Metamath's Python verifier - its trusted kernel - is just 700 lines of Python short: https://github.com/david-a-wheeler/mmverify.py/blob/master/m...
Metamath Zero's Haskell implementation 700, and the C implementation 1000 lines (or 1800 overall) https://github.com/digama0/mm0
How do other proof systems compare?
Some bug counts: https://tristan.st/blog/in_search_of_falsehood
My favorite minimalistic example of the Metamath base language (which higher level languages can compile down to), which, saved as, say, prop.mm can be verified with the verifier:
$c wff $. $( we use this $constant as a type of formula (well formed formula) $)
$c ( ) ! -> $. $( brackets, negation, implication $)
$v A B C $. $( $variables to be used in formulas $)
wa $f wff A $. $( $floating hypothesis "wa" which says, that A is a well-formed formula $)
wb $f wff B $.
wc $f wff C $.
$( The following assertions define the rules to create formulas $)
$( In Metamath (unlike Metamath Zero), definitions also use the $axiom statement type $)
wng $a wff ! A $. $( "not A is a well-formed-formula" - mandatory hypotheses are (wa) $)
wim $a wff ( A -> B ) $. $( "A implies B is a well-formed-formula" - mandatory hypotheses are (wa, wb) $)
$c |- $. $( this $constant will be used as a type of provable formula $)
$( Schemes of $axioms of propositional logic $)
a1 $a |- ( A -> ( B -> A ) ) $.
a2 $a |- ( ( A -> ( B -> C ) ) -> ( ( A -> B ) -> ( A -> C ) ) ) $.
a3 $a |- ( ( ! A -> ! B ) -> ( B -> A ) ) $.
$( Definition of the Modus Ponens rule of inference in new scope; otherwise $essential hypotheses (inputs) mp1, mp2 will become mandatory for all upcoming assertions $)
${
mp1 $e |- A $.
mp2 $e |- ( A -> B ) $.
mp $a |- B $. $( mandatory hypotheses of "mp" are (wa, wb, mp1, mp2) $)
$}
$( A $proof states the string of symbols to be proven, followed by a list of labels used by the stack machine $)
$( $floating and $essential hypotheses are pushed onto the top of the stack, $axioms and $proofs transform it by using the top of the stack as inputs $)
$( When the stack is empty at the end, the proof is successful, and the proved statement can be reused in further proofs using its label $)
$( " A implies ( B implies C) is a well-formed-formula" $)
formula1 $p wff ( A -> ( B -> C ) ) $= wa wb wc wim wim $.
$( "( A -> A ) -> ( A -> A ) is true (follows from the axioms)" $)
formula2 $p |- ( ( A -> A ) -> ( A -> A ) ) $= wa wa wa wim wim
wa wa wim wa wa wim wim
wa wa a1
wa wa wa a2
mp $.
According to [0], "Rocq’s kernel spans approximately 41K lines of OCaml code, while Lean’s kernel consists of approximately 8K lines of C++ code."
[0] https://dl.acm.org/doi/pdf/10.1145/3747511