theorem shrupto (a n: nat): $ shr (upto n) a = upto (n - a) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
anl |
shr (upto n) a = upto (n - a) /\ upto n % 2 ^ a = upto (min n a) -> shr (upto n) a = upto (n - a) |
| 2 |
|
uptolem |
shr (upto n) a = upto (n - a) /\ upto n % 2 ^ a = upto (min n a) |
| 3 |
1, 2 |
ax_mp |
shr (upto n) a = upto (n - 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)