theorem lemuld (G: wff) (a b c d: nat):
$ G -> a <= b $ >
$ G -> c <= d $ >
$ G -> a * c <= b * d $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
lemul1a |
a <= b -> a * c <= b * c |
| 2 |
|
hyp h1 |
G -> a <= b |
| 3 |
1, 2 |
syl |
G -> a * c <= b * c |
| 4 |
|
lemul2a |
c <= d -> b * c <= b * d |
| 5 |
|
hyp h2 |
G -> c <= d |
| 6 |
4, 5 |
syl |
G -> b * c <= b * d |
| 7 |
3, 6 |
letrd |
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,
muleq,
add0,
addS,
mul0,
mulS)