Proof Step: c_0_312

name: c_0_312 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_7 c_0_7 c_0_296 ⊕ ord_less_eq_real times_times_real X1 divide_divide_real X5 X6 X5 ⊕ X6 = zero_zero_real ⊖ ord_less_eq_real zero_zero_real divide_divide_real X5 X6 ⊖ ord_less_eq_real X1 X6 c_0_7->c_0_296 c_0_8 ⊕ divide_divide_real X11 divide_divide_real X15 X40 = divide_divide_real times_times_real X11 X40 X15 c_0_8->c_0_296 c_0_297 ⊕ times_times_real semiri2110766477t_real X2 divide_divide_real X1 semiri2110766477t_real times_times_nat X2 X2 = divide_divide_real X1 semiri2110766477t_real X2 c_0_8->c_0_297 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_296 c_0_9->c_0_297 c_0_19 ⊕ divide_divide_real times_times_real X690 X11 times_times_real X690 X690 = divide_divide_real X11 X690 c_0_19->c_0_297 c_0_37 c_0_37 c_0_37->c_0_296 c_0_38 ⊕ semiri2110766477t_real times_times_nat X14 X23 = times_times_real semiri2110766477t_real X14 semiri2110766477t_real X23 c_0_38->c_0_297 c_0_312 ⊕ semiri2110766477t_real times_times_nat X2 X2 = zero_zero_real ⊕ ord_less_eq_real divide_divide_real X1 semiri2110766477t_real X2 X1 ⊖ ord_less_eq_real zero_zero_real divide_divide_real X1 semiri2110766477t_real times_times_nat X2 X2 ⊖ ord_less_eq_real semiri2110766477t_real X2 semiri2110766477t_real times_times_nat X2 X2 c_0_296->c_0_312 c_0_297->c_0_312 c_0_323 ⊕ $false c_0_312->c_0_323

Input Dependencies

c_0_7 c_0_8 c_0_9 c_0_19 c_0_37 c_0_38

Assumptions

c_0_296 c_0_297

Conclusion

c_0_312

Dependents

c_0_323

Formula

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

Source

inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_297])])