Theorem take0 ≪ | index | src | ≫

theorem take0 (l: nat): $ take l 0 = 0 $;

Step	Hyp	Ref	Expression
1		leneq0	len (take l 0) = 0 <-> take l 0 = 0
2		eqtr	len (take l 0) = min (len l) 0 -> min (len l) 0 = 0 -> len (take l 0) = 0
3		takelen	len (take l 0) = min (len l) 0
4	2, 3	ax_mp	min (len l) 0 = 0 -> len (take l 0) = 0
5		le02	min (len l) 0 <= 0 <-> min (len l) 0 = 0
6		minle2	min (len l) 0 <= 0
7	5, 6	mpbi	min (len l) 0 = 0
8	4, 7	ax_mp	len (take l 0) = 0
9	1, 8	mpbi	take 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)