Proof Step: c_0_303

name: c_0_303 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_44 ⊕ times_times_real times_times_real X6 X17 X18 = times_times_real X6 times_times_real X17 X18 c_0_277 ⊕ times_times_real times_times_real X2 X4 X6 = times_times_real X2 times_times_real X4 X6 c_0_44->c_0_277 c_0_46 ⊕ ring_1_of_int_real times_times_int X31 X5 = times_times_real ring_1_of_int_real X31 ring_1_of_int_real X5 c_0_281 ⊕ times_times_real ring_1_of_int_real X1 ring_1_of_int_real X3 = ring_1_of_int_real times_times_int X1 X3 c_0_46->c_0_281 c_0_303 ⊕ times_times_real ring_1_of_int_real X1 times_times_real ring_1_of_int_real X3 X2 = times_times_real ring_1_of_int_real times_times_int X1 X3 X2 c_0_277->c_0_303 c_0_281->c_0_303 c_0_317 ⊕ ord_less_eq_real times_times_real ring_1_of_int_real X1 X2 zero_zero_real ⊕ ord_less_eq_real zero_zero_real ring_1_of_int_real X3 ⊖ ord_less_eq_real zero_zero_real times_times_real ring_1_of_int_real times_times_int X1 X3 X2 c_0_303->c_0_317 c_0_318 ⊕ ord_less_eq_real zero_zero_real times_times_real ring_1_of_int_real times_times_int X1 X3 X2 ⊖ ord_less_eq_real zero_zero_real ring_1_of_int_real times_times_int X1 X3 ⊖ ord_less_eq_real zero_zero_real X2 c_0_303->c_0_318

Input Dependencies

c_0_44 c_0_46

Assumptions

c_0_277 c_0_281

Conclusion

c_0_303

Dependents

c_0_317 c_0_318

Formula

! [X1: int,X3: int,X2: real] :
  ( ( times_times_real @ ( ring_1_of_int_real @ X1 ) @ ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ X2 ) )
  = ( times_times_real @ ( ring_1_of_int_real @ ( times_times_int @ X1 @ X3 ) ) @ X2 ) )

Source

inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_281])])