Proof Step: c_0_302

name: c_0_302 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_43 c_0_43 c_0_280 ⊕ ord_less_eq_real zero_zero_real X2 ⊕ ord_less_eq_real X4 zero_zero_real ⊖ ord_less_eq_real zero_zero_real times_times_real X2 X4 c_0_43->c_0_280 c_0_45 ⊕ times_times_real X17 times_times_real X6 X18 = times_times_real X6 times_times_real X17 X18 c_0_278 ⊕ times_times_real X2 times_times_real X4 X6 = times_times_real X4 times_times_real X2 X6 c_0_45->c_0_278 c_0_302 ⊕ ord_less_eq_real times_times_real X2 X4 zero_zero_real ⊕ ord_less_eq_real zero_zero_real X6 ⊖ ord_less_eq_real zero_zero_real times_times_real X2 times_times_real X6 X4 c_0_280->c_0_302 c_0_278->c_0_302 c_0_317 ⊕ ord_less_eq_real times_times_real ring_1_of_int_real X1 X2 zero_zero_real ⊕ ord_less_eq_real zero_zero_real ring_1_of_int_real X3 ⊖ ord_less_eq_real zero_zero_real times_times_real ring_1_of_int_real times_times_int X1 X3 X2 c_0_302->c_0_317

Input Dependencies

c_0_43 c_0_45

Assumptions

c_0_280 c_0_278

Conclusion

c_0_302

Dependents

c_0_317

Formula

! [X2: real,X6: real,X4: real] :
  ( ( ord_less_eq_real @ ( times_times_real @ X2 @ X4 ) @ zero_zero_real )
  | ( ord_less_eq_real @ zero_zero_real @ X6 )
  | ~ ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X2 @ ( times_times_real @ X6 @ X4 ) ) ) )

Source

inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_280,c_0_278])])