Description: Base case of the induction in cusgrsize . The size of a (complete) simple graph with 1 vertex is 0=((1-1)*1)/2. (Contributed by Alexander van der Vekens, 2-Jan-2018) (Revised by AV, 7-Nov-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | cusgrsizeindb0.v | |
|
cusgrsizeindb0.e | |
||
Assertion | cusgrsizeindb1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cusgrsizeindb0.v | |
|
2 | cusgrsizeindb0.e | |
|
3 | 1 2 | usgr1v0e | |
4 | oveq1 | |
|
5 | 1nn0 | |
|
6 | 2z | |
|
7 | 1lt2 | |
|
8 | 7 | olci | |
9 | bcval4 | |
|
10 | 5 6 8 9 | mp3an | |
11 | 4 10 | eqtrdi | |
12 | 11 | eqeq2d | |
13 | 12 | adantl | |
14 | 3 13 | mpbird | |