Proof Step: c_0_184

name: c_0_184 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_17 ⊕ round_down = ? c_0_150 ⊕ round_down X1 X2 = times_times_real ring_1_of_int_real archim1031974863r_real times_times_real X2 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X1 powr_real numeral_numeral_real bit0 one uminus_uminus_real ring_1_of_int_real X1 c_0_17->c_0_150 c_0_184 ⊕ times_times_real ring_1_of_int_real archim1031974863r_real times_times_real X2 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X1 powr_real numeral_numeral_real bit0 one uminus_uminus_real ring_1_of_int_real X1 = round_down X1 X2 c_0_150->c_0_184 c_0_219 ⊕ real_of_float float2 archim1031974863r_real times_times_real X2 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X1 uminus_uminus_int X1 = round_down X1 X2 c_0_184->c_0_219

Input Dependencies

c_0_17

Assumptions

c_0_150

Conclusion

c_0_184

Dependents

c_0_219

Formula

! [X1: int,X2: real] :
  ( ( times_times_real @ ( ring_1_of_int_real @ ( archim1031974863r_real @ ( times_times_real @ X2 @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ X1 ) ) ) ) ) @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ X1 ) ) ) )
  = ( round_down @ X1 @ X2 ) )

Source

inference(evalgc,[status(thm)],[c_0_150])