Theorem takeall ≪ | index | src | ≫

theorem takeall (l n: nat): $ len l <= n -> take l n = l $;

Step	Hyp	Ref	Expression
1		append02	take l n ++ 0 = take l n
2		takedrop	take l n ++ drop l n = l
3		dropall	len l <= n -> drop l n = 0
4	3	eqcomd	len l <= n -> 0 = drop l n
5	4	appendeq2d	len l <= n -> take l n ++ 0 = take l n ++ drop l n
6	2, 5	syl6eq	len l <= n -> take l n ++ 0 = l
7	1, 6	syl5eqr	len l <= n -> take l n = 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)