:: SYSREL semantic presentation

S is set
R is set
[:S,R:] is Relation-like set
dom [:S,R:] is set
rng [:S,R:] is set
S is set
R is set
[:S,R:] is Relation-like set

x /\ [:S,R:] is Relation-like set
dom (x /\ [:S,R:]) is set
rng (x /\ [:S,R:]) is set

rng x is set
rng [:S,R:] is set
(rng x) /\ (rng [:S,R:]) is set
(rng x) /\ R is set
dom x is set
dom [:S,R:] is set
(dom x) /\ (dom [:S,R:]) is set
(dom x) /\ S is set
S is set
R is set
[:S,R:] is Relation-like set

x /\ [:S,R:] is Relation-like set
dom (x /\ [:S,R:]) is set
rng (x /\ [:S,R:]) is set
S /\ R is set
(dom (x /\ [:S,R:])) /\ (rng (x /\ [:S,R:])) is set
S /\ (rng (x /\ [:S,R:])) is set
S is set
R is set
[:S,R:] is Relation-like set

dom x is set
rng x is set
x /\ [:S,R:] is Relation-like set
S is set
R is set
[:S,R:] is Relation-like set
[:R,S:] is Relation-like set

y is set
z is set
[y,z] is set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
[z,y] is set
{z,y} is non empty set
{z} is non empty set
{{z,y},{z}} is non empty set
S is set
R is set
[:S,R:] is Relation-like set

[:R,S:] is Relation-like set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set

(S \/ R) * x is Relation-like set

(S * x) \/ (R * x) is Relation-like set
y is set
z is set
[y,z] is set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
y is set
[y,y] is set
{y,y} is non empty set
{{y,y},{y}} is non empty set
[y,z] is set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
y is set
[y,y] is set
{y,y} is non empty set
{{y,y},{y}} is non empty set
[y,z] is set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
y is set
[y,y] is set
{y,y} is non empty set
{{y,y},{y}} is non empty set
[y,z] is set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
S is set
R is set
[:S,R:] is Relation-like set
[:R,S:] is Relation-like set
[:S,R:] \/ [:R,S:] is Relation-like set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set

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

y /\ [:x,R:] is Relation-like set

y /\ [:S,x:] is Relation-like set
z is set
y is set
[z,y] is set
{z,y} is non empty set
{z} is non empty set
{{z,y},{z}} is non empty set
z is set
y is set
[z,y] is set
{z,y} is non empty set
{z} is non empty set
{{z,y},{z}} is non empty set
S is set
R is set
[:S,R:] is Relation-like set
x is set
y is set
x \/ y is set

(z | x) \/ (z | y) is Relation-like set
z /\ [:S,R:] is Relation-like set
[:x,R:] is Relation-like set
[:y,R:] is Relation-like set
[:x,R:] \/ [:y,R:] is Relation-like set
z /\ ([:x,R:] \/ [:y,R:]) is Relation-like set
z /\ [:x,R:] is Relation-like set
z /\ [:y,R:] is Relation-like set
(z /\ [:x,R:]) \/ (z /\ [:y,R:]) is Relation-like set
(z | x) \/ (z /\ [:y,R:]) is Relation-like set
S is set
R is set
[:S,R:] is Relation-like set
[:R,S:] is Relation-like set
[:S,R:] \/ [:R,S:] is Relation-like set

S /\ R is set
rng x is set
[:S,(rng x):] is Relation-like set
x /\ [:S,(rng x):] is Relation-like set
([:S,R:] \/ [:R,S:]) /\ [:S,(rng x):] is Relation-like set
[:S,R:] /\ [:S,(rng x):] is Relation-like set
[:R,S:] /\ [:S,(rng x):] is Relation-like set
([:S,R:] /\ [:S,(rng x):]) \/ ([:R,S:] /\ [:S,(rng x):]) is Relation-like set
S /\ (rng x) is set
[:(S /\ R),(S /\ (rng x)):] is Relation-like set

(S ~) \/ (R ~) is Relation-like set
S is set

[:S,S:] is Relation-like set
R is set
x is set
[R,x] is set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
S is set

(id S) * (id S) is Relation-like S -defined S -valued set
dom (id S) is set
S is set
{S} is non empty set

[S,S] is set
{S,S} is non empty set
{{S,S},{S}} is non empty set
{[S,S]} is non empty Relation-like set

S is set

R is set
S \/ R is set
id (S \/ R) is Relation-like S \/ R -defined S \/ R -valued set

(id S) \/ (id R) is Relation-like set
S /\ R is set
id (S /\ R) is Relation-like S /\ R -defined S /\ R -valued set
(id S) /\ (id R) is Relation-like set
S \ R is M2( bool S)
bool S is set
id (S \ R) is Relation-like S \ R -defined S \ R -valued set
(id S) \ (id R) is Relation-like S -defined S -valued M2( bool (id S))
bool (id S) is set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
S is set

R is set

S \/ R is set
(id S) \/ (id R) is Relation-like set
S is set

R is set
S \ R is M2( bool S)
bool S is set
id (S \ R) is Relation-like S \ R -defined S \ R -valued set
(id (S \ R)) \ (id S) is Relation-like S \ R -defined S \ R -valued M2( bool (id (S \ R)))
bool (id (S \ R)) is set

dom S is set

R is set
x is set
[R,x] is set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
y is set
[R,y] is set
{R,y} is non empty set
{{R,y},{R}} is non empty set
S is set

R \/ (R ~) is Relation-like set
x is set
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
x is set
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
y is set
[y,y] is set
{y,y} is non empty set
{y} is non empty set
{{y,y},{y}} is non empty set
S 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
S is set
[:S,S:] is Relation-like set

dom R is set

R \ (id (dom R)) is Relation-like M2( bool R)
bool R is set
R \ (id S) is Relation-like M2( bool R)
rng R is set

R \ (id (rng R)) is Relation-like M2( bool R)
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
S is set

R \ (id S) is Relation-like M2( bool R)
bool R is set
(id S) * (R \ (id S)) is Relation-like S -defined set
dom (R \ (id S)) is set
dom R is set
(dom R) \ S is M2( bool (dom R))
bool (dom R) is set
(R \ (id S)) * (id S) is Relation-like S -valued set
rng (R \ (id S)) is set
rng R is set
(rng R) \ S is M2( bool (rng R))
bool (rng R) 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
y is set
[x,y] is set
{x,y} is non empty set
{{x,y},{x}} is non empty set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
dom (id S) is set
(dom R) \ (dom (id S)) is M2( bool (dom R))
x is set
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
y is set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
y is set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
rng (id S) is set
(rng R) \ (rng (id S)) is M2( bool (rng R))

rng S is set

S \ (id (rng S)) is Relation-like M2( bool S)
bool S is set
S * (S \ (id (rng S))) is Relation-like set
dom S is set

S \ (id (dom S)) is Relation-like M2( bool S)
(S \ (id (dom S))) * S is Relation-like set
R is set
[R,R] is set
{R,R} is non empty set
{R} is non empty set
{{R,R},{R}} is non empty set
x is set
[x,R] is set
{x,R} is non empty set
{x} is non empty set
{{x,R},{x}} is non empty set
y is set
[x,y] is set
{x,y} is non empty set
{{x,y},{x}} is non empty set
[y,R] is set
{y,R} is non empty set
{y} is non empty set
{{y,R},{y}} is non empty set
R is set
[R,R] is set
{R,R} is non empty set
{R} is non empty set
{{R,R},{R}} is non empty set
x is set
[R,x] is set
{R,x} is non empty set
{{R,x},{R}} is non empty set
y is set
[R,y] is set
{R,y} is non empty set
{{R,y},{R}} is non empty set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set

rng S is set

S \ (id (rng S)) is Relation-like M2( bool S)
bool S is set
S * (S \ (id (rng S))) is Relation-like set
S /\ (id (rng S)) is Relation-like set

dom R is set

R \ (id (dom R)) is Relation-like M2( bool R)
bool R is set
(R \ (id (dom R))) * R is Relation-like set
R /\ (id (dom R)) is Relation-like set
S is set

R \ (id S) is Relation-like M2( bool R)
bool R is set
R * (R \ (id S)) is Relation-like set
rng R is set

R \ (id (rng R)) is Relation-like M2( bool R)
R * (R \ (id (rng R))) is Relation-like set
(R \ (id S)) * R is Relation-like set
dom R is set

R \ (id (dom R)) is Relation-like M2( bool R)
(R \ (id (dom R))) * R is Relation-like set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
z is set
[x,z] is set
{x,z} is non empty set
{{x,z},{x}} is non empty set
[z,y] is set
{z,y} is non empty set
{z} is non empty set
{{z,y},{z}} is non empty set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
z is set
[x,z] is set
{x,z} is non empty set
{{x,z},{x}} is non empty set
[z,y] is set
{z,y} is non empty set
{z} is non empty set
{{z,y},{z}} is non empty set

dom S is set

S /\ (id (dom S)) is Relation-like set
S is set
R is set
[S,R] is set
{S,R} is non empty set
{S} is non empty set
{{S,R},{S}} is non empty set

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

x /\ (id (dom x)) is Relation-like set
dom (x) is set

(S) is Relation-like set
dom S is set

S /\ (id (dom S)) is Relation-like set
dom (S) is set
rng (S) is set
R is set
x is set
[R,x] is set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
[R,R] is set
{R,R} is non empty set
{{R,R},{R}} is non empty set
R is set
x is set
[x,R] is set
{x,R} is non empty set
{x} is non empty set
{{x,R},{x}} is non empty set
[R,R] is set
{R,R} is non empty set
{R} is non empty set
{{R,R},{R}} is non empty set
S is set
[S,S] is set
{S,S} is non empty set
{S} is non empty set
{{S,S},{S}} is non empty set

(R) is Relation-like set
dom R is set

R /\ (id (dom R)) is Relation-like set
dom (R) is set
rng (R) is set
rng R is set
x is set
[S,x] is set
{S,x} is non empty set
{{S,x},{S}} is non empty set

(S) is Relation-like set
dom S is set

S /\ (id (dom S)) is Relation-like set
dom (S) is set
id (dom (S)) is Relation-like dom (S) -defined dom (S) -valued set
R is set
x is set
[R,x] is set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
y is set
[R,y] is set
{R,y} is non empty set
{{R,y},{R}} is non empty set
S is set
R is set
[S,R] is set
{S,R} is non empty set
{S} is non empty set
{{S,R},{S}} is non empty set

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

x /\ (id (dom x)) is Relation-like set
x \ (x) is Relation-like M2( bool x)
bool x is set
x * (x \ (x)) is Relation-like set
dom (x) is set
(dom x) \ (dom (x)) is M2( bool (dom x))
bool (dom x) is set
(x \ (x)) * x is Relation-like set
rng x is set
(rng x) \ (dom (x)) is M2( bool (rng x))
bool (rng x) is set
y is set
[S,y] is set
{S,y} is non empty set
{{S,y},{S}} is non empty set
[y,R] is set
{y,R} is non empty set
{y} is non empty set
{{y,R},{y}} is non empty set
[S,S] is set
{S,S} is non empty set
{{S,S},{S}} is non empty set
y is set
[S,y] is set
{S,y} is non empty set
{{S,y},{S}} is non empty set
[y,R] is set
{y,R} is non empty set
{y} is non empty set
{{y,R},{y}} is non empty set
[R,R] is set
{R,R} is non empty set
{R} is non empty set
{{R,R},{R}} is non empty set
S is set
R is set
[S,R] is set
{S,R} is non empty set
{S} is non empty set
{{S,R},{S}} is non empty set

dom x is set

x \ (id (dom x)) is Relation-like M2( bool x)
bool x is set
x * (x \ (id (dom x))) is Relation-like set
(x) is Relation-like set
x /\ (id (dom x)) is Relation-like set
dom (x) is set
(dom x) \ (dom (x)) is M2( bool (dom x))
bool (dom x) is set
(x \ (id (dom x))) * x is Relation-like set
rng x is set
(rng x) \ (dom (x)) is M2( bool (rng x))
bool (rng x) is set
x \ (x) is Relation-like M2( bool x)

dom S is set

S \ (id (dom S)) is Relation-like M2( bool S)
bool S is set
S * (S \ (id (dom S))) is Relation-like set
(S) is Relation-like set
S /\ (id (dom S)) is Relation-like set
dom (S) is set
rng S is set
rng (S) is set
(S \ (id (dom S))) * S is Relation-like set
R is set
x is set
[x,R] is set
{x,R} is non empty set
{x} is non empty set
{{x,R},{x}} is non empty set
y is set
[x,y] is set
{x,y} is non empty set
{{x,y},{x}} is non empty set
[y,R] is set
{y,R} is non empty set
{y} is non empty set
{{y,R},{y}} is non empty set
R is set
x is set
[R,x] is set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
y is set
[R,y] is set
{R,y} is non empty set
{{R,y},{R}} is non empty set
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set

(S) is Relation-like set
dom S is set

S /\ (id (dom S)) is Relation-like set
dom (S) is set
rng (S) is set
rng S is set

(S) is Relation-like set
dom S is set

S /\ (id (dom S)) is Relation-like set
dom (S) is set
id (dom (S)) is Relation-like dom (S) -defined dom (S) -valued set
rng (S) is set
id (rng (S)) is Relation-like rng (S) -defined rng (S) -valued set

(S) is Relation-like set
dom S is set

S /\ (id (dom S)) is Relation-like set
dom (S) is set
id (dom (S)) is Relation-like dom (S) -defined dom (S) -valued set
rng (S) is set
id (rng (S)) is Relation-like rng (S) -defined rng (S) -valued set
R is set
x is set
[R,x] is set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
S is set

R \ (id S) is Relation-like M2( bool R)
bool R is set
(id S) * (R \ (id S)) is Relation-like S -defined set

(R \ (id S)) * (id S) is Relation-like S -valued set

(id S) * R is Relation-like S -defined set
R \/ (id S) is Relation-like set
(id S) * (R \/ (id S)) is Relation-like S -defined set
(R \ (id S)) \/ (id S) is Relation-like set
(id S) * ((R \ (id S)) \/ (id S)) is Relation-like S -defined set
(id S) * (id S) is Relation-like S -defined S -valued set
{} \/ ((id S) * (id S)) is Relation-like set
R * (id S) is Relation-like S -valued set
R \/ (id S) is Relation-like set
(R \/ (id S)) * (id S) is Relation-like S -valued set
(R \ (id S)) \/ (id S) is Relation-like set
((R \ (id S)) \/ (id S)) * (id S) is Relation-like S -valued set
(id S) * (id S) is Relation-like S -defined S -valued set
{} \/ ((id S) * (id S)) is Relation-like set

(S) is Relation-like set
dom S is set

S /\ (id (dom S)) is Relation-like set
dom (S) is set
id (dom (S)) is Relation-like dom (S) -defined dom (S) -valued set
S \ (id (dom (S))) is Relation-like M2( bool S)
bool S is set
(id (dom (S))) * (S \ (id (dom (S)))) is Relation-like dom (S) -defined set
S | (dom (S)) is Relation-like set
rng (S) is set
S | (rng (S)) is Relation-like set
id (rng (S)) is Relation-like rng (S) -defined rng (S) -valued set
S \ (id (rng (S))) is Relation-like M2( bool S)
(S \ (id (rng (S)))) * (id (rng (S))) is Relation-like rng (S) -valued set
(dom (S)) |` S is Relation-like set
(rng (S)) |` S is Relation-like set

dom S is set

S \ (id (dom S)) is Relation-like M2( bool S)
bool S is set
S * (S \ (id (dom S))) is Relation-like set
(S) is Relation-like set
S /\ (id (dom S)) is Relation-like set
dom (S) is set
id (dom (S)) is Relation-like dom (S) -defined dom (S) -valued set
S \ (id (dom (S))) is Relation-like M2( bool S)
(id (dom (S))) * (S \ (id (dom (S)))) is Relation-like dom (S) -defined set
(S \ (id (dom S))) * S is Relation-like set
(S \ (id (dom (S)))) * (id (dom (S))) is Relation-like dom (S) -valued set
S \ (S) is Relation-like M2( bool S)
S \ (S) is Relation-like M2( bool S)

dom R is set

R \ (id (dom R)) is Relation-like M2( bool R)
bool R is set
R * (R \ (id (dom R))) is Relation-like set
S * (R \ (id (dom R))) is Relation-like set

(R \ (id (dom R))) * R is Relation-like set
(R \ (id (dom R))) * S is Relation-like set

(S) is Relation-like set
dom S is set

S /\ (id (dom S)) is Relation-like set

dom R is set

R \ (id (dom R)) is Relation-like M2( bool R)
bool R is set
R * (R \ (id (dom R))) is Relation-like set
(R) is Relation-like set
R /\ (id (dom R)) is Relation-like set

(R \ (id (dom R))) * R is Relation-like set
S * (R \ (id (dom R))) is Relation-like set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
z is set
[x,z] is set
{x,z} is non empty set
{{x,z},{x}} is non empty set
[z,y] is set
{z,y} is non empty set
{z} is non empty set
{{z,y},{z}} is non empty set
(R \ (id (dom R))) * S is Relation-like set
x is set
y is set
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
z is set
[x,z] is set
{x,z} is non empty set
{{x,z},{x}} is non empty set
[z,y] is set
{z,y} is non empty set
{z} is non empty set
{{z,y},{z}} is non empty set

dom S is set

S \ (id (dom S)) is Relation-like M2( bool S)
bool S is set
S * (S \ (id (dom S))) is Relation-like set
(S) is Relation-like set
S /\ (id (dom S)) is Relation-like set
(S \ (id (dom S))) * S is Relation-like set

dom R is set

R \ (id (dom R)) is Relation-like M2( bool R)
bool R is set
R * (R \ (id (dom R))) is Relation-like set

(R) is Relation-like set
R /\ (id (dom R)) is Relation-like set
(R \ (id (dom R))) * R is Relation-like set