Proof Step: c_0_275

name: c_0_275 syntax: thf role: plain inference: rw

Proof State Overview

proof_step c_0_0 c_0_0 c_0_155 ⊕ powr_real numeral_numeral_real X8 zero_zero_real = one_one_real c_0_0->c_0_155 c_0_221 ⊕ float2 X1 zero_zero_int = float_of ring_1_of_int_real X1 c_0_0->c_0_221 c_0_250 ⊕ real_of_float float_of ring_1_of_int_real X1 = ring_1_of_int_real X1 c_0_0->c_0_250 c_0_1 c_0_1 c_0_1->c_0_155 c_0_1->c_0_221 c_0_1->c_0_250 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_155 c_0_2->c_0_221 c_0_2->c_0_250 c_0_3 ⊕ ord_less_real zero_zero_real numeral_numeral_real X11 c_0_3->c_0_155 c_0_3->c_0_221 c_0_3->c_0_250 c_0_4 ⊖ zero_zero_real = numeral_numeral_real X11 c_0_4->c_0_155 c_0_4->c_0_221 c_0_4->c_0_250 c_0_5 c_0_5 c_0_5->c_0_155 c_0_5->c_0_221 c_0_5->c_0_250 c_0_6 ⊕ powr_real powr_real X4 X6 X17 = powr_real X4 times_times_real X6 X17 c_0_6->c_0_155 c_0_6->c_0_221 c_0_6->c_0_250 c_0_7 ⊕ times_times_real X6 zero_zero_real = zero_zero_real c_0_7->c_0_155 c_0_7->c_0_221 c_0_7->c_0_250 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_249 ⊕ real_of_float float2 archim1031974863r_real times_times_real X2 powr_real numeral_numeral_real bit0 one zero_zero_real zero_zero_int = round_down zero_zero_int X2 c_0_8->c_0_249 c_0_8->c_0_221 c_0_8->c_0_250 c_0_11 ⊕ ring_1_of_int_real zero_zero_int = zero_zero_real c_0_11->c_0_249 c_0_11->c_0_221 c_0_11->c_0_250 c_0_12 ⊕ times_times_real X6 one_one_real = X6 c_0_156 ⊕ times_times_real X2 one_one_real = X2 c_0_12->c_0_156 c_0_12->c_0_221 c_0_12->c_0_250 c_0_17 ⊕ round_down = ? c_0_17->c_0_249 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_249 c_0_19 ⊕ float_of real_of_float X841 = X841 c_0_19->c_0_221 c_0_19->c_0_250 c_0_37 ⊕ uminus_uminus_int zero_zero_int = zero_zero_int c_0_37->c_0_249 c_0_275 ⊕ round_down zero_zero_int X2 = ring_1_of_int_real archim1031974863r_real X2 c_0_249->c_0_275 c_0_155->c_0_275 c_0_156->c_0_275 c_0_221->c_0_275 c_0_250->c_0_275 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_275->c_0_297

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_37

Assumptions

c_0_249 c_0_155 c_0_156 c_0_221 c_0_250

Conclusion

c_0_275

Dependents

c_0_297

Formula

! [X2: real] :
  ( ( round_down @ zero_zero_int @ X2 )
  = ( ring_1_of_int_real @ ( archim1031974863r_real @ X2 ) ) )

Source

inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_249,c_0_155]),c_0_156]),c_0_221]),c_0_250])