Proof Step: c_0_36

name: c_0_36 syntax: thf role: plain inference: split_conjunct

Proof State Overview

proof_step c_0_0 c_0_0 c_0_8 c_0_8 c_0_0->c_0_8 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 c_0_41 ⊕ member_msg X1 synth X3 ⊕ member_msg mPair X1 X2 X3 ⊖ member_msg mPair X1 X2 synth X3 c_0_36->c_0_41

Input Dependencies

c_0_0

Assumptions

c_0_8

Conclusion

c_0_36

Dependents

c_0_41

Formula

! [X1: msg,X2: msg,X3: set_msg] :
  ( ( member_msg @ X1 @ ( synth @ X3 ) )
  | ( member_msg @ ( mPair @ X1 @ X2 ) @ X3 )
  | ~ ( member_msg @ ( mPair @ X1 @ X2 ) @ ( synth @ X3 ) ) )

Source

inference(split_conjunct,[status(thm)],[c_0_8])