Proof Step: c_0_189

name: c_0_189 syntax: thf role: plain inference: distribute

Proof State Overview

proof_step c_0_43 c_0_43 c_0_189 c_0_189 c_0_43->c_0_189 c_0_222 ⊕ ord_less_eq_real zero_zero_real times_times_real X2 X4 ⊖ ord_less_eq_real X2 zero_zero_real ⊖ ord_less_eq_real X4 zero_zero_real c_0_189->c_0_222 c_0_225 ⊕ ord_less_eq_real X2 zero_zero_real ⊕ ord_less_eq_real zero_zero_real X4 ⊖ ord_less_eq_real zero_zero_real times_times_real X2 X4 c_0_189->c_0_225 c_0_226 ⊕ ord_less_eq_real X2 zero_zero_real ⊕ ord_less_eq_real zero_zero_real X4 ⊖ ord_less_eq_real zero_zero_real times_times_real X4 X2 c_0_189->c_0_226

Input Dependencies

c_0_43

Assumptions

c_0_43

Conclusion

c_0_189

Dependents

c_0_222 c_0_225 c_0_226

Formula

! [X3367: real,X3368: real] :
  ( ( ( ord_less_eq_real @ X3367 @ zero_zero_real )
    | ( ord_less_eq_real @ zero_zero_real @ X3367 )
    | ~ ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X3367 @ X3368 ) ) )
  & ( ( ord_less_eq_real @ X3368 @ zero_zero_real )
    | ( ord_less_eq_real @ zero_zero_real @ X3367 )
    | ~ ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X3367 @ X3368 ) ) )
  & ( ( ord_less_eq_real @ X3367 @ zero_zero_real )
    | ( ord_less_eq_real @ zero_zero_real @ X3368 )
    | ~ ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X3367 @ X3368 ) ) )
  & ( ( ord_less_eq_real @ X3368 @ zero_zero_real )
    | ( ord_less_eq_real @ zero_zero_real @ X3368 )
    | ~ ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X3367 @ X3368 ) ) )
  & ( ~ ( ord_less_eq_real @ zero_zero_real @ X3367 )
    | ~ ( ord_less_eq_real @ zero_zero_real @ X3368 )
    | ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X3367 @ X3368 ) ) )
  & ( ~ ( ord_less_eq_real @ X3367 @ zero_zero_real )
    | ~ ( ord_less_eq_real @ X3368 @ zero_zero_real )
    | ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X3367 @ X3368 ) ) ) )

Source

inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])