Theorem sucupto ≪ | index | src | ≫

theorem sucupto (n: nat): $ suc (upto n) = 2 ^ n $;

Step	Hyp	Ref	Expression
1		eqtr3	upto n + 1 = suc (upto n) -> upto n + 1 = 2 ^ n -> suc (upto n) = 2 ^ n
2		add12	upto n + 1 = suc (upto n)
3	2	eqtr3*	upto n + 1 = 2 ^ n -> suc (upto n) = 2 ^ n
4		uptoadd1	upto n + 1 = 2 ^ n
5	2, 4	eqtr3*	suc (upto n) = 2 ^ n

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)