Proof Step: c_0_319

name: c_0_319 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_0 c_0_0 c_0_306 ⊕ ord_less_eq_int one_one_int archim1031974863r_real times_times_real x powr_real numeral_numeral_real bit0 one ring_1_of_int_real p c_0_0->c_0_306 c_0_4 ⊖ zero_zero_real = numeral_numeral_real X11 c_0_4->c_0_306 c_0_5 c_0_5 c_0_5->c_0_306 c_0_6 ⊕ powr_real powr_real X4 X6 X17 = powr_real X4 times_times_real X6 X17 c_0_6->c_0_306 c_0_7 ⊕ times_times_real X6 zero_zero_real = zero_zero_real c_0_7->c_0_306 c_0_9 c_0_9 c_0_305 ⊖ ord_less_eq_int one_one_int archim1031974863r_real X2 ⊖ ord_less_eq_real X2 zero_zero_real c_0_9->c_0_305 c_0_10 c_0_10 c_0_10->c_0_305 c_0_10->c_0_306 c_0_13 c_0_13 c_0_13->c_0_305 c_0_14 ⊖ ord_less_eq_real one_one_real zero_zero_real c_0_14->c_0_305 c_0_15 c_0_15 c_0_15->c_0_306 c_0_16 ⊕ ord_less_eq_real X6 X6 c_0_16->c_0_306 c_0_20 c_0_20 c_0_20->c_0_305 c_0_21 c_0_21 c_0_21->c_0_305 c_0_22 c_0_22 c_0_22->c_0_306 c_0_23 ⊕ ord_less_eq_real ring_1_of_int_real archim1031974863r_real X4 X4 c_0_23->c_0_305 c_0_23->c_0_306 c_0_24 c_0_24 c_0_24->c_0_306 c_0_25 ⊕ ord_less_eq_real zero_zero_real powr_real X4 X16 c_0_25->c_0_306 c_0_26 ⊕ x = powr_real numeral_numeral_real bit0 one log numeral_numeral_real bit0 one x c_0_26->c_0_306 c_0_28 ⊕ ring_1_of_int_real one_one_int = one_one_real c_0_28->c_0_305 c_0_29 ⊕ archim1031974863r_real zero_zero_real = zero_zero_int c_0_29->c_0_305 c_0_30 ⊕ ord_less_eq_real powr_real numeral_numeral_real bit0 one zero_zero_real ring_1_of_int_real archim1031974863r_real powr_real numeral_numeral_real bit0 one zero_zero_real c_0_30->c_0_306 c_0_31 ⊕ ord_less_eq_real powr_real numeral_numeral_real bit0 one ring_1_of_int_real uminus_uminus_int p x c_0_31->c_0_306 c_0_32 ⊕ ord_less_eq_real one_one_real numeral_numeral_real X11 c_0_32->c_0_306 c_0_38 ⊕ ord_less_eq_real ring_1_of_int_real archim1031974863r_real powr_real numeral_numeral_real bit0 one zero_zero_real ring_1_of_int_real archim1031974863r_real times_times_real x powr_real numeral_numeral_real bit0 one ring_1_of_int_real p c_0_38->c_0_306 c_0_319 ⊖ ord_less_eq_real times_times_real x powr_real numeral_numeral_real bit0 one ring_1_of_int_real p zero_zero_real c_0_305->c_0_319 c_0_306->c_0_319 c_0_327 ⊕ $false c_0_319->c_0_327

Input Dependencies

c_0_0 c_0_4 c_0_5 c_0_6 c_0_7 c_0_9 c_0_10 c_0_13 c_0_14 c_0_15 c_0_16 c_0_20 c_0_21 c_0_22 c_0_23 c_0_24 c_0_25 c_0_26 c_0_28 c_0_29 c_0_30 c_0_31 c_0_32 c_0_38

Assumptions

c_0_305 c_0_306

Conclusion

c_0_319

Dependents

c_0_327

Formula

~ ( ord_less_eq_real @ ( times_times_real @ x @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ p ) ) ) @ zero_zero_real )

Source

inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_306])])