Proof Step: c_0_8

name: c_0_8 syntax: thf role: plain inference: distribute

Proof State Overview

proof_step c_0_0 c_0_0 c_0_6 c_0_6 c_0_0->c_0_6 c_0_8 c_0_8 c_0_6->c_0_8 c_0_11 ⊕ member_msg X1 synth X3 ⊕ member_msg mPair X2 X1 X3 ⊖ member_msg mPair X2 X1 synth X3 c_0_8->c_0_11 c_0_36 ⊕ member_msg X1 synth X3 ⊕ member_msg mPair X1 X2 X3 ⊖ member_msg mPair X1 X2 synth X3 c_0_8->c_0_36

Input Dependencies

c_0_0

Assumptions

c_0_6

Conclusion

c_0_8

Dependents

c_0_11 c_0_36

Formula

! [X2676: msg,X2677: msg,X2678: set_msg] :
  ( ( ( member_msg @ X2676 @ ( synth @ X2678 ) )
    | ( member_msg @ ( mPair @ X2676 @ X2677 ) @ X2678 )
    | ~ ( member_msg @ ( mPair @ X2676 @ X2677 ) @ ( synth @ X2678 ) ) )
  & ( ( member_msg @ X2677 @ ( synth @ X2678 ) )
    | ( member_msg @ ( mPair @ X2676 @ X2677 ) @ X2678 )
    | ~ ( member_msg @ ( mPair @ X2676 @ X2677 ) @ ( synth @ X2678 ) ) ) )

Source

inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])