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0001 <!DOCTYPE html> 0002 <html><head> 0003 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/> 0004 <title>test.mm</title> 0005 <meta name="generator" content="KF5::SyntaxHighlighting - Definition (Metamath) - Theme (Breeze Dark)"/> 0006 </head><body style="background-color:#232629;color:#cfcfc2"><pre> 0007 <span style="color:#7a7c7d;">$( Modified version of demo0.mm from 1-Jan-04 $)</span> 0008 0009 <span style="color:#7a7c7d;">$(</span> 0010 <span style="color:#7a7c7d;"> PUBLIC DOMAIN DEDICATION</span> 0011 0012 <span style="color:#7a7c7d;">This file is placed in the public domain per the Creative Commons Public</span> 0013 <span style="color:#7a7c7d;">Domain Dedication. http://creativecommons.org/licenses/publicdomain/</span> 0014 0015 <span style="color:#7a7c7d;">Norman Megill - email: nm at alum.mit.edu</span> 0016 <span style="color:#7a7c7d;">$)</span> 0017 0018 <span style="font-weight:bold;">$c</span><span style="color:#8e44ad;"> 0 + = -> ( ) term wff |- </span><span style="font-weight:bold;">$.</span> 0019 0020 <span style="font-weight:bold;">$v</span><span style="color:#27aeae;"> t r s P Q </span><span style="font-weight:bold;">$.</span> 0021 0022 <span style="color:#da4453;">tt</span> <span style="font-weight:bold;">$f</span> <span style="color:#8e44ad;">term</span><span style="color:#27aeae;"> t </span><span style="font-weight:bold;">$.</span> 0023 <span style="color:#da4453;">tr</span> <span style="font-weight:bold;">$f</span> <span style="color:#8e44ad;">term</span><span style="color:#27aeae;"> r </span><span style="font-weight:bold;">$.</span> 0024 <span style="color:#da4453;">ts</span> <span style="font-weight:bold;">$f</span> <span style="color:#8e44ad;">term</span><span style="color:#27aeae;"> s </span><span style="font-weight:bold;">$.</span> 0025 <span style="color:#da4453;">wp</span> <span style="font-weight:bold;">$f</span> <span style="color:#8e44ad;">wff</span><span style="color:#27aeae;"> P </span><span style="font-weight:bold;">$.</span> 0026 <span style="color:#da4453;">wq</span> <span style="font-weight:bold;">$f</span> <span style="color:#8e44ad;">wff</span><span style="color:#27aeae;"> Q </span><span style="font-weight:bold;">$.</span> 0027 0028 <span style="color:#da4453;">tze</span> <span style="font-weight:bold;">$a</span> <span style="color:#8e44ad;">term</span><span style="color:#27aeae;"> 0 </span><span style="font-weight:bold;">$.</span> 0029 <span style="color:#da4453;">tpl</span> <span style="font-weight:bold;">$a</span> <span style="color:#8e44ad;">term</span><span style="color:#27aeae;"> ( t + r ) </span><span style="font-weight:bold;">$.</span> 0030 0031 <span style="color:#da4453;">weq</span> <span style="font-weight:bold;">$a</span> <span style="color:#8e44ad;">wff</span><span style="color:#27aeae;"> t = r </span><span style="font-weight:bold;">$.</span> 0032 <span style="color:#da4453;">wim</span> <span style="font-weight:bold;">$a</span> <span style="color:#8e44ad;">wff</span><span style="color:#27aeae;"> ( P -> Q ) </span><span style="font-weight:bold;">$.</span> 0033 0034 <span style="color:#da4453;">a1</span> <span style="font-weight:bold;">$a</span> <span style="color:#8e44ad;">|-</span><span style="color:#27aeae;"> ( t = r -> ( t = s -> r = s ) ) </span><span style="font-weight:bold;">$.</span> 0035 <span style="color:#da4453;">a2</span> <span style="font-weight:bold;">$a</span> <span style="color:#8e44ad;">|-</span><span style="color:#27aeae;"> ( t + 0 ) = t </span><span style="font-weight:bold;">$.</span> 0036 <span style="font-weight:bold;">${</span> 0037 <span style="color:#7a7c7d;">$( Define the modus ponens inference rule $)</span> 0038 <span style="color:#da4453;">min</span> <span style="font-weight:bold;">$e</span> <span style="color:#8e44ad;">|-</span><span style="color:#27aeae;"> P </span><span style="font-weight:bold;">$.</span> 0039 <span style="color:#da4453;">maj</span> <span style="font-weight:bold;">$e</span> <span style="color:#8e44ad;">|-</span><span style="color:#27aeae;"> ( P -> Q ) </span><span style="font-weight:bold;">$.</span> 0040 <span style="color:#da4453;">mp</span> <span style="font-weight:bold;">$a</span> <span style="color:#8e44ad;">|-</span><span style="color:#27aeae;"> Q </span><span style="font-weight:bold;">$.</span> 0041 <span style="font-weight:bold;">$}</span> 0042 0043 <span style="color:#da4453;">th1</span> <span style="font-weight:bold;">$p</span> <span style="color:#8e44ad;">|-</span><span style="color:#27aeae;"> t = t </span><span style="font-weight:bold;">$=</span> 0044 <span style="color:#da4453;"> </span><span style="color:#7a7c7d;">$( Here is its proof: $)</span> 0045 <span style="color:#da4453;"> tt tze tpl tt weq tt tt weq tt a2 tt tze tpl</span> 0046 <span style="color:#da4453;"> tt weq tt tze tpl tt weq tt tt weq wim tt a2</span> 0047 <span style="color:#da4453;"> tt tze tpl tt tt a1 mp mp</span> 0048 <span style="font-weight:bold;">$.</span> 0049 </pre></body></html>