Proof Step: c_0_316

name: c_0_316 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_301 ⊕ times_times_real powr_real numeral_numeral_real bit0 one ring_1_of_int_real X1 ring_1_of_int_real X3 = real_of_float float2 X3 X1 c_0_8->c_0_301 c_0_33 ⊕ times_times_real = ? c_0_33->c_0_301 c_0_43 c_0_43 c_0_300 ⊕ ord_less_eq_real times_times_real X2 X4 zero_zero_real ⊕ ord_less_eq_real zero_zero_real X6 ⊖ ord_less_eq_real zero_zero_real times_times_real X2 times_times_real X4 X6 c_0_43->c_0_300 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_300 c_0_316 ⊕ ord_less_eq_real times_times_real X2 powr_real numeral_numeral_real bit0 one ring_1_of_int_real X1 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 X2 real_of_float float2 X3 X1 c_0_300->c_0_316 c_0_301->c_0_316 c_0_327 ⊕ $false c_0_316->c_0_327

Input Dependencies

c_0_8 c_0_33 c_0_43 c_0_44

Assumptions

c_0_300 c_0_301

Conclusion

c_0_316

Dependents

c_0_327

Formula

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

Source

inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_301])])