Proof: Do Stack At Unchanged 81

Let's prove the following theorem:

if the following are true:
  • expression state at time 81 = "call_returned"
  • stack at time 81 = [ ]

then stack at time 82 = [ ]

Proof:

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Given
1 expression state at time 81 = "call_returned"
2 stack at time 81 = [ ]
Proof Table
# Claim Reason
1 stack at time (81 + 1) = stack at time 81 if expression state at time 81 = "call_returned", then stack at time (81 + 1) = stack at time 81
2 stack at time (81 + 1) = [ ] if stack at time (81 + 1) = stack at time 81 and stack at time 81 = [ ], then stack at time (81 + 1) = [ ]
3 81 + 1 = 82 81 + 1 = 82
4 stack at time (81 + 1) = stack at time 82 if 81 + 1 = 82, then stack at time (81 + 1) = stack at time 82
5 stack at time 82 = [ ] if stack at time (81 + 1) = stack at time 82 and stack at time (81 + 1) = [ ], then stack at time 82 = [ ]

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