theorem ocaseval (S: set) {i: nat} (n z: nat):
$ ocase z S @ n = recn z (\ i, S @ fst i) n $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
recneq3 |
a1 = n -> recn z (\ i, S @ fst i) a1 = recn z (\ i, S @ fst i) n |
| 2 |
1 |
applame |
(\ a1, recn z (\ i, S @ fst i) a1) @ n = recn z (\ i, S @ fst i) n |
| 3 |
2 |
conv ocase |
ocase z S @ n = recn z (\ i, S @ fst i) 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)