Theorem divlemul2r ≪ | index | src | ≫

theorem divlemul2r (a b c: nat): $ b != 0 -> a <= c * b -> a // b <= c $;

Step	Hyp	Ref	Expression
1		leeq2	c * b = b * c -> (a <= c * b <-> a <= b * c)
2		mulcom	c * b = b * c
3	1, 2	ax_mp	a <= c * b <-> a <= b * c
4		divlemul1r	b != 0 -> a <= b * c -> a // b <= c
5	3, 4	syl5bi	b != 0 -> a <= c * b -> a // b <= c

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)