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theorem divid (a: nat): $ a != 0 -> a // a = 1 $;

Step	Hyp	Ref	Expression
1		diveq1	a * 1 = a -> a * 1 // a = a // a
2		mul12	a * 1 = a
3	1, 2	ax_mp	a * 1 // a = a // a
4		muldiv2	a != 0 -> a * 1 // a = 1
5	3, 4	syl5eqr	a != 0 -> a // a = 1

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)