unique tips: fix various \pendsof and \pancsof to refer to \py not \p

diff --git a/invariants.tex b/invariants.tex
index bc3813e6b83593e5d5ad0ad9c2b59c9a0f53d000..bd77d69d3da86844bd1b74b89ccad2ed902c3187 100644 (file)
--- a/invariants.tex
+++ b/invariants.tex
@@ -19,7 +19,7 @@ We maintain these each time we construct a new commit. \\
   \bigforall_{C,\p} C \haspatch \p \lor C \nothaspatch \p
 }\]
 \[\eqn{Unique Tips:}{
-  \bigforall_{C,\p} C \haspatch \p \implies \pendsof{C}{\p} = \{ T \}
+  \bigforall_{C,\p} C \haspatch \p \implies \pendsof{C}{\py} = \{ T \}
 }\]
 \[\eqn{Foreign Inclusion:}{
   \bigforall_{D \text{ s.t. } \patchof{D} = \bot} D \isin C \equiv D \leq C

diff --git a/lemmas.tex b/lemmas.tex
index 40cc5f488a6403581a1561936be982097dc5327f..937398207615e337585cdf7773d0c33f66f6a9f6 100644 (file)
--- a/lemmas.tex
+++ b/lemmas.tex
@@ -133,12 +133,12 @@ $$
  \Big[
    C \hasparents \{ A \}
  \Big] \implies \left[
-   \bigforall_{P \patchisin C} \pendsof{C}{\p} = \{ T \}
+   \bigforall_{P \patchisin C} \pendsof{C}{\py} = \{ T \}
  \right]
 $$
 \proof{
-  Trivial for $C \in \p$.
-  For $C \not\in \p$, $\pancsof{C}{\p} = \pancsof{A}{\p}$,
+  Trivial for $C \in \py$.
+  For $C \not\in \py$, $\pancsof{C}{\py} = \pancsof{A}{\py}$,
   so Unique Tips of $A$ suffices.
 }
 

diff --git a/merge.tex b/merge.tex
index 45b7f66f0cbddd4eeedba8446a19ee11ebb5bf16..7ca8446e353b04cfae492b534290e11335daceb2 100644 (file)
--- a/merge.tex
+++ b/merge.tex
@@ -48,9 +48,9 @@ $L \in \pn$, $R \in \pry$, $M = \baseof{R}$.
 }\]
 \[ \eqn{ Suitable Tip }{
     \bigexists_T
-      \pendsof{J}{\p} = \{ T \}
+      \pendsof{J}{\py} = \{ T \}
      \land
-      \forall_{E \in \pendsof{K}{\p}} T \ge E
+      \forall_{E \in \pendsof{K}{\py}} T \ge E
     , \text{where} \{J,K\} = \{L,R\}
 }\]
 \[ \eqn{ Foreign Merges }{