Proof Step: c_0_314

name: c_0_314 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_0 c_0_0 c_0_297 ⊕ times_times_real powr_real numeral_numeral_real bit0 one ring_1_of_int_real X1 round_down X1 X2 = ring_1_of_int_real archim1031974863r_real times_times_real X2 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X1 c_0_0->c_0_297 c_0_1 c_0_1 c_0_1->c_0_297 c_0_2 ⊕ powr_real numeral_numeral_real X45 numeral_numeral_real X11 = power_power_real numeral_numeral_real X45 numeral_numeral_nat X11 c_0_2->c_0_297 c_0_3 ⊕ ord_less_real zero_zero_real numeral_numeral_real X11 c_0_3->c_0_297 c_0_4 ⊖ zero_zero_real = numeral_numeral_real X11 c_0_4->c_0_297 c_0_5 c_0_5 c_0_5->c_0_297 c_0_6 ⊕ powr_real powr_real X4 X6 X17 = powr_real X4 times_times_real X6 X17 c_0_6->c_0_297 c_0_7 ⊕ times_times_real X6 zero_zero_real = zero_zero_real c_0_7->c_0_297 c_0_8 ⊕ real_of_float float2 X793 X794 = times_times_real ring_1_of_int_real X793 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X794 c_0_8->c_0_297 c_0_11 ⊕ ring_1_of_int_real zero_zero_int = zero_zero_real c_0_11->c_0_297 c_0_12 ⊕ times_times_real X6 one_one_real = X6 c_0_296 ⊕ ord_less_eq_real one_one_real X2 ⊖ ord_less_eq_real X4 times_times_real X4 X2 ⊖ ord_less_real zero_zero_real X4 c_0_12->c_0_296 c_0_12->c_0_297 c_0_17 ⊕ round_down = ? c_0_17->c_0_297 c_0_18 ⊕ ring_1_of_int_real uminus_uminus_int X5 = uminus_uminus_real ring_1_of_int_real X5 c_0_18->c_0_297 c_0_19 ⊕ float_of real_of_float X841 = X841 c_0_19->c_0_297 c_0_35 ⊕ round_down X172 times_times_real X4 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X173 = times_times_real powr_real numeral_numeral_real bit0 one ring_1_of_int_real X173 round_down plus_plus_int X172 X173 X4 c_0_35->c_0_297 c_0_36 ⊕ plus_plus_int zero_zero_int X204 = X204 c_0_36->c_0_297 c_0_37 ⊕ uminus_uminus_int zero_zero_int = zero_zero_int c_0_37->c_0_297 c_0_42 c_0_42 c_0_42->c_0_296 c_0_314 ⊕ ord_less_eq_real one_one_real round_down X1 X2 ⊖ ord_less_eq_real powr_real numeral_numeral_real bit0 one ring_1_of_int_real X1 ring_1_of_int_real archim1031974863r_real times_times_real X2 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X1 ⊖ ord_less_real zero_zero_real powr_real numeral_numeral_real bit0 one ring_1_of_int_real X1 c_0_296->c_0_314 c_0_297->c_0_314 c_0_327 ⊕ $false c_0_314->c_0_327

Input Dependencies

c_0_0 c_0_1 c_0_2 c_0_3 c_0_4 c_0_5 c_0_6 c_0_7 c_0_8 c_0_11 c_0_12 c_0_17 c_0_18 c_0_19 c_0_35 c_0_36 c_0_37 c_0_42

Assumptions

c_0_296 c_0_297

Conclusion

c_0_314

Dependents

c_0_327

Formula

! [X2: real,X1: int] :
  ( ( ord_less_eq_real @ one_one_real @ ( round_down @ X1 @ X2 ) )
  | ~ ( ord_less_eq_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ X1 ) ) @ ( ring_1_of_int_real @ ( archim1031974863r_real @ ( times_times_real @ X2 @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ X1 ) ) ) ) ) )
  | ~ ( ord_less_real @ zero_zero_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ X1 ) ) ) )

Source

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