Proof Step: c_0_216

name: c_0_216 syntax: thf role: plain inference: distribute

Proof State Overview

proof_step c_0_48 c_0_48 c_0_216 c_0_216 c_0_48->c_0_216 c_0_247 ⊕ ord_less_eq_real X1 zero_zero_real ⊕ ord_less_eq_real zero_zero_real X5 ⊖ ord_less_eq_real zero_zero_real times_times_real X1 X5 c_0_216->c_0_247

Input Dependencies

c_0_48

Assumptions

c_0_48

Conclusion

c_0_216

Dependents

c_0_247

Formula

! [X2859: real,X2860: real] :
  ( ( ( ord_less_eq_real @ X2859 @ zero_zero_real )
    | ( ord_less_eq_real @ zero_zero_real @ X2859 )
    | ~ ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X2859 @ X2860 ) ) )
  & ( ( ord_less_eq_real @ X2860 @ zero_zero_real )
    | ( ord_less_eq_real @ zero_zero_real @ X2859 )
    | ~ ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X2859 @ X2860 ) ) )
  & ( ( ord_less_eq_real @ X2859 @ zero_zero_real )
    | ( ord_less_eq_real @ zero_zero_real @ X2860 )
    | ~ ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X2859 @ X2860 ) ) )
  & ( ( ord_less_eq_real @ X2860 @ zero_zero_real )
    | ( ord_less_eq_real @ zero_zero_real @ X2860 )
    | ~ ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X2859 @ X2860 ) ) )
  & ( ~ ( ord_less_eq_real @ zero_zero_real @ X2859 )
    | ~ ( ord_less_eq_real @ zero_zero_real @ X2860 )
    | ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X2859 @ X2860 ) ) )
  & ( ~ ( ord_less_eq_real @ X2859 @ zero_zero_real )
    | ~ ( ord_less_eq_real @ X2860 @ zero_zero_real )
    | ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X2859 @ X2860 ) ) ) )

Source

inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])