Theorem znsubpos ≪ | index | src | ≫

theorem znsubpos (m n: nat): $ n <= m -> m -ZN n = b0 (m - n) $;

Step	Hyp	Ref	Expression
1		lenlt	n <= m <-> ~m < n
2		ifneg	~m < n -> if (m < n) (b1 (n - suc m)) (b0 (m - n)) = b0 (m - n)
3	2	conv znsub	~m < n -> m -ZN n = b0 (m - n)
4	1, 3	sylbi	n <= m -> m -ZN n = b0 (m - 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), axs_peano (peano1, peano2, peano5, addeq, add0, addS)