Proof Step: c_0_23

name: c_0_23 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_0 ⊕ keysFor = ? c_0_17 ⊕ image_nat_nat invKey collect_nat ? = keysFor X4 c_0_0->c_0_17 c_0_23 ⊕ image_nat_nat invKey collect_nat ? = keysFor X4 c_0_17->c_0_23 c_0_30 ⊕ keysFor X4 = bot_bot_set_nat ⊖ ? = bot_bot_nat_o c_0_23->c_0_30

Input Dependencies

c_0_0

Assumptions

c_0_17

Conclusion

c_0_23

Dependents

c_0_30

Formula

! [X4: set_msg] :
  ( ( image_nat_nat @ invKey
    @ ( collect_nat
      @ ^ [Z0: nat] :
        ? [X4847: msg] : ( member_msg @ ( crypt @ Z0 @ X4847 ) @ X4 ) ) )
  = ( keysFor @ X4 ) )

Source

inference(evalgc,[status(thm)],[c_0_17])