Theorem shrshlid ≪ | index | src | ≫

theorem shrshlid (a b: nat): $ shr (shl a b) b = a $;

Step	Hyp	Ref	Expression
1		muldiv1	2 ^ b != 0 -> a * 2 ^ b // 2 ^ b = a
2	1	conv shl, shr	2 ^ b != 0 -> shr (shl a b) b = a
3		pow2ne0	2 ^ b != 0
4	2, 3	ax_mp	shr (shl a b) b = 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)