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Document unbound variables are basically universal #4306

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Document unbound variables are basically universal #4306

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Document unbound variables are basically universal
david-a-wheeler Oct 21, 2024
0c028ae
Note that class variables as postulates are fine
david-a-wheeler Oct 21, 2024
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10 changes: 10 additions & 0 deletions set.mm
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Expand Up @@ -431159,6 +431159,16 @@ be applied for new theorems (formerly, the class and wff variables
~ mmtheorems32.html#mm3146s also describes the
metatheorem that underlies this.

<p>You should read any statement starting with ` |- `
and having one or more unbound set variable(s) as universally
quantified over those
variables. So if you state ` |- 0 < k ` , say as a postulate,
that's saying " ` 0 < k ` is derivable in the empty context"
which is a strong statement,
equivalent to ` A. k 0 < k ` , which without further context is false.
The same is not true for class variables (e.g., ` 0 < K ` is typically
safe to postulate).

<p><b>Additional rules for definitions</b>

<p>Standard Metamath verifiers do not distinguish between axioms and
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