52 lines
1.3 KiB
Plaintext
52 lines
1.3 KiB
Plaintext
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$( demo0.mm 1-Jan-04 $)
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$(
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~~ PUBLIC DOMAIN ~~
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This work is waived of all rights, including copyright, according to the CC0
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Public Domain Dedication. http://creativecommons.org/publicdomain/zero/1.0/
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Norman Megill - email: nm at alum.mit.edu
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$)
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$( This file is the introductory formal system example described
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in Chapter 2 of the Meamath book. $)
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$( Declare the constant symbols we will use $)
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$c 0 + = -> ( ) term wff |- $.
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$( Declare the metavariables we will use $)
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$v t r s P Q $.
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$( Specify properties of the metavariables $)
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tt $f term t $.
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tr $f term r $.
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ts $f term s $.
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wp $f wff P $.
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wq $f wff Q $.
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$( Define "term" (part 1) $)
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tze $a term 0 $.
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$( Define "term" (part 2) $)
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tpl $a term ( t + r ) $.
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$( Define "wff" (part 1) $)
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weq $a wff t = r $.
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$( Define "wff" (part 2) $)
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wim $a wff ( P -> Q ) $.
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$( State axiom a1 $)
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a1 $a |- ( t = r -> ( t = s -> r = s ) ) $.
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$( State axiom a2 $)
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a2 $a |- ( t + 0 ) = t $.
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${
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min $e |- P $.
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maj $e |- ( P -> Q ) $.
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$( Define the modus ponens inference rule $)
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mp $a |- Q $.
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$}
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$( Prove a theorem $)
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th1 $p |- t = t $=
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$( Here is its proof: $)
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tt tze tpl tt weq tt tt weq tt a2 tt tze tpl
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tt weq tt tze tpl tt weq tt tt weq wim tt a2
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tt tze tpl tt tt a1 mp mp
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$.
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