Case 3: Does $A + B$ have positive upper and lower density that are equal? This is the literal interpretation of "positive density" which was falsified.

1sorry ↔2  ({x | (Nat.digits 3 x).toFinset ⊆ {0, 1}} + {x | (Nat.digits 4 x).toFinset ⊆ {0, 1}}).lowerDensity = 0 ∧3    0 < ({x | (Nat.digits 3 x).toFinset ⊆ {0, 1}} + {x | (Nat.digits 4 x).toFinset ⊆ {0, 1}}).upperDensity