Proof Step: c_0_315

name: c_0_315 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step 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_299 ⊕ times_times_real ring_1_of_int_real X1 times_times_real X2 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X3 = times_times_real X2 real_of_float float2 X1 X3 c_0_8->c_0_299 c_0_43 c_0_43 c_0_298 ⊕ ord_less_eq_real zero_zero_real times_times_real X2 times_times_real X4 X6 ⊖ ord_less_eq_real X6 zero_zero_real ⊖ ord_less_eq_real times_times_real X2 X4 zero_zero_real c_0_43->c_0_298 c_0_44 ⊕ times_times_real times_times_real X6 X17 X18 = times_times_real X6 times_times_real X17 X18 c_0_44->c_0_298 c_0_45 ⊕ times_times_real X17 times_times_real X6 X18 = times_times_real X6 times_times_real X17 X18 c_0_45->c_0_299 c_0_315 ⊕ ord_less_eq_real zero_zero_real times_times_real X2 real_of_float float2 X1 X3 ⊖ ord_less_eq_real times_times_real ring_1_of_int_real X1 X2 zero_zero_real ⊖ ord_less_eq_real powr_real numeral_numeral_real bit0 one ring_1_of_int_real X3 zero_zero_real c_0_298->c_0_315 c_0_299->c_0_315 c_0_327 ⊕ $false c_0_315->c_0_327

Input Dependencies

c_0_8 c_0_43 c_0_44 c_0_45

Assumptions

c_0_298 c_0_299

Conclusion

c_0_315

Dependents

c_0_327

Formula

! [X1: int,X2: real,X3: int] :
  ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ X2 @ ( real_of_float @ ( float2 @ X1 @ X3 ) ) ) )
  | ~ ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ X1 ) @ X2 ) @ zero_zero_real )
  | ~ ( ord_less_eq_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ X3 ) ) @ zero_zero_real ) )

Source

inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_298,c_0_299])])