Proof Step: c_0_30

name: c_0_30 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_0 ⊕ keysFor = ? c_0_23 ⊕ image_nat_nat invKey collect_nat ? = keysFor X4 c_0_0->c_0_23 c_0_1 ⊕ image_nat_nat X327 bot_bot_set_nat = bot_bot_set_nat c_0_25 ⊕ image_nat_nat X78 bot_bot_set_nat = bot_bot_set_nat c_0_1->c_0_25 c_0_3 ⊕ bot_bot_set_nat = collect_nat bot_bot_nat_o c_0_24 ⊕ collect_nat bot_bot_nat_o = bot_bot_set_nat c_0_3->c_0_24 c_0_30 ⊕ keysFor X4 = bot_bot_set_nat ⊖ ? = bot_bot_nat_o c_0_23->c_0_30 c_0_24->c_0_30 c_0_25->c_0_30 c_0_35 c_0_35 c_0_30->c_0_35

Input Dependencies

c_0_0 c_0_1 c_0_3

Assumptions

c_0_23 c_0_24 c_0_25

Conclusion

c_0_30

Dependents

c_0_35

Formula

! [X4: set_msg] :
  ( ( ( keysFor @ X4 )
    = bot_bot_set_nat )
  | ( ( ^ [Z0: nat] :
        ? [X4848: msg] : ( member_msg @ ( crypt @ Z0 @ X4848 ) @ X4 ) )
   != bot_bot_nat_o ) )

Source

inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_23,c_0_24]),c_0_25])])