Proof: Do Arg Stack At Unchanged 51

Let's prove the following theorem:

if the following are true:

expression state at time 51 = "return"
arguments stack at time 51 = [ [ 2, [ ] ], [ ] ]

then arguments stack at time 52 = [ [ 2, [ ] ], [ ] ]

Proof:

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Given

1	expression state at time 51 = "return"
2	arguments stack at time 51 = [ [ 2, [ ] ], [ ] ]

Proof Table

#	Claim	Reason
1	arguments stack at time (51 + 1) = arguments stack at time 51	if expression state at time 51 = "return", then arguments stack at time (51 + 1) = arguments stack at time 51 (Return (3))
2	arguments stack at time (51 + 1) = [ [ 2, [ ] ], [ ] ]	if arguments stack at time (51 + 1) = arguments stack at time 51 and arguments stack at time 51 = [ [ 2, [ ] ], [ ] ], then arguments stack at time (51 + 1) = [ [ 2, [ ] ], [ ] ] (Transitive Property of Equality)
3	51 + 1 = 52	51 + 1 = 52 (Fixed Value Statement)
4	arguments stack at time (51 + 1) = arguments stack at time 52	if 51 + 1 = 52, then arguments stack at time (51 + 1) = arguments stack at time 52 (Substitution)
5	arguments stack at time 52 = [ [ 2, [ ] ], [ ] ]	if arguments stack at time (51 + 1) = arguments stack at time 52 and arguments stack at time (51 + 1) = [ [ 2, [ ] ], [ ] ], then arguments stack at time 52 = [ [ 2, [ ] ], [ ] ] (Transitive Property of Equality Variation 2)

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