theorem boolodd (n: nat): $ bool n -> (odd n <-> true n) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
dfodd2 |
odd n <-> true (n % 2) |
| 2 |
|
modlteq |
n < 2 -> n % 2 = n |
| 3 |
2 |
conv bool |
bool n -> n % 2 = n |
| 4 |
3 |
trueeqd |
bool n -> (true (n % 2) <-> true n) |
| 5 |
1, 4 |
syl5bb |
bool n -> (odd n <-> true 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),
axs_peano
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)