theorem leaddid1 (a b: nat): $ a <= a + b $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addeq2 | x = b -> a + x = a + b |
|
2 | 1 | eqeq1d | x = b -> (a + x = a + b <-> a + b = a + b) |
3 | 2 | iexe | a + b = a + b -> E. x a + x = a + b |
4 | 3 | conv le | a + b = a + b -> a <= a + b |
5 | eqid | a + b = a + b |
|
6 | 4, 5 | ax_mp | a <= a + b |