Theorem drop0 ≪ | index | src | ≫

theorem drop0 (l: nat): $ drop l 0 = l $;

Step	Hyp	Ref	Expression
1		eqtr3	0 ++ drop l 0 = drop l 0 -> 0 ++ drop l 0 = l -> drop l 0 = l
2		append0	0 ++ drop l 0 = drop l 0
3	1, 2	ax_mp	0 ++ drop l 0 = l -> drop l 0 = l
4		eqtr3	take l 0 ++ drop l 0 = 0 ++ drop l 0 -> take l 0 ++ drop l 0 = l -> 0 ++ drop l 0 = l
5		appendeq1	take l 0 = 0 -> take l 0 ++ drop l 0 = 0 ++ drop l 0
6		take0	take l 0 = 0
7	5, 6	ax_mp	take l 0 ++ drop l 0 = 0 ++ drop l 0
8	4, 7	ax_mp	take l 0 ++ drop l 0 = l -> 0 ++ drop l 0 = l
9		takedrop	take l 0 ++ drop l 0 = l
10	8, 9	ax_mp	0 ++ drop l 0 = l
11	3, 10	ax_mp	drop l 0 = l

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)