per cases ( n is empty or not n is empty ) ;

suppose n is empty ; :: thesis: for b₁ being Relation of (n -tuples_on X) st b₁ = n -placesOf R holds
b₁ is symmetric

hence for b₁ being Relation of (n -tuples_on X) st b₁ = n -placesOf R holds
b₁ is symmetric by Lm13; :: thesis: verum

end;

suppose not n is empty ; :: thesis: for b₁ being Relation of (n -tuples_on X) st b₁ = n -placesOf R holds
b₁ is symmetric

hence for b₁ being Relation of (n -tuples_on X) st b₁ = n -placesOf R holds
b₁ is symmetric by Lm16; :: thesis: verum

end;

end;