Proof: Do Arg Stack At Unchanged 8

Let's prove the following theorem:

if the following are true:

expression state at time 8 = "return"
arguments stack at time 8 = [ [ ], [ ] ]

then arguments stack at time 9 = [ [ ], [ ] ]

Proof:

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Given

1	expression state at time 8 = "return"
2	arguments stack at time 8 = [ [ ], [ ] ]

Proof Table

#	Claim	Reason
1	arguments stack at time (8 + 1) = arguments stack at time 8	if expression state at time 8 = "return", then arguments stack at time (8 + 1) = arguments stack at time 8 (Return (3))
2	arguments stack at time (8 + 1) = [ [ ], [ ] ]	if arguments stack at time (8 + 1) = arguments stack at time 8 and arguments stack at time 8 = [ [ ], [ ] ], then arguments stack at time (8 + 1) = [ [ ], [ ] ] (Transitive Property of Equality)
3	8 + 1 = 9	8 + 1 = 9 (Fixed Value Statement)
4	arguments stack at time (8 + 1) = arguments stack at time 9	if 8 + 1 = 9, then arguments stack at time (8 + 1) = arguments stack at time 9 (Substitution)
5	arguments stack at time 9 = [ [ ], [ ] ]	if arguments stack at time (8 + 1) = arguments stack at time 9 and arguments stack at time (8 + 1) = [ [ ], [ ] ], then arguments stack at time 9 = [ [ ], [ ] ] (Transitive Property of Equality Variation 2)

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