Metamath Proof Explorer
Description: A sum is less than the whole if each term is less than half.
(Contributed by Thierry Arnoux, 29-Nov-2017)
|
|
Ref |
Expression |
|
Hypotheses |
le2halvesd.1 |
|
|
|
le2halvesd.2 |
|
|
|
le2halvesd.3 |
|
|
|
le2halvesd.4 |
|
|
|
le2halvesd.5 |
|
|
Assertion |
le2halvesd |
|
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
le2halvesd.1 |
|
2 |
|
le2halvesd.2 |
|
3 |
|
le2halvesd.3 |
|
4 |
|
le2halvesd.4 |
|
5 |
|
le2halvesd.5 |
|
6 |
3
|
rehalfcld |
|
7 |
1 2 6 6 4 5
|
le2addd |
|
8 |
3
|
recnd |
|
9 |
8
|
2halvesd |
|
10 |
7 9
|
breqtrd |
|