Proof Step: c_0_17

name: c_0_17 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_0 ⊕ keysFor = ? c_0_11 ⊕ keysFor X4 = image_nat_nat invKey collect_nat ? c_0_0->c_0_11 c_0_17 ⊕ image_nat_nat invKey collect_nat ? = keysFor X4 c_0_11->c_0_17 c_0_23 ⊕ image_nat_nat invKey collect_nat ? = keysFor X4 c_0_17->c_0_23

Input Dependencies

c_0_0

Assumptions

c_0_11

Conclusion

c_0_17

Dependents

c_0_23

Formula

! [X4: set_msg] :
  ( ( image_nat_nat @ invKey
    @ ( collect_nat
      @ ^ [Z0: nat] :
        ? [X4846: msg] : ( member_msg @ ( crypt @ Z0 @ X4846 ) @ X4 ) ) )
  = ( keysFor @ X4 ) )

Source

inference(evalgc,[status(thm)],[c_0_11])