Theorem shr02 ≪ | index | src | ≫

theorem shr02 (a: nat): $ shr a 0 = a $;

Step	Hyp	Ref	Expression
1		eqtr	shr a 0 = a // 1 -> a // 1 = a -> shr a 0 = a
2		diveq2	2 ^ 0 = 1 -> a // 2 ^ 0 = a // 1
3	2	conv shr	2 ^ 0 = 1 -> shr a 0 = a // 1
4		pow0	2 ^ 0 = 1
5	3, 4	ax_mp	shr a 0 = a // 1
6	1, 5	ax_mp	a // 1 = a -> shr a 0 = a
7		div12	a // 1 = a
8	6, 7	ax_mp	shr a 0 = a

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)