Step |
Hyp |
Ref |
Expression |
1 |
|
idlsrgval.1 |
|
2 |
|
idlsrgval.2 |
|
3 |
|
idlsrgval.3 |
|
4 |
|
idlsrgval.4 |
|
5 |
|
elex |
|
6 |
|
fvexd |
|
7 |
|
simpr |
|
8 |
|
simpl |
|
9 |
8
|
fveq2d |
|
10 |
7 9
|
eqtrd |
|
11 |
10 1
|
eqtr4di |
|
12 |
11
|
opeq2d |
|
13 |
8
|
fveq2d |
|
14 |
13 2
|
eqtr4di |
|
15 |
14
|
opeq2d |
|
16 |
8
|
fveq2d |
|
17 |
8
|
fveq2d |
|
18 |
17 3
|
eqtr4di |
|
19 |
18
|
fveq2d |
|
20 |
19 4
|
eqtr4di |
|
21 |
20
|
oveqd |
|
22 |
16 21
|
fveq12d |
|
23 |
11 11 22
|
mpoeq123dv |
|
24 |
23
|
opeq2d |
|
25 |
12 15 24
|
tpeq123d |
|
26 |
11
|
rabeqdv |
|
27 |
11 26
|
mpteq12dv |
|
28 |
27
|
rneqd |
|
29 |
28
|
opeq2d |
|
30 |
11
|
sseq2d |
|
31 |
30
|
anbi1d |
|
32 |
31
|
opabbidv |
|
33 |
32
|
opeq2d |
|
34 |
29 33
|
preq12d |
|
35 |
25 34
|
uneq12d |
|
36 |
6 35
|
csbied |
|
37 |
|
df-idlsrg |
Could not format IDLsrg = ( r e. _V |-> [_ ( LIdeal ` r ) / b ]_ ( { <. ( Base ` ndx ) , b >. , <. ( +g ` ndx ) , ( LSSum ` r ) >. , <. ( .r ` ndx ) , ( i e. b , j e. b |-> ( ( RSpan ` r ) ` ( i ( LSSum ` ( mulGrp ` r ) ) j ) ) ) >. } u. { <. ( TopSet ` ndx ) , ran ( i e. b |-> { j e. b | -. i C_ j } ) >. , <. ( le ` ndx ) , { <. i , j >. | ( { i , j } C_ b /\ i C_ j ) } >. } ) ) : No typesetting found for |- IDLsrg = ( r e. _V |-> [_ ( LIdeal ` r ) / b ]_ ( { <. ( Base ` ndx ) , b >. , <. ( +g ` ndx ) , ( LSSum ` r ) >. , <. ( .r ` ndx ) , ( i e. b , j e. b |-> ( ( RSpan ` r ) ` ( i ( LSSum ` ( mulGrp ` r ) ) j ) ) ) >. } u. { <. ( TopSet ` ndx ) , ran ( i e. b |-> { j e. b | -. i C_ j } ) >. , <. ( le ` ndx ) , { <. i , j >. | ( { i , j } C_ b /\ i C_ j ) } >. } ) ) with typecode |- |
38 |
|
tpex |
|
39 |
|
prex |
|
40 |
38 39
|
unex |
|
41 |
36 37 40
|
fvmpt |
Could not format ( R e. _V -> ( IDLsrg ` R ) = ( { <. ( Base ` ndx ) , I >. , <. ( +g ` ndx ) , .(+) >. , <. ( .r ` ndx ) , ( i e. I , j e. I |-> ( ( RSpan ` R ) ` ( i .(x) j ) ) ) >. } u. { <. ( TopSet ` ndx ) , ran ( i e. I |-> { j e. I | -. i C_ j } ) >. , <. ( le ` ndx ) , { <. i , j >. | ( { i , j } C_ I /\ i C_ j ) } >. } ) ) : No typesetting found for |- ( R e. _V -> ( IDLsrg ` R ) = ( { <. ( Base ` ndx ) , I >. , <. ( +g ` ndx ) , .(+) >. , <. ( .r ` ndx ) , ( i e. I , j e. I |-> ( ( RSpan ` R ) ` ( i .(x) j ) ) ) >. } u. { <. ( TopSet ` ndx ) , ran ( i e. I |-> { j e. I | -. i C_ j } ) >. , <. ( le ` ndx ) , { <. i , j >. | ( { i , j } C_ I /\ i C_ j ) } >. } ) ) with typecode |- |
42 |
5 41
|
syl |
Could not format ( R e. V -> ( IDLsrg ` R ) = ( { <. ( Base ` ndx ) , I >. , <. ( +g ` ndx ) , .(+) >. , <. ( .r ` ndx ) , ( i e. I , j e. I |-> ( ( RSpan ` R ) ` ( i .(x) j ) ) ) >. } u. { <. ( TopSet ` ndx ) , ran ( i e. I |-> { j e. I | -. i C_ j } ) >. , <. ( le ` ndx ) , { <. i , j >. | ( { i , j } C_ I /\ i C_ j ) } >. } ) ) : No typesetting found for |- ( R e. V -> ( IDLsrg ` R ) = ( { <. ( Base ` ndx ) , I >. , <. ( +g ` ndx ) , .(+) >. , <. ( .r ` ndx ) , ( i e. I , j e. I |-> ( ( RSpan ` R ) ` ( i .(x) j ) ) ) >. } u. { <. ( TopSet ` ndx ) , ran ( i e. I |-> { j e. I | -. i C_ j } ) >. , <. ( le ` ndx ) , { <. i , j >. | ( { i , j } C_ I /\ i C_ j ) } >. } ) ) with typecode |- |