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Add ringidvalg to iset.mm
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This is ringidval from set.mm with an additional set existence
condition.  The proof is taken from a portion of the set.mm proof.
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jkingdon committed Dec 30, 2024
1 parent 17a9351 commit 20472e1
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11 changes: 11 additions & 0 deletions iset.mm
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Expand Up @@ -147475,6 +147475,17 @@ since the target of the homomorphism (operator ` O ` in our model) need
(Revised by Mario Carneiro, 27-Dec-2014.) $)
df-ur $a |- 1r = ( 0g o. mulGrp ) $.

${
ringidval.g $e |- G = ( mulGrp ` R ) $.
ringidval.u $e |- .1. = ( 1r ` R ) $.
$( The value of the unity element of a ring. (Contributed by NM,
27-Aug-2011.) (Revised by Mario Carneiro, 27-Dec-2014.) $)
ringidvalg $p |- ( R e. V -> .1. = ( 0g ` G ) ) $=
( wcel cur cfv cmgp c0g cvv wceq elex ccom df-ur fveq1i wfn fnmgp fvco2
mpan eqtrid syl fveq2i 3eqtr4g ) ADGZAHIZAJIZKIZBCKIUFALGZUGUIMADNUJUGAKJ
OZIZUIAHUKPQJLRUJULUIMSLKJATUAUBUCFCUHKEUDUE $.
$}


$(
#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#
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5 changes: 5 additions & 0 deletions mmil.raw.html
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Expand Up @@ -10708,6 +10708,11 @@
on ` ( Base `` R ) C_ A `</td>
</tr>

<tr>
<td>ringidval</td>
<td>~ ringidvalg</td>
</tr>

<tr>
<td>df-drng</td>
<td><i>none</i></td>
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