Proof Step: c_0_181

name: c_0_181 syntax: thf role: plain inference: distribute

Proof State Overview

proof_step c_0_42 c_0_42 c_0_181 c_0_181 c_0_42->c_0_181 c_0_216 ⊕ ord_less_eq_real X4 X6 ⊖ ord_less_eq_real times_times_real X2 X4 times_times_real X2 X6 ⊖ ord_less_real zero_zero_real X2 c_0_181->c_0_216

Input Dependencies

c_0_42

Assumptions

c_0_42

Conclusion

c_0_181

Dependents

c_0_216

Formula

! [X2488: real,X2489: real,X2490: real] :
  ( ( ~ ( ord_less_eq_real @ ( times_times_real @ X2488 @ X2489 ) @ ( times_times_real @ X2488 @ X2490 ) )
    | ( ord_less_eq_real @ X2489 @ X2490 )
    | ~ ( ord_less_real @ zero_zero_real @ X2488 ) )
  & ( ~ ( ord_less_eq_real @ X2489 @ X2490 )
    | ( ord_less_eq_real @ ( times_times_real @ X2488 @ X2489 ) @ ( times_times_real @ X2488 @ X2490 ) )
    | ~ ( ord_less_real @ zero_zero_real @ X2488 ) ) )

Source

inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])