theorem splitoptS (G: wff) (a b c: nat) (p: wff):
$ G -> a = suc c -> p $ >
$ G -> b = c -> a = suc b -> p $;
Step | Hyp | Ref | Expression |
1 |
|
hyp h |
G -> a = suc c -> p |
2 |
|
anll |
G /\ b = c /\ a = suc b -> G |
3 |
|
anr |
G /\ b = c /\ a = suc b -> a = suc b |
4 |
|
anlr |
G /\ b = c /\ a = suc b -> b = c |
5 |
4 |
suceqd |
G /\ b = c /\ a = suc b -> suc b = suc c |
6 |
3, 5 |
eqtrd |
G /\ b = c /\ a = suc b -> a = suc c |
7 |
1, 2, 6 |
sylc |
G /\ b = c /\ a = suc b -> p |
8 |
7 |
exp |
G /\ b = c -> a = suc b -> p |
9 |
8 |
exp |
G -> b = c -> a = suc b -> p |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp),
axs_pred_calc
(ax_gen,
ax_4,
ax_5,
ax_6,
ax_7),
axs_peano
(peano2)