Theorem dropall ≪ | index | src | ≫

theorem dropall (l n: nat): $ len l <= n -> drop l n = 0 $;

Step	Hyp	Ref	Expression
1		leneq0	len (drop l n) = 0 <-> drop l n = 0
2		droplen	len (drop l n) = len l - n
3		lesubeq0	len l <= n <-> len l - n = 0
4	3	bi1i	len l <= n -> len l - n = 0
5	2, 4	syl5eq	len l <= n -> len (drop l n) = 0
6	1, 5	sylib	len l <= n -> drop l n = 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)