theorem sndleid (a: nat): $ snd a <= a $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
leeq2 |
fst a, snd a = a -> (snd a <= fst a, snd a <-> snd a <= a) |
| 2 |
|
fstsnd |
fst a, snd a = a |
| 3 |
1, 2 |
ax_mp |
snd a <= fst a, snd a <-> snd a <= a |
| 4 |
|
leprid2 |
snd a <= fst a, snd a |
| 5 |
3, 4 |
mpbi |
snd a <= a |
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)