Theorem zlelttr | index | src |

theorem zlelttr (a b c: nat): $ a <=Z b -> b  a 
    
StepHypRefExpression
1 zletr
c <=Z a -> a <=Z b -> c <=Z b
2 1 conv zle
~a <Z c -> a <=Z b -> ~b <Z c
3 2 com12
a <=Z b -> ~a <Z c -> ~b <Z c
4 3 con4d
a <=Z b -> b <Z c -> a <Z 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)