Theorem len1 ≪ | index | src | ≫

theorem len1 (a: nat): $ len (a : 0) = 1 $;

Step	Hyp	Ref	Expression
1		eqtr	len (a : 0) = suc (len 0) -> suc (len 0) = 1 -> len (a : 0) = 1
2		lenS	len (a : 0) = suc (len 0)
3	1, 2	ax_mp	suc (len 0) = 1 -> len (a : 0) = 1
4		suceq	len 0 = 0 -> suc (len 0) = suc 0
5	4	conv d1	len 0 = 0 -> suc (len 0) = 1
6		len0	len 0 = 0
7	5, 6	ax_mp	suc (len 0) = 1
8	3, 7	ax_mp	len (a : 0) = 1

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_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)