Description: A shorter sum of nonnegative extended reals is smaller than a longer one. (Contributed by Glauco Siliprandi, 17-Aug-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | sge0lessmpt.a | |
|
sge0lessmpt.b | |
||
sge0lessmpt.c | |
||
Assertion | sge0lessmpt | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sge0lessmpt.a | |
|
2 | sge0lessmpt.b | |
|
3 | sge0lessmpt.c | |
|
4 | id | |
|
5 | 3 | resmptd | |
6 | 5 | eqcomd | |
7 | 4 6 | syl | |
8 | 7 | fveq2d | |
9 | eqid | |
|
10 | 2 9 | fmptd | |
11 | 1 10 | sge0less | |
12 | 8 11 | eqbrtrd | |