Error about the fact that type specified by $f statement is global even if variable is not.

[Sylvain Kerjean]

Hello,

In the metamath book, p114 there is this assertion :

The type declared by a $f statement for a given label is global even if the
variable is not (e.g., a database may not have wff P  in one local scope and
class P  in another). 

I can guess the justification was to speed up verification of types with no soundness weakness, but it seems not to be inforced in metamath-exe :

this minimal example doesn't trigger an error message (variable v is declared with types A then B, and used in both proofs).

So should we add  an erratum to he book errata list, or file an issue to metamath-exe ?

================

$c A B $.

${
$v v $.
tA $f A v $.

hypA $e A v $.
conA $p A v $= hypA $.
$}

${
$v v $.
tB $f B v $.

hypB $e B v $.
conB $p B v $= hypB $.
$}

[Glauco]

I've tested the example myself, and the Metamath program verifies it without errors.

Given the explicit statement in the book, I lean toward considering this as a potential issue in metamath-exe rather than an erratum for the book.

How does metamathknife handle this case?

[Mario Carneiro]

metamath-knife also permits it. I think not all mm verifiers support it though; I originally advocated for adding this rule to simplify verifiers that don't do scoped c/v (e.g. because they build a grammar for the database and use that to check everything).

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