Uniformize databases preambles and typgraphic conventions (#3779)

demo0.mm

@@ -1,50 +1,80 @@
-$( demo0.mm  1-Jan-04 $)
+$( This is the Metamath database demo0.mm. $)
+
+$( Metamath is a formal language and associated computer program for
+   archiving, verifying, and studying mathematical proofs, created by Norman
+   Dwight Megill (1950--2021).  For more information, visit
+   https://us.metamath.org and
+   https://github.com/metamath/set.mm, and feel free to ask questions at
+   https://groups.google.com/g/metamath. $)
+
+$( The database demo0.mm was created by Norman Megill.  This is the version
+   of 1-Jan-2004. $)
+
+
+$( !
+#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#
+  Metamath source file demo0.mm
+#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#
 
-$(
                            ~~ PUBLIC DOMAIN ~~
 This work is waived of all rights, including copyright, according to the CC0
 Public Domain Dedication.  http://creativecommons.org/publicdomain/zero/1.0/
 
-Norman Megill
+Norman Megill - http://metamath.org
+
+$)
+
+
+$(
+#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#
+  demo0.mm: An introductory formal system example
+#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#
+
+  This file is the introductory formal system example described in Chapter 2 of
+  the Metamath book.
 
 $)
 
+$( Declare the constant symbols we will use. $)
+  $c 0 + = -> ( ) term wff |- $.
+
+$( Declare the metavariables we will use. $)
+  $v t r s P Q $.
+
+$( Specify properties of the metavariables. $)
+  tt $f term t $.
+  tr $f term r $.
+  ts $f term s $.
+  wp $f wff P $.
+  wq $f wff Q $.
+
+$( Define "term" (part 1 of 2). $)
+  tze $a term 0 $.
+
+$( Define "term" (part 2 of 2). $)
+  tpl $a term ( t + r ) $.
+
+$( Define "wff" (part 1 of 2). $)
+  weq $a wff t = r $.
+
+$( Define "wff" (part 2 of 2). $)
+  wim $a wff ( P -> Q ) $.
+
+$( State axiom ~ a1 . $)
+  a1 $a |- ( t = r -> ( t = s -> r = s ) ) $.
+
+$( State axiom ~ a2 . $)
+  a2 $a |- ( t + 0 ) = t $.
+
+  ${
+    min $e |- P $.
+    maj $e |- ( P -> Q ) $.
+    $( Define the modus ponens inference rule. $)
+    mp  $a |- Q $.
+  $}
 
-$( This file is the introductory formal system example described
-   in Chapter 2 of the Meamath book. $)
-
-$( Declare the constant symbols we will use $)
-    $c 0 + = -> ( ) term wff |- $.
-$( Declare the metavariables we will use $)
-    $v t r s P Q $.
-$( Specify properties of the metavariables $)
-    tt $f term t $.
-    tr $f term r $.
-    ts $f term s $.
-    wp $f wff P $.
-    wq $f wff Q $.
-$( Define "term" (part 1) $)
-    tze $a term 0 $.
-$( Define "term" (part 2) $)
-    tpl $a term ( t + r ) $.
-$( Define "wff" (part 1) $)
-    weq $a wff t = r $.
-$( Define "wff" (part 2) $)
-    wim $a wff ( P -> Q ) $.
-$( State axiom a1 $)
-    a1 $a |- ( t = r -> ( t = s -> r = s ) ) $.
-$( State axiom a2 $)
-    a2 $a |- ( t + 0 ) = t $.
-    ${
-       min $e |- P $.
-       maj $e |- ( P -> Q ) $.
-$( Define the modus ponens inference rule $)
-       mp  $a |- Q $.
-    $}
-$( Prove a theorem $)
-    th1 $p |- t = t $=
+$( Prove a theorem. $)
+  th1 $p |- t = t $=
   $( Here is its proof: $)
-       tt tze tpl tt weq tt tt weq tt a2 tt tze tpl
-       tt weq tt tze tpl tt weq tt tt weq wim tt a2
-       tt tze tpl tt tt a1 mp mp
-     $.
+    tt tze tpl tt weq tt tt weq tt a2 tt tze tpl tt weq tt tze tpl tt weq tt tt
+    weq wim tt a2 tt tze tpl tt tt a1 mp mp $.

hol.mm

@@ -5,14 +5,14 @@
    Dwight Megill (1950--2021).  For more information, visit
    https://us.metamath.org and
    https://github.com/metamath/set.mm, and feel free to ask questions at
-   https://groups.google.com/group/metamath. $)
+   https://groups.google.com/g/metamath. $)
 
 $( The database hol.mm was created by Mario Carneiro on 7-Oct-2014. $)
 
 
 $( !
 #*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#
-  Metamath source file for higher order logic
+  Metamath source file for higher-order logic
 #*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#
 
                            ~~ PUBLIC DOMAIN ~~