Proof Step: c_0_182

name: c_0_182 syntax: thf role: plain inference: split_conjunct

Proof State Overview

proof_step 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_148 ⊕ round_down X2532 times_times_real X2533 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X2534 = times_times_real powr_real numeral_numeral_real bit0 one ring_1_of_int_real X2534 round_down plus_plus_int X2532 X2534 X2533 c_0_35->c_0_148 c_0_182 ⊕ round_down X1 times_times_real X2 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X3 = times_times_real powr_real numeral_numeral_real bit0 one ring_1_of_int_real X3 round_down plus_plus_int X1 X3 X2 c_0_148->c_0_182 c_0_217 ⊕ times_times_real powr_real numeral_numeral_real bit0 one ring_1_of_int_real X3 round_down plus_plus_int X1 X3 X2 = round_down X1 times_times_real X2 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X3 c_0_182->c_0_217

Input Dependencies

c_0_35

Assumptions

c_0_148

Conclusion

c_0_182

Dependents

c_0_217

Formula

! [X1: int,X3: int,X2: real] :
  ( ( round_down @ X1 @ ( times_times_real @ X2 @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ X3 ) ) ) )
  = ( times_times_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ X3 ) ) @ ( round_down @ ( plus_plus_int @ X1 @ X3 ) @ X2 ) ) )

Source

inference(split_conjunct,[status(thm)],[c_0_148])