Proof Step: c_0_317

name: c_0_317 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_43 c_0_43 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_43->c_0_302 c_0_44 ⊕ times_times_real times_times_real X6 X17 X18 = times_times_real X6 times_times_real X17 X18 c_0_303 ⊕ times_times_real ring_1_of_int_real X1 times_times_real ring_1_of_int_real X3 X2 = times_times_real ring_1_of_int_real times_times_int X1 X3 X2 c_0_44->c_0_303 c_0_45 ⊕ times_times_real X17 times_times_real X6 X18 = times_times_real X6 times_times_real X17 X18 c_0_45->c_0_302 c_0_46 ⊕ ring_1_of_int_real times_times_int X31 X5 = times_times_real ring_1_of_int_real X31 ring_1_of_int_real X5 c_0_46->c_0_303 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 c_0_303->c_0_317 c_0_327 ⊕ $false c_0_317->c_0_327

Input Dependencies

c_0_43 c_0_44 c_0_45 c_0_46

Assumptions

c_0_302 c_0_303

Conclusion

c_0_317

Dependents

c_0_327

Formula

! [X1: int,X3: int,X2: real] :
  ( ( 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 ) ) )

Source

inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_302,c_0_303])])