theorem zlt01eq (a: nat): $ a a = b1 (a // 2) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
bitr |
(a <Z 0 <-> odd a) -> (odd a <-> a = b1 (a // 2)) -> (a <Z 0 <-> a = b1 (a // 2)) |
| 2 |
|
zlt01 |
a <Z 0 <-> odd a |
| 3 |
1, 2 |
ax_mp |
(odd a <-> a = b1 (a // 2)) -> (a <Z 0 <-> a = b1 (a // 2)) |
| 4 |
|
eqb1 |
odd a <-> a = b1 (a // 2) |
| 5 |
3, 4 |
ax_mp |
a <Z 0 <-> a = b1 (a // 2) |
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_set
(elab,
ax_8),
axs_the
(theid,
the0),
axs_peano
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)