Theorem lelttr ≪ | index | src | ≫

theorem lelttr (a b c: nat): $ a <= b -> b < c -> a < c $;

Step	Hyp	Ref	Expression
1		lesuc	a <= b <-> suc a <= suc b
2		letr	suc a <= suc b -> suc b <= c -> suc a <= c
3	2	conv lt	suc a <= suc b -> b < c -> a < c
4	1, 3	sylbi	a <= b -> b < c -> a < 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_peano (peano2, peano5, addeq, add0, addS)