Theorem zip02 ≪ | index | src | ≫

theorem zip02 (l: nat): $ zip l 0 = 0 $;


len (zip l 0) = 0 <-> zip l 0 = 0
len (zip l 0) = min (len l) (len 0) -> min (len l) (len 0) = 0 -> len (zip l 0) = 0
len (zip l 0) = min (len l) (len 0)
min (len l) (len 0) = 0 -> len (zip l 0) = 0
min (len l) (len 0) = min (len l) 0 -> min (len l) 0 = 0 -> min (len l) (len 0) = 0
len 0 = 0 -> min (len l) (len 0) = min (len l) 0
len 0 = 0
min (len l) (len 0) = min (len l) 0
min (len l) 0 = 0 -> min (len l) (len 0) = 0
0 <= len l -> min (len l) 0 = 0
0 <= len l
min (len l) 0 = 0
min (len l) (len 0) = 0
len (zip l 0) = 0
zip l 0 = 0

Step	Hyp	Ref	Expression
1		leneq0	len (zip l 0) = 0 <-> zip l 0 = 0
2		eqtr	len (zip l 0) = min (len l) (len 0) -> min (len l) (len 0) = 0 -> len (zip l 0) = 0
3		ziplen	len (zip l 0) = min (len l) (len 0)
4	2, 3	ax_mp	min (len l) (len 0) = 0 -> len (zip l 0) = 0
5		eqtr	min (len l) (len 0) = min (len l) 0 -> min (len l) 0 = 0 -> min (len l) (len 0) = 0
6		mineq2	len 0 = 0 -> min (len l) (len 0) = min (len l) 0
7		len0	len 0 = 0
8	6, 7	ax_mp	min (len l) (len 0) = min (len l) 0
9	5, 8	ax_mp	min (len l) 0 = 0 -> min (len l) (len 0) = 0
10		eqmin2	0 <= len l -> min (len l) 0 = 0
11		le01	0 <= len l
12	10, 11	ax_mp	min (len l) 0 = 0
13	9, 12	ax_mp	min (len l) (len 0) = 0
14	4, 13	ax_mp	len (zip l 0) = 0
15	1, 14	mpbi	zip l 0 = 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)