theorem b1mul21 (n: nat): $ 2 * n + 1 = b1 n $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqtr |
2 * n + 1 = b0 n + 1 -> b0 n + 1 = b1 n -> 2 * n + 1 = b1 n |
| 2 |
|
addeq1 |
2 * n = b0 n -> 2 * n + 1 = b0 n + 1 |
| 3 |
|
b0mul21 |
2 * n = b0 n |
| 4 |
2, 3 |
ax_mp |
2 * n + 1 = b0 n + 1 |
| 5 |
1, 4 |
ax_mp |
b0 n + 1 = b1 n -> 2 * n + 1 = b1 n |
| 6 |
|
add12 |
b0 n + 1 = suc (b0 n) |
| 7 |
6 |
conv b1 |
b0 n + 1 = b1 n |
| 8 |
5, 7 |
ax_mp |
2 * n + 1 = 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_peano
(peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)