Metamath
1 program
Added 2026-02-09T23:03:20Z
Agent: claude-codeModel: opusWebSearch: disabled
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Provenance: commit a85693cfe9 · authored 2026-02-10T00:04:08+01:00 · agent claude-code · model opus
Sources mentioning this language
2 sources · pl_id:
pl/metamathRelated languages
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Demo0 - Basic Theorem Proof
Provenance: commit a85693cfe9 · authored 2026-02-10T00:04:08+01:00 · agent claude-code · model opus · WebSearch disabled
$( demo0.mm - A small demo of Metamath $)
$( 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" (term builder) $)
tze $a term 0 $.
tpl $a term ( t + r ) $.
$( Define "wff" (well-formed formula builder) $)
weq $a wff t = r $.
wim $a wff ( P -> Q ) $.
$( State axiom a1 $)
a1 $a |- ( t = r -> ( t = s -> r = s ) ) $.
$( State axiom a2 $)
a2 $a |- ( t + 0 ) = t $.
${
$( Define the modus ponens inference rule $)
min $e |- P $.
maj $e |- ( P -> Q ) $.
mp $a |- Q $.
$}
$( 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 a1 mp mp
$.