Proof Step: c_0_111

name: c_0_111 syntax: thf role: plain inference: distribute

Proof State Overview

proof_step c_0_22 c_0_22 c_0_111 c_0_111 c_0_22->c_0_111 c_0_135 ⊕ X2 = X4 ⊖ ord_less_eq_real X2 X4 ⊖ ord_less_eq_real X4 X2 c_0_111->c_0_135

Input Dependencies

c_0_22

Assumptions

c_0_22

Conclusion

c_0_111

Dependents

c_0_135

Formula

! [X2516: real,X2517: real] :
  ( ( ~ ( ord_less_eq_real @ X2517 @ X2516 )
    | ( X2517 = X2516 )
    | ~ ( ord_less_eq_real @ X2516 @ X2517 ) )
  & ( ( X2517 != X2516 )
    | ( ord_less_eq_real @ X2517 @ X2516 )
    | ~ ( ord_less_eq_real @ X2516 @ X2517 ) ) )

Source

inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])