let F1, F2 be set ; :: thesis: ( ( for x being set holds

( x in F1 iff x is RoughSet of X ) ) & ( for x being set holds

( x in F2 iff x is RoughSet of X ) ) implies F1 = F2 )

assume A2: ( ( for x being set holds

( x in F1 iff x is RoughSet of X ) ) & ( for x being set holds

( x in F2 iff x is RoughSet of X ) ) ) ; :: thesis: F1 = F2

for x being object holds

( x in F1 iff x in F2 ) by A2;

hence F1 = F2 by TARSKI:2; :: thesis: verum

( x in F1 iff x is RoughSet of X ) ) & ( for x being set holds

( x in F2 iff x is RoughSet of X ) ) implies F1 = F2 )

assume A2: ( ( for x being set holds

( x in F1 iff x is RoughSet of X ) ) & ( for x being set holds

( x in F2 iff x is RoughSet of X ) ) ) ; :: thesis: F1 = F2

for x being object holds

( x in F1 iff x in F2 ) by A2;

hence F1 = F2 by TARSKI:2; :: thesis: verum