+\[\eqn{Foreign Contents}{
+ \bigforall_{C \in \foreign}
+ D \le C \implies \isforeign{D}
+}\]
+\[\eqn{Bases' Children}{
+ C \hasparent D \land D \in \pdn
+ \implies
+ C \in \pdn \lor C \in \pdy
+}\]
+
+We also assign each new commit $C$ to zero or one of the sets $\p$, as
+stated in the definition of $\patchof{C}$ in the summary for each kind
+of commit.
+
+A commit $C$ which satisfies all of the above is said to be
+``conformant''.
+
+For each operation we will perform which generates a new commit, we
+will assume the conformance of the existing history and prove the
+conformance of the new commit.