I propose to use (the new version of) frlmgsum in step 85 and to replace 
step 84 by

d7::eqid           |-   (   k
                        e.  ( 0 ... N )
                        |-> ( n e. ( 1 ... N ) |-> ( ( w ` k ) x. C ) ) )
                      = (   k
                        e.  ( 0 ... N )
                        |-> ( n e. ( 1 ... N ) |-> ( ( w ` k ) x. C ) ) )
d13:15:mptex       |-    ( n e. ( 1 ... N ) |-> ( ( w ` k ) x. C ) )
                      e. _V
d9:d13:a1i         |- (  (  ( ph /\ w : ( 0 ... N ) --> QQ )
                         /\ k e. ( 0 ... N ) )
                      ->    ( n e. ( 1 ... N ) |-> ( ( w ` k ) x. C ) )
                         e. _V )
d12::snex       |- { 0 } e. _V
d11:15,d12:xpex    |- ( ( 1 ... N ) X. { 0 } ) e. _V
d10:d11:a1i        |- (  ( ph /\ w : ( 0 ... N ) --> QQ )
                      -> ( ( 1 ... N ) X. { 0 } ) e. _V )
84:d7,45,d9,d10:fsuppmptdm |- (  ( ph /\ w : ( 0 ... N ) --> QQ )
                      -> (   k
                         e.  ( 0 ... N )
                         |-> ( n e. ( 1 ... N ) |-> ( ( w ` k ) x. C ) ) )
                         finSupp
                         ( ( 1 ... N ) X. { 0 } ) )

On Saturday, April 25, 2020 at 9:24:12 AM UTC+2, Alexander van der Vekens 
wrote:
>
> The problem is that the proof uses an old version of frlmgsum: Either 
> frlmgsumOLD (deprecated!) must be used in step 85, or step 84 must be 
> adapted to comply with the new version of frlmgsum.
>
> Alexander
>
>

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