Proof Step: c_0_157

name: c_0_157 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_9 c_0_9 c_0_127 ⊕ ord_less_eq_real X2 X4 ⊖ ord_less_eq_real X2 X6 ⊖ ord_less_eq_real X6 X4 c_0_9->c_0_127 c_0_10 c_0_10 c_0_128 ⊕ ord_less_eq_real one_one_real ring_1_of_int_real X1 ⊖ ord_less_eq_int one_one_int X1 c_0_10->c_0_128 c_0_157 ⊕ ord_less_eq_real one_one_real X2 ⊖ ord_less_eq_real ring_1_of_int_real X1 X2 ⊖ ord_less_eq_int one_one_int X1 c_0_127->c_0_157 c_0_128->c_0_157 c_0_194 ⊖ ord_less_eq_int one_one_int X1 ⊖ ord_less_eq_int X1 zero_zero_int c_0_157->c_0_194

Input Dependencies

c_0_9 c_0_10

Assumptions

c_0_127 c_0_128

Conclusion

c_0_157

Dependents

c_0_194

Formula

! [X2: real,X1: int] :
  ( ( ord_less_eq_real @ one_one_real @ X2 )
  | ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ X1 ) @ X2 )
  | ~ ( ord_less_eq_int @ one_one_int @ X1 ) )

Source

inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128])])