theorem zdvdneg1 (a b: nat): $ -uZ a |Z b <-> a |Z b $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
dvdeq1 |
zabs (-uZ a) = zabs a -> (zabs (-uZ a) || zabs b <-> zabs a || zabs b) |
| 2 |
1 |
conv zdvd |
zabs (-uZ a) = zabs a -> (-uZ a |Z b <-> a |Z b) |
| 3 |
|
zabsneg |
zabs (-uZ a) = zabs a |
| 4 |
2, 3 |
ax_mp |
-uZ a |Z b <-> a |Z 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_set
(elab,
ax_8),
axs_the
(theid,
the0),
axs_peano
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)