pub theorem repeatS (a n: nat): $ repeat a (suc n) = a : repeat a n $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqtr |
repeat a (suc n) = (\ x, a : x) @ rec 0 (\ x, a : x) n -> (\ x, a : x) @ rec 0 (\ x, a : x) n = a : repeat a n -> repeat a (suc n) = a : repeat a n |
| 2 |
|
recS |
rec 0 (\ x, a : x) (suc n) = (\ x, a : x) @ rec 0 (\ x, a : x) n |
| 3 |
2 |
conv repeat |
repeat a (suc n) = (\ x, a : x) @ rec 0 (\ x, a : x) n |
| 4 |
1, 3 |
ax_mp |
(\ x, a : x) @ rec 0 (\ x, a : x) n = a : repeat a n -> repeat a (suc n) = a : repeat a n |
| 5 |
|
conseq2 |
x = repeat a n -> a : x = a : repeat a n |
| 6 |
5 |
applame |
(\ x, a : x) @ repeat a n = a : repeat a n |
| 7 |
6 |
conv repeat |
(\ x, a : x) @ rec 0 (\ x, a : x) n = a : repeat a n |
| 8 |
4, 7 |
ax_mp |
repeat a (suc n) = a : repeat a 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)