theorem b1le (a b: nat): $ a <= b <-> b1 a <= b1 b $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
bitr |
(a <= b <-> b0 a <= b0 b) -> (b0 a <= b0 b <-> b1 a <= b1 b) -> (a <= b <-> b1 a <= b1 b) |
| 2 |
|
b0le |
a <= b <-> b0 a <= b0 b |
| 3 |
1, 2 |
ax_mp |
(b0 a <= b0 b <-> b1 a <= b1 b) -> (a <= b <-> b1 a <= b1 b) |
| 4 |
|
lesuc |
b0 a <= b0 b <-> suc (b0 a) <= suc (b0 b) |
| 5 |
4 |
conv b1 |
b0 a <= b0 b <-> b1 a <= b1 b |
| 6 |
3, 5 |
ax_mp |
a <= b <-> b1 a <= b1 b |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp,
itru),
axs_pred_calc
(ax_gen,
ax_4,
ax_5,
ax_6,
ax_7,
ax_10,
ax_11,
ax_12),
axs_peano
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)