theorem b0ltb1 (a b: nat): $ b0 a < b1 b <-> a <= b $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bicom | (a <= b <-> b0 a < b1 b) -> (b0 a < b1 b <-> a <= b) |
|
| 2 | b1le | a <= b <-> b1 a <= b1 b |
|
| 3 | 2 | conv b1, lt | a <= b <-> b0 a < b1 b |
| 4 | 1, 3 | ax_mp | b0 a < b1 b <-> a <= b |