Description: The limit of a product over one. (Contributed by Scott Fenton, 15-Dec-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | climprod1.1 | |- Z = ( ZZ>= ` M ) |
|
climprod1.2 | |- ( ph -> M e. ZZ ) |
||
Assertion | climprod1 | |- ( ph -> seq M ( x. , ( Z X. { 1 } ) ) ~~> 1 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | climprod1.1 | |- Z = ( ZZ>= ` M ) |
|
2 | climprod1.2 | |- ( ph -> M e. ZZ ) |
|
3 | 1 | prodfclim1 | |- ( M e. ZZ -> seq M ( x. , ( Z X. { 1 } ) ) ~~> 1 ) |
4 | 2 3 | syl | |- ( ph -> seq M ( x. , ( Z X. { 1 } ) ) ~~> 1 ) |