Proof Step: c_0_150

name: c_0_150 syntax: thf role: plain inference: split_conjunct

Proof State Overview

proof_step c_0_17 ⊕ round_down = ? c_0_119 ⊕ round_down X2178 X2179 = times_times_real ring_1_of_int_real archim1031974863r_real times_times_real X2179 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X2178 powr_real numeral_numeral_real bit0 one uminus_uminus_real ring_1_of_int_real X2178 c_0_17->c_0_119 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_119->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

Input Dependencies

c_0_17

Assumptions

c_0_119

Conclusion

c_0_150

Dependents

c_0_184

Formula

! [X2: real,X1: int] :
  ( ( 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 ) ) ) ) )

Source

inference(split_conjunct,[status(thm)],[c_0_119])