foreign notation: change \bot to \foreign everywhere

[topbloke-formulae.git] / lemmas.tex

diff --git a/lemmas.tex b/lemmas.tex
index 937398207615e337585cdf7773d0c33f66f6a9f6..72e00d61fc5b23d82252989bc578c8f18596a289 100644 (file)
--- a/lemmas.tex
+++ b/lemmas.tex
@@ -175,12 +175,12 @@ $$
   \right]
  \implies
   \left[
-   \bigforall_{D \text{ s.t. } \patchof{D} = \bot}
+   \bigforall_{D \text{ s.t. } \patchof{D} = \foreign}
      D \isin C \equiv D \le C
   \right]
 $$
 \proof{
-Consider some $D$ s.t. $\patchof{D} = \bot$.
+Consider some $D$ s.t. $\patchof{D} = \foreign$.
 If $D = C$, trivially true.  For $D \neq C$,
 by Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
 And by Exact Ancestors $D \le L \equiv D \le C$.
@@ -192,20 +192,20 @@ Given conformant commits $A \in \set A$,
 $$
    \left[
     C \hasparents \set A \land
-    \patchof{C} = \bot \land
-      \bigforall_{A \in \set A} \patchof{A} = \bot
+    \patchof{C} = \foreign \land
+      \bigforall_{A \in \set A} \patchof{A} = \foreign
    \right]
   \implies
    \left[
   \bigforall_{D}
     D \le C
    \implies
-    \patchof{D} = \bot
+    \patchof{D} = \foreign
    \right]
 $$
 \proof{
-Consider some $D \le C$.  If $D = C$, $\patchof{D} = \bot$ trivially.
+Consider some $D \le C$.  If $D = C$, $\patchof{D} = \foreign$ trivially.
 If $D \neq C$ then $D \le A$ where $A \in \set A$.  By Foreign
-Contents of $A$, $\patchof{D} = \bot$.
+Contents of $A$, $\patchof{D} = \foreign$.
 }