Proof Step: c_0_10

name: c_0_10 syntax: thf role: plain inference: split_conjunct

Proof State Overview

proof_step c_0_0 c_0_0 c_0_7 ⊖ order_998966685r_on_b field_b X2897 X2897 ⊖ order_998966684r_on_a field_a X2898 X2898 ⊕ ordinal_wo_rel2_b_a X2897 X2898 c_0_0->c_0_7 c_0_10 ⊕ ordinal_wo_rel2_b_a X3 X2 ⊖ order_998966685r_on_b field_b X3 X3 ⊖ order_998966684r_on_a field_a X2 X2 c_0_7->c_0_10 c_0_16 ⊕ ordinal_wo_rel2_b_a X3 X2 ⊖ order_998966685r_on_b field_b X3 X3 ⊖ order_998966684r_on_a field_a X2 X2 c_0_10->c_0_16

Input Dependencies

c_0_0

Assumptions

c_0_7

Conclusion

c_0_10

Dependents

c_0_16

Formula

! [X3: set_Product_prod_b_b,X2: set_Product_prod_a_a] :
  ( ( ordinal_wo_rel2_b_a @ X3 @ X2 )
  | ~ ( order_998966685r_on_b @ ( field_b @ X3 ) @ X3 )
  | ~ ( order_998966684r_on_a @ ( field_a @ X2 ) @ X2 ) )

Source

inference(split_conjunct,[status(thm)],[c_0_7])