:: SYSREL 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

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

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

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 is Relation-like set

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

dom (x /\ [:S,R:]) is set

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

x /\ {} is Relation-like 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 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

x 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

x is Relation-like set

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

[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

[: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 is Relation-like set

R is Relation-like set

S \/ R is Relation-like set

x is Relation-like set

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

S * x is Relation-like set

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

z is Relation-like 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 is Relation-like set

y | x is Relation-like set

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

x |` y 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 is Relation-like set

z | x is Relation-like set

z | y is Relation-like 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

x is Relation-like set

x | 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 is Relation-like set

S ~ is Relation-like set

R is Relation-like set

R ~ is Relation-like set

S \/ R is Relation-like set

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

S is set

id S is Relation-like S -defined S -valued 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 is Relation-like S -defined S -valued 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

id {S} is Relation-like {S} -defined {S} -valued 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},{S}:] is Relation-like set

S is set

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

R is set

S \/ R is set

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

id R is Relation-like R -defined 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

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

R is set

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

S \/ R is set

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

S is set

id S is Relation-like S -defined S -valued 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

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

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

R is Relation-like set

R ~ is Relation-like 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

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

R is Relation-like set

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

S is set

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

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

R is Relation-like set

dom R is set

id (dom R) is Relation-like dom R -defined dom R -valued 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

id (rng R) is Relation-like rng R -defined rng R -valued 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

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

R is Relation-like 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))

S is Relation-like set

S * S is Relation-like set

rng S is set

id (rng S) is Relation-like rng S -defined rng S -valued 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

id (dom S) is Relation-like dom S -defined dom S -valued 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

S is Relation-like set

S * S is Relation-like set

rng S is set

id (rng S) is Relation-like rng S -defined rng S -valued 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

R is Relation-like set

R * R is Relation-like set

dom R is set

id (dom R) is Relation-like dom R -defined dom R -valued 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

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

R is Relation-like 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

id (rng R) is Relation-like rng R -defined rng R -valued 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

id (dom R) is Relation-like dom R -defined dom R -valued 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

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 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

(x) is Relation-like set

dom x is set

id (dom x) is Relation-like dom x -defined dom x -valued set

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

dom (x) is set

S is Relation-like set

(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 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

(R) is Relation-like set

dom R is set

id (dom R) is Relation-like dom R -defined dom R -valued 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

(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 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

x * x is Relation-like set

(x) is Relation-like set

dom x is set

id (dom x) is Relation-like dom x -defined dom x -valued 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

x is Relation-like set

x * x is Relation-like set

dom x is set

id (dom x) is Relation-like dom x -defined dom x -valued 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)

S is Relation-like set

S * 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

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

(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 set

dom (S) is set

rng (S) is set

rng S is set

S is Relation-like set

(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 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

(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 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

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

R is Relation-like 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 | S is Relation-like set

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

S |` R is Relation-like 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

(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 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

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

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)

S is Relation-like set

R is Relation-like set

S * R is Relation-like set

dom R is set

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

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

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

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

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

S is Relation-like set

(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 set

R is Relation-like set

S * R is Relation-like set

dom R is set

id (dom R) is Relation-like dom R -defined dom R -valued 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 * S 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

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

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

R is Relation-like set

S * R is Relation-like set

dom R is set

id (dom R) is Relation-like dom R -defined dom R -valued 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 * S 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