How to use rewrite on a subexpression of the current goal

How to use rewrite on a subexpression of the current goal

References

Reference NO 1

http://stackoverflow.com/questions/13645979/how-to-use-rewrite-on-a-subexpression-of-the-current-goal

Reference NO 2

http://stackoverflow.com/questions/8874951/unable-to-find-an-instance-for-the-variable

Reference NO 3

http://stackoverflow.com/questions/14209304/adding-hypotheses-that-are-not-in-the-current-hypotheses

Reference NO 4

http://stackoverflow.com/questions/6103810/strange-behavior-of-semicolon-in-coq

Reference NO 5

http://dream.inf.ed.ac.uk/publications/pre-96/nancy.ps.gz

Reference NO 6

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.41.6396&rep=rep1&type=pdf

Reference NO 7

http://coq.inria.fr/refman/Reference-Manual010.html

Reference NO 8

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