<beginfold id='1'>$(</beginfold id='1'> Modified version of demo0.mm from 1-Jan-04 <endfold id='1'>$)</endfold id='1'>

<beginfold id='1'>$(</beginfold id='1'>
                      PUBLIC DOMAIN DEDICATION

This file is placed in the public domain per the Creative Commons Public
Domain Dedication. http://creativecommons.org/licenses/publicdomain/

Norman Megill - email: nm at alum.mit.edu
<endfold id='1'>$)</endfold id='1'>

$c 0 + = -> ( ) term wff |- $.

$v t r s P Q $.

tt $f term t $.
tr $f term r $.
ts $f term s $.
wp $f wff P $.
wq $f wff Q $.

tze $a term 0 $.
tpl $a term ( t + r ) $.

weq $a wff t = r $.
wim $a wff ( P -> Q ) $.

a1 $a |- ( t = r -> ( t = s -> r = s ) ) $.
a2 $a |- ( t + 0 ) = t $.
<beginfold id='2'>${</beginfold id='2'>
    <beginfold id='1'>$(</beginfold id='1'> Define the modus ponens inference rule <endfold id='1'>$)</endfold id='1'>
    min $e |- P $.
    maj $e |- ( P -> Q ) $.
    mp  $a |- Q $.
<endfold id='2'>$}</endfold id='2'>

th1 $p |- t = t <beginfold id='3'>$=</beginfold id='3'>
    <beginfold id='1'>$(</beginfold id='1'> Here is its proof: <endfold id='1'>$)</endfold id='1'>
    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
<endfold id='3'>$.</endfold id='3'>
