3 We maintain these each time we construct a new commit. \\
5 C \has D \implies C \ge D
8 \bigforall_{C \in \py} \pendsof{C}{\pn} = \{ B \}
10 \[\eqn{Tip Contents:}{
11 \bigforall_{C \in \py} D \isin C \equiv
12 { D \isin \baseof{C} \lor \atop
13 (D \in \py \land D \le C) }
15 \[\eqn{Base Acyclic:}{
16 \bigforall_{C \in \pn} D \isin C \implies D \notin \py
19 \bigforall_{C,\p} C \haspatch \p \lor C \nothaspatch \p
22 \bigforall_{C,\p} C \haspatch \p \implies \pendsof{C}{\p} = \{ T \}
24 \[\eqn{Foreign Inclusion:}{
25 \bigforall_{D \text{ s.t. } \patchof{D} = \bot} D \isin C \equiv D \leq C
27 \[\eqn{Foreign Contents:}{
28 \bigforall_{C \text{ s.t. } \patchof{C} = \bot}
29 D \le C \implies \patchof{D} = \bot
32 We also assign each new commit $C$ to zero or one of the sets $\p$, as
33 stated in the definition of $\patchof{C}$ in the summary for each kind
36 A commit $C$ which satisfies all of the above is said to be
39 For each operation we will perform which generates a new commit, we
40 will assume the conformance of the existing history and prove the
41 conformance of the new commit.