h,x]] is non empty set
{[f,g],[h,x]} is Relation-like non empty set

{{[f,g],[h,x]},{[f,g]}} is non empty set

y . (f,h) is set
[f,h] is non empty set
{f,h} is non empty set
{{f,h},{f}} is non empty set
y . [f,h] is set

(y,b) is Relation-like Function-like set
dom (y,b) is set
(y,b) . ([f,g],[h,x]) is set
(y,b) . [[f,g],[h,x]] is set
b . (g,x) is set
[g,x] is non empty set
{g,x} is non empty set
{g} is non empty trivial set
{{g,x},{g}} is non empty set
b . [g,x] is set
[(y . (f,h)),(b . (g,x))] is non empty set
{(y . (f,h)),(b . (g,x))} is non empty set
{(y . (f,h))} is non empty trivial set
{{(y . (f,h)),(b . (g,x))},{(y . (f,h))}} is non empty set
dom y is set
dom b is set

rng f is set

(f,g) is Relation-like Function-like set
rng (f,g) is set
rng g is set
[:(rng f),(rng g):] is Relation-like set
h is set
dom (f,g) is set
x is set
(f,g) . x is set
dom f is set
dom g is set
y is set
z is set
[y,z] is non empty set
{y,z} is non empty set
{y} is non empty trivial set
{{y,z},{y}} is non empty set
b is set
nm is set
[b,nm] is non empty set
{b,nm} is non empty set
{b} is non empty trivial set
{{b,nm},{b}} is non empty set
[[y,z],[b,nm]] is non empty set
{[y,z],[b,nm]} is Relation-like non empty set

{{[y,z],[b,nm]},{[y,z]}} is non empty set
[y,b] is non empty set
{y,b} is non empty set
{{y,b},{y}} is non empty set
[z,nm] is non empty set
{z,nm} is non empty set
{z} is non empty trivial set
{{z,nm},{z}} is non empty set
f . [y,b] is set
g . [z,nm] is set
(f,g) . ([y,z],[b,nm]) is set
(f,g) . [[y,z],[b,nm]] is set
f . (y,b) is set
g . (z,nm) is set
[(f . (y,b)),(g . (z,nm))] is non empty set
{(f . (y,b)),(g . (z,nm))} is non empty set
{(f . (y,b))} is non empty trivial set
{{(f . (y,b)),(g . (z,nm))},{(f . (y,b))}} is non empty set
f is set
g is set
[:f,g:] is Relation-like set
h is set
[:f,h:] is Relation-like set
x is set
[:h,x:] is Relation-like set
[:g,x:] is Relation-like set
[:[:f,h:],[:g,x:]:] is Relation-like set

dom y is set

dom b is set
(y,b) is Relation-like Function-like set
dom (y,b) is set
z is set
nm is set
y is set
[nm,y] is non empty set
{nm,y} is non empty set
{nm} is non empty trivial set
{{nm,y},{nm}} is non empty set
R is set
y9 is set
[R,y9] is non empty set
{R,y9} is non empty set
{R} is non empty trivial set
{{R,y9},{R}} is non empty set
[[nm,y],[R,y9]] is non empty set
{[nm,y],[R,y9]} is Relation-like non empty set

{{[nm,y],[R,y9]},{[nm,y]}} is non empty set
[nm,R] is non empty set
{nm,R} is non empty set
{{nm,R},{nm}} is non empty set
[y,y9] is non empty set
{y,y9} is non empty set
{y} is non empty trivial set
{{y,y9},{y}} is non empty set
f is set
g is set
[:f,g:] is Relation-like set
h is set
[:f,h:] is Relation-like set
x is set
[:h,x:] is Relation-like set
[:g,x:] is Relation-like set
[:[:f,h:],[:g,x:]:] is Relation-like set

dom y is set

dom b is set
(y,b) is Relation-like Function-like set
dom (y,b) is set
z is set
nm is set
R is set
[nm,R] is non empty set
{nm,R} is non empty set
{nm} is non empty trivial set
{{nm,R},{nm}} is non empty set
y is set
y9 is set
[y,y9] is non empty set
{y,y9} is non empty set
{y} is non empty trivial set
{{y,y9},{y}} is non empty set
x is set
x9 is set
[x,x9] is non empty set
{x,x9} is non empty set
{x} is non empty trivial set
{{x,x9},{x}} is non empty set
[x,y] is non empty set
{x,y} is non empty set
{{x,y},{x}} is non empty set
[x9,y9] is non empty set
{x9,y9} is non empty set
{x9} is non empty trivial set
{{x9,y9},{x9}} is non empty set
f is set
g is set
[:f,g:] is Relation-like set
h is set
[:[:f,g:],h:] is Relation-like set
bool [:[:f,g:],h:] is set
x is set
[:f,x:] is Relation-like set
y is set
[:x,y:] is Relation-like set
[:g,y:] is Relation-like set
[:[:f,x:],[:g,y:]:] is Relation-like set
b is set
[:[:x,y:],b:] is Relation-like set
bool [:[:x,y:],b:] is set
[:h,b:] is Relation-like set
[:[:[:f,x:],[:g,y:]:],[:h,b:]:] is Relation-like set
bool [:[:[:f,x:],[:g,y:]:],[:h,b:]:] is set

(z,nm) is Relation-like Function-like set
rng (z,nm) is set
rng z is Element of bool h
bool h is set
rng nm is Element of bool b
bool b is set
[:(rng z),(rng nm):] is Relation-like set

bool [:f,g:] is set

bool [:x,y:] is set
dom (z,nm) is set
f is set
g is set
[:f,g:] is Relation-like set
h is set
[:[:f,g:],h:] is Relation-like set
bool [:[:f,g:],h:] is set
x is set
[:f,x:] is Relation-like set
y is set
[:x,y:] is Relation-like set
[:g,y:] is Relation-like set
[:[:f,x:],[:g,y:]:] is Relation-like set
b is set
[:[:x,y:],b:] is Relation-like set
bool [:[:x,y:],b:] is set
[:h,b:] is Relation-like set
[:[:[:f,x:],[:g,y:]:],[:h,b:]:] is Relation-like set
bool [:[:[:f,x:],[:g,y:]:],[:h,b:]:] is set

(z,nm) is Relation-like Function-like set
rng (z,nm) is set
rng z is Element of bool h
bool h is set
rng nm is Element of bool b
bool b is set
[:(rng z),(rng nm):] is Relation-like set