Proof Step: c_0_11

name: c_0_11 syntax: thf role: plain inference: split_conjunct

Proof State Overview

proof_step c_0_0 ⊕ keysFor = ? c_0_8 ⊕ keysFor X2955 = image_nat_nat invKey collect_nat ? c_0_0->c_0_8 c_0_11 ⊕ keysFor X4 = image_nat_nat invKey collect_nat ? c_0_8->c_0_11 c_0_17 ⊕ image_nat_nat invKey collect_nat ? = keysFor X4 c_0_11->c_0_17

Input Dependencies

c_0_0

Assumptions

c_0_8

Conclusion

c_0_11

Dependents

c_0_17

Formula

! [X4: set_msg] :
  ( ( keysFor @ X4 )
  = ( image_nat_nat @ invKey
    @ ( collect_nat
      @ ^ [Z0: nat] :
        ? [X4845: msg] : ( member_msg @ ( crypt @ Z0 @ X4845 ) @ X4 ) ) ) )

Source

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