Proof: Do Arg Stack At Unchanged 5

Let's prove the following theorem:

if the following are true:
  • expression state at time 5 = "return"
  • arguments stack at time 5 = [ [ 2, [ ] ], [ ] ]

then arguments stack at time 6 = [ [ 2, [ ] ], [ ] ]

Proof:

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Given
1 expression state at time 5 = "return"
2 arguments stack at time 5 = [ [ 2, [ ] ], [ ] ]
Proof Table
# Claim Reason
1 arguments stack at time (5 + 1) = arguments stack at time 5 if expression state at time 5 = "return", then arguments stack at time (5 + 1) = arguments stack at time 5
2 arguments stack at time (5 + 1) = [ [ 2, [ ] ], [ ] ] if arguments stack at time (5 + 1) = arguments stack at time 5 and arguments stack at time 5 = [ [ 2, [ ] ], [ ] ], then arguments stack at time (5 + 1) = [ [ 2, [ ] ], [ ] ]
3 5 + 1 = 6 5 + 1 = 6
4 arguments stack at time (5 + 1) = arguments stack at time 6 if 5 + 1 = 6, then arguments stack at time (5 + 1) = arguments stack at time 6
5 arguments stack at time 6 = [ [ 2, [ ] ], [ ] ] if arguments stack at time (5 + 1) = arguments stack at time 6 and arguments stack at time (5 + 1) = [ [ 2, [ ] ], [ ] ], then arguments stack at time 6 = [ [ 2, [ ] ], [ ] ]

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