Proof Step: c_0_315

name: c_0_315 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_8 ⊕ divide_divide_real X11 divide_divide_real X15 X40 = divide_divide_real times_times_real X11 X40 X15 c_0_302 ⊕ ord_less_eq_real zero_zero_real times_times_real X1 divide_divide_real X5 X6 ⊖ ord_less_eq_real zero_zero_real X6 ⊖ ord_less_eq_real zero_zero_real times_times_real X1 X5 c_0_8->c_0_302 c_0_300 ⊕ times_times_real semiri2110766477t_real X2 divide_divide_real semiri2110766477t_real X7 X1 = divide_divide_real semiri2110766477t_real times_times_nat X2 X7 X1 c_0_8->c_0_300 c_0_9 ⊕ times_times_real X11 divide_divide_real X15 X40 = divide_divide_real times_times_real X11 X15 X40 c_0_9->c_0_302 c_0_9->c_0_300 c_0_38 ⊕ semiri2110766477t_real times_times_nat X14 X23 = times_times_real semiri2110766477t_real X14 semiri2110766477t_real X23 c_0_38->c_0_300 c_0_274 ⊕ times_times_real semiri2110766477t_real X2 semiri2110766477t_real X7 = semiri2110766477t_real times_times_nat X2 X7 c_0_38->c_0_274 c_0_39 c_0_39 c_0_39->c_0_302 c_0_49 ⊕ ord_less_eq_real zero_zero_real semiri2110766477t_real X23 c_0_301 ⊕ ord_less_eq_real zero_zero_real semiri2110766477t_real X2 c_0_49->c_0_301 c_0_315 ⊕ ord_less_eq_real zero_zero_real divide_divide_real semiri2110766477t_real times_times_nat X2 X7 X1 ⊖ ord_less_eq_real zero_zero_real X1 c_0_302->c_0_315 c_0_300->c_0_315 c_0_274->c_0_315 c_0_301->c_0_315 c_0_323 ⊕ $false c_0_315->c_0_323

Input Dependencies

c_0_8 c_0_9 c_0_38 c_0_39 c_0_49

Assumptions

c_0_302 c_0_300 c_0_274 c_0_301

Conclusion

c_0_315

Dependents

c_0_323

Formula

! [X2: nat,X7: nat,X1: real] :
  ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ ( semiri2110766477t_real @ ( times_times_nat @ X2 @ X7 ) ) @ X1 ) )
  | ~ ( ord_less_eq_real @ zero_zero_real @ X1 ) )

Source

inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_302,c_0_300]),c_0_274]),c_0_301])])])