Theorem rlrec0 ≪ | index | src | ≫

theorem rlrec0 (S: set) (z: nat): $ rlrec z S 0 = z $;

Step	Hyp	Ref	Expression
1		eqtr	rlrec z S 0 = lrec z (\\ a1, \\ a2, \ a3, S @ (rev a2, a1, a3)) 0 -> lrec z (\\ a1, \\ a2, \ a3, S @ (rev a2, a1, a3)) 0 = z -> rlrec z S 0 = z
2		lreceq3	rev 0 = 0 -> lrec z (\\ a1, \\ a2, \ a3, S @ (rev a2, a1, a3)) (rev 0) = lrec z (\\ a1, \\ a2, \ a3, S @ (rev a2, a1, a3)) 0
3	2	conv rlrec	rev 0 = 0 -> rlrec z S 0 = lrec z (\\ a1, \\ a2, \ a3, S @ (rev a2, a1, a3)) 0
4		rev0	rev 0 = 0
5	3, 4	ax_mp	rlrec z S 0 = lrec z (\\ a1, \\ a2, \ a3, S @ (rev a2, a1, a3)) 0
6	5	eqtr*	lrec z (\\ a1, \\ a2, \ a3, S @ (rev a2, a1, a3)) 0 = z -> rlrec z S 0 = z
7		lrec0	lrec z (\\ a1, \\ a2, \ a3, S @ (rev a2, a1, a3)) 0 = z
8	5, 7	eqtr*	rlrec z S 0 = z

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)