for f1, f2 being Function of atomic_LTL ,the BasicAssign of (LTLModel AtomicFamily ,AtomicBasicAsgn ) st ( for a being set st a in atomic_LTL holds
f1 . a = AtomicAsgn a ) & ( for a being set st a in atomic_LTL holds
f2 . a = AtomicAsgn a ) holds
f1 = f2

proof

let f1, f2 be Function of atomic_LTL ,the BasicAssign of (LTLModel AtomicFamily ,AtomicBasicAsgn ); :: thesis: ( ( for a being set st a in atomic_LTL holds
f1 . a = AtomicAsgn a ) & ( for a being set st a in atomic_LTL holds
f2 . a = AtomicAsgn a ) implies f1 = f2 )
assume that
B1: for a being set st a in atomic_LTL holds
f1 . a = AtomicAsgn a and
B2: for a being set st a in atomic_LTL holds
f2 . a = AtomicAsgn a ; :: thesis: f1 = f2
for a being set st a in atomic_LTL holds
f1 . a = f2 . a

proof

let a be set ; :: thesis: ( a in atomic_LTL implies f1 . a = f2 . a )
assume C1: a in atomic_LTL ; :: thesis: f1 . a = f2 . a
f1 . a = AtomicAsgn a by B1, C1;
hence f1 . a = f2 . a by B2, C1; :: thesis: verum

end;

hence f1 = f2 by FUNCT_2:18; :: thesis: verum

end;

hence for b₁, b₂ being Function of atomic_LTL ,the BasicAssign of (LTLModel AtomicFamily ,AtomicBasicAsgn ) st ( for a being set st a in atomic_LTL holds
b₁ . a = AtomicAsgn a ) & ( for a being set st a in atomic_LTL holds
b₂ . a = AtomicAsgn a ) holds
b₁ = b₂ ; :: thesis: verum