Theorem shladd ≪ | index | src | ≫

theorem shladd (a b c: nat): $ shl (a + b) c = shl a c + shl b c $;

Step	Hyp	Ref	Expression
1		addmul	(a + b) * 2 ^ c = a * 2 ^ c + b * 2 ^ c
2	1	conv shl	shl (a + b) c = shl a c + shl b c

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_peano (peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)