Description: Division of a positive number by both sides of 'less than'. (Contributed by Glauco Siliprandi, 11-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ltdiv2dd.a | |- ( ph -> A e. RR+ ) |
|
ltdiv2dd.b | |- ( ph -> B e. RR+ ) |
||
ltdiv2dd.c | |- ( ph -> C e. RR+ ) |
||
ltdiv2dd.altb | |- ( ph -> A < B ) |
||
Assertion | ltdiv2dd | |- ( ph -> ( C / B ) < ( C / A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltdiv2dd.a | |- ( ph -> A e. RR+ ) |
|
2 | ltdiv2dd.b | |- ( ph -> B e. RR+ ) |
|
3 | ltdiv2dd.c | |- ( ph -> C e. RR+ ) |
|
4 | ltdiv2dd.altb | |- ( ph -> A < B ) |
|
5 | 1 2 3 | ltdiv2d | |- ( ph -> ( A < B <-> ( C / B ) < ( C / A ) ) ) |
6 | 4 5 | mpbid | |- ( ph -> ( C / B ) < ( C / A ) ) |