theorem letrue (a b: nat): $ a <= b -> true a -> true b $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
lt01 |
0 < a <-> a != 0 |
| 2 |
1 |
conv true |
0 < a <-> true a |
| 3 |
|
lt01 |
0 < b <-> b != 0 |
| 4 |
3 |
conv true |
0 < b <-> true b |
| 5 |
2, 4 |
imeqi |
0 < a -> 0 < b <-> true a -> true b |
| 6 |
|
ltletr |
0 < a -> a <= b -> 0 < b |
| 7 |
6 |
com12 |
a <= b -> 0 < a -> 0 < b |
| 8 |
5, 7 |
sylib |
a <= b -> true a -> true 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_peano
(peano1,
peano2,
peano5,
addeq,
add0,
addS)