  Interaction between clique number $\omega(G) $ and chromatic number $\chi(G)
$ of a graph is a well studied topic in graph theory. Perfect Graph Theorems
are probably the most important results in this direction. Graph $G$ is called
\emph{perfect} if $\chi(H)=\omega(H)$ for every induced subgraph $H$ of $G$.
The Strong Perfect Graph Theorem (SPGT) states that a graph is perfect if and
only if it does not contain an odd hole (or an odd anti-hole) as its induced
subgraph. The Weak Perfect Graph Theorem (WPGT) states that a graph is perfect
if and only if its complement is perfect. In this paper, we present a formal
framework for verifying these results. We model finite simple graphs in the
constructive type theory of Coq Proof Assistant without adding any axiom to it.
Finally, we use this framework to present a constructive proof of the
Lov\'{a}sz Replication Lemma, which is the central idea in the proof of Weak
Perfect Graph Theorem.
