Description: The norm of the ring of the integers. (Contributed by Thierry Arnoux, 8-Nov-2017) (Revised by AV, 13-Jun-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | zzsnm | |- ( M e. ZZ -> ( abs ` M ) = ( ( norm ` ZZring ) ` M ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zringnm | |- ( norm ` ZZring ) = ( abs |` ZZ ) |
|
2 | 1 | eqcomi | |- ( abs |` ZZ ) = ( norm ` ZZring ) |
3 | 2 | fveq1i | |- ( ( abs |` ZZ ) ` M ) = ( ( norm ` ZZring ) ` M ) |
4 | fvres | |- ( M e. ZZ -> ( ( abs |` ZZ ) ` M ) = ( abs ` M ) ) |
|
5 | 3 4 | syl5reqr | |- ( M e. ZZ -> ( abs ` M ) = ( ( norm ` ZZring ) ` M ) ) |