theorem zlelttr (a b c: nat): $ a <=Z b -> ba
Step Hyp Ref Expression 1 zletr c <=Z a -> a <=Z b -> c <=Z b2 1 conv zle ~a <Z c -> a <=Z b -> ~b <Z c3 2 com12 a <=Z b -> ~a <Z c -> ~b <Z c4 3 con4d a <=Z b -> b <Z c -> a <Z cAxiom 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)