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@@ -976,9 +976,20 @@ symmetry of equality, for instance with tactics \verb:Transitivity: and
\begin{coq_example}
Apply foo.
Transitivity (f O); Symmetry; Trivial.
+\end{coq_example}
+In case the equality $t=u$ generated by \verb:Replace: $u$ \verb:with:
+$t$ is an assumption
+(possibly modulo symmetry), it will be automatically proved and the
+corresponding goal will not appear. For instance:
+\begin{coq_example}
+Restart.
+Replace (f O) with O.
+Rewrite f10; Rewrite foo; Trivial.
Save.
\end{coq_example}
+
+
\subsection{Predicate calculus over Type}
We just explained the basis of first-order reasoning in the universe