Proof Step: c_0_305

name: c_0_305 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_9 c_0_9 c_0_283 ⊖ ord_less_eq_real ring_1_of_int_real X1 zero_zero_real ⊖ ord_less_eq_int one_one_int X1 c_0_9->c_0_283 c_0_284 ⊕ ord_less_eq_real ring_1_of_int_real archim1031974863r_real X2 X4 ⊖ ord_less_eq_real X2 X4 c_0_9->c_0_284 c_0_10 c_0_10 c_0_10->c_0_283 c_0_13 c_0_13 c_0_13->c_0_283 c_0_14 ⊖ ord_less_eq_real one_one_real zero_zero_real c_0_14->c_0_283 c_0_20 c_0_20 c_0_20->c_0_283 c_0_21 c_0_21 c_0_21->c_0_283 c_0_23 ⊕ ord_less_eq_real ring_1_of_int_real archim1031974863r_real X4 X4 c_0_23->c_0_284 c_0_28 ⊕ ring_1_of_int_real one_one_int = one_one_real c_0_28->c_0_283 c_0_29 ⊕ archim1031974863r_real zero_zero_real = zero_zero_int c_0_29->c_0_283 c_0_305 ⊖ ord_less_eq_int one_one_int archim1031974863r_real X2 ⊖ ord_less_eq_real X2 zero_zero_real c_0_283->c_0_305 c_0_284->c_0_305 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

Input Dependencies

c_0_9 c_0_10 c_0_13 c_0_14 c_0_20 c_0_21 c_0_23 c_0_28 c_0_29

Assumptions

c_0_283 c_0_284

Conclusion

c_0_305

Dependents

c_0_319

Formula

! [X2: real] :
  ( ~ ( ord_less_eq_int @ one_one_int @ ( archim1031974863r_real @ X2 ) )
  | ~ ( ord_less_eq_real @ X2 @ zero_zero_real ) )

Source

inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_284])])