Step |
Hyp |
Ref |
Expression |
1 |
|
m2cpm.s |
|- S = ( N ConstPolyMat R ) |
2 |
|
m2cpm.t |
|- T = ( N matToPolyMat R ) |
3 |
|
m2cpm.a |
|- A = ( N Mat R ) |
4 |
|
m2cpm.b |
|- B = ( Base ` A ) |
5 |
|
eqid |
|- ( Poly1 ` R ) = ( Poly1 ` R ) |
6 |
|
eqid |
|- ( N Mat ( Poly1 ` R ) ) = ( N Mat ( Poly1 ` R ) ) |
7 |
|
eqid |
|- ( Base ` ( N Mat ( Poly1 ` R ) ) ) = ( Base ` ( N Mat ( Poly1 ` R ) ) ) |
8 |
2 3 4 5 6 7
|
mat2pmatf1 |
|- ( ( N e. Fin /\ R e. Ring ) -> T : B -1-1-> ( Base ` ( N Mat ( Poly1 ` R ) ) ) ) |
9 |
1 2 3 4
|
m2cpmf |
|- ( ( N e. Fin /\ R e. Ring ) -> T : B --> S ) |
10 |
9
|
frnd |
|- ( ( N e. Fin /\ R e. Ring ) -> ran T C_ S ) |
11 |
|
f1ssr |
|- ( ( T : B -1-1-> ( Base ` ( N Mat ( Poly1 ` R ) ) ) /\ ran T C_ S ) -> T : B -1-1-> S ) |
12 |
8 10 11
|
syl2anc |
|- ( ( N e. Fin /\ R e. Ring ) -> T : B -1-1-> S ) |