Proof: Do Arg Stack At Unchanged 31

Let's prove the following theorem:

if the following are true:
  • expression state at time 31 = "return"
  • arguments stack at time 31 = [ [ ], [ ] ]

then arguments stack at time 32 = [ [ ], [ ] ]

Proof:

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Given
1 expression state at time 31 = "return"
2 arguments stack at time 31 = [ [ ], [ ] ]
Proof Table
# Claim Reason
1 arguments stack at time (31 + 1) = arguments stack at time 31 if expression state at time 31 = "return", then arguments stack at time (31 + 1) = arguments stack at time 31
2 arguments stack at time (31 + 1) = [ [ ], [ ] ] if arguments stack at time (31 + 1) = arguments stack at time 31 and arguments stack at time 31 = [ [ ], [ ] ], then arguments stack at time (31 + 1) = [ [ ], [ ] ]
3 31 + 1 = 32 31 + 1 = 32
4 arguments stack at time (31 + 1) = arguments stack at time 32 if 31 + 1 = 32, then arguments stack at time (31 + 1) = arguments stack at time 32
5 arguments stack at time 32 = [ [ ], [ ] ] if arguments stack at time (31 + 1) = arguments stack at time 32 and arguments stack at time (31 + 1) = [ [ ], [ ] ], then arguments stack at time 32 = [ [ ], [ ] ]

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