Theorem mul22 ≪ | index | src | ≫

theorem mul22 (a: nat): $ a * 2 = a + a $;

Step	Hyp	Ref	Expression
1		eqtr	a * 2 = a * 1 + a -> a * 1 + a = a + a -> a * 2 = a + a
2		mulS2	a * suc 1 = a * 1 + a
3	2	conv d2	a * 2 = a * 1 + a
4	1, 3	ax_mp	a * 1 + a = a + a -> a * 2 = a + a
5		addeq1	a * 1 = a -> a * 1 + a = a + a
6		mul12	a * 1 = a
7	5, 6	ax_mp	a * 1 + a = a + a
8	4, 7	ax_mp	a * 2 = a + 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_peano (peano2, peano5, addeq, add0, addS, mul0, mulS)