Theorem zltletr ≪ | index | src | ≫ 

theorem zltletr (a b c: nat): $ a  b <=Z c -> a 
    

      
        
StepHypRefExpression

        

          1
          
          zletr
          
b <=Z c -> c <=Z a -> b <=Z a

        

        

          2
          1
          conv zle
          
b <=Z c -> ~a <Z c -> ~a <Z b

        

        

          3
          2
          con4d
          
b <=Z c -> a <Z b -> a <Z c

        

        

          4
          3
          com12
          
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)