theorem ltleaddd (G: wff) (a b c d: nat):
$ G -> a < b $ >
$ G -> c <= d $ >
$ G -> a + c < b + d $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
ltadd1 |
a < b <-> a + c < b + c |
| 2 |
|
hyp h1 |
G -> a < b |
| 3 |
1, 2 |
sylib |
G -> a + c < b + c |
| 4 |
|
leadd2 |
c <= d <-> b + c <= b + d |
| 5 |
|
hyp h2 |
G -> c <= d |
| 6 |
4, 5 |
sylib |
G -> b + c <= b + d |
| 7 |
3, 6 |
ltletrd |
G -> a + c < b + d |
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
(peano2,
peano5,
addeq,
add0,
addS)