theorem b1dvd2 (n: nat): $ ~2 || b1 n $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
con2b |
(2 || b1 n <-> ~2 || b0 n) -> (2 || b0 n <-> ~2 || b1 n) |
| 2 |
|
d2dvdS |
2 || suc (b0 n) <-> ~2 || b0 n |
| 3 |
2 |
conv b1 |
2 || b1 n <-> ~2 || b0 n |
| 4 |
1, 3 |
ax_mp |
2 || b0 n <-> ~2 || b1 n |
| 5 |
|
b0dvd2 |
2 || b0 n |
| 6 |
4, 5 |
mpbi |
~2 || b1 n |
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)