Description: The "complement" of a member of a finite set of sequential integers. (Contributed by NM, 20-Nov-2005)
Ref | Expression | ||
---|---|---|---|
Assertion | fzrev3i | |- ( K e. ( M ... N ) -> ( ( M + N ) - K ) e. ( M ... N ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfzelz | |- ( K e. ( M ... N ) -> K e. ZZ ) |
|
2 | fzrev3 | |- ( K e. ZZ -> ( K e. ( M ... N ) <-> ( ( M + N ) - K ) e. ( M ... N ) ) ) |
|
3 | 1 2 | syl | |- ( K e. ( M ... N ) -> ( K e. ( M ... N ) <-> ( ( M + N ) - K ) e. ( M ... N ) ) ) |
4 | 3 | ibi | |- ( K e. ( M ... N ) -> ( ( M + N ) - K ) e. ( M ... N ) ) |