Theorem repeatS ≪ | index | src | ≫

pub theorem repeatS (a n: nat): $ repeat a (suc n) = a : repeat a n $;

Step	Hyp	Ref	Expression
1		eqtr	repeat a (suc n) = (\ x, a : x) @ rec 0 (\ x, a : x) n -> (\ x, a : x) @ rec 0 (\ x, a : x) n = a : repeat a n -> repeat a (suc n) = a : repeat a n
2		recS	rec 0 (\ x, a : x) (suc n) = (\ x, a : x) @ rec 0 (\ x, a : x) n
3	2	conv repeat	repeat a (suc n) = (\ x, a : x) @ rec 0 (\ x, a : x) n
4	3	eqtr*	(\ x, a : x) @ rec 0 (\ x, a : x) n = a : repeat a n -> repeat a (suc n) = a : repeat a n
5		conseq2	x = repeat a n -> a : x = a : repeat a n
6	5	applame	(\ x, a : x) @ repeat a n = a : repeat a n
7	6	conv repeat	(\ x, a : x) @ rec 0 (\ x, a : x) n = a : repeat a n
8	3, 7	eqtr*	repeat a (suc n) = a : repeat a 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)