theorem leaddid2 (a b: nat): $ a <= b + a $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | leeq | a = a -> a + b = b + a -> (a <= a + b <-> a <= b + a) |
|
| 2 | eqid | a = a |
|
| 3 | 1, 2 | ax_mp | a + b = b + a -> (a <= a + b <-> a <= b + a) |
| 4 | addcom | a + b = b + a |
|
| 5 | 3, 4 | ax_mp | a <= a + b <-> a <= b + a |
| 6 | leaddid1 | a <= a + b |
|
| 7 | 5, 6 | mpbi | a <= b + a |