Question

Would anyone give me a generalized poof of superposition principle because all we do is observe and learn...........doesn't feel quite good

Answer 1

In physics and systems theory, the superposition principle [1], also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y).
Mathematically, for a linear system, F, defined by F(x) = y, where x is some sort of stimulus (input) and y is some sort of response (output), the superposition (i.e., sum) of stimuli yields a superposition of the respective responses:
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The superposition principle holds because, by definition, a linear system must be additive. Superposition may sometimes imply linearity, depending on whether homogeneity is included or implied in the definition of superposition.

Answer 2

the above answers generalises but if you need an insightful explanation ...consider a load(resistive,linear) with 2 voltage sources..this circuit can be analysed as the sum of responses to individual sources...for example if V1(volt source 1) produces 1A through the load and V2 2A then the sum(with direction consideration) is the total output.
but take a diode with cutoff 0.7 volts.and V1 producing 0.3V across it ,V2 0.4V across it in same direction for the individual values the diode remains off....but for the sum 0.7V it gets short ...this is non-linearity and superposition cannot be applied.