Proof: Do Arg Stack At Unchanged 16

Let's prove the following theorem:

if the following are true:
  • expression state at time 16 = "return"
  • arguments stack at time 16 = [ [ 1, [ ] ], [ ] ]

then arguments stack at time 17 = [ [ 1, [ ] ], [ ] ]

Proof:

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Given
1 expression state at time 16 = "return"
2 arguments stack at time 16 = [ [ 1, [ ] ], [ ] ]
Proof Table
# Claim Reason
1 arguments stack at time (16 + 1) = arguments stack at time 16 if expression state at time 16 = "return", then arguments stack at time (16 + 1) = arguments stack at time 16
2 arguments stack at time (16 + 1) = [ [ 1, [ ] ], [ ] ] if arguments stack at time (16 + 1) = arguments stack at time 16 and arguments stack at time 16 = [ [ 1, [ ] ], [ ] ], then arguments stack at time (16 + 1) = [ [ 1, [ ] ], [ ] ]
3 16 + 1 = 17 16 + 1 = 17
4 arguments stack at time (16 + 1) = arguments stack at time 17 if 16 + 1 = 17, then arguments stack at time (16 + 1) = arguments stack at time 17
5 arguments stack at time 17 = [ [ 1, [ ] ], [ ] ] if arguments stack at time (16 + 1) = arguments stack at time 17 and arguments stack at time (16 + 1) = [ [ 1, [ ] ], [ ] ], then arguments stack at time 17 = [ [ 1, [ ] ], [ ] ]

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