Theorem snocne0 ≪ | index | src | ≫

theorem snocne0 (a b: nat): $ a |> b != 0 $;

Step	Hyp	Ref	Expression
1		len0	len 0 = 0
2		leneq	a \|> b = 0 -> len (a \|> b) = len 0
3	1, 2	syl6eq	a \|> b = 0 -> len (a \|> b) = 0
4		sucne0	len (a \|> b) = suc (len a) -> len (a \|> b) != 0
5	4	conv ne	len (a \|> b) = suc (len a) -> ~len (a \|> b) = 0
6		snoclen	len (a \|> b) = suc (len a)
7	5, 6	ax_mp	~len (a \|> b) = 0
8	3, 7	mt	~a \|> b = 0
9	8	conv ne	a \|> b != 0

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)