Proof: Do Stack At Unchanged 23

Let's prove the following theorem:

if the following are true:
  • expression state at time 23 = "return"
  • stack at time 23 = [ ]

then stack at time 24 = [ ]

Proof:

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Given
1 expression state at time 23 = "return"
2 stack at time 23 = [ ]
Proof Table
# Claim Reason
1 stack at time (23 + 1) = stack at time 23 if expression state at time 23 = "return", then stack at time (23 + 1) = stack at time 23
2 stack at time (23 + 1) = [ ] if stack at time (23 + 1) = stack at time 23 and stack at time 23 = [ ], then stack at time (23 + 1) = [ ]
3 23 + 1 = 24 23 + 1 = 24
4 stack at time (23 + 1) = stack at time 24 if 23 + 1 = 24, then stack at time (23 + 1) = stack at time 24
5 stack at time 24 = [ ] if stack at time (23 + 1) = stack at time 24 and stack at time (23 + 1) = [ ], then stack at time 24 = [ ]

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