Proof: Do Stack At Unchanged 31

Let's prove the following theorem:

if the following are true:

expression state at time 31 = "return"
stack at time 31 = [ ]

then stack at time 32 = [ ]

Proof:

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Given

1	expression state at time 31 = "return"
2	stack at time 31 = [ ]

Proof Table

#	Claim	Reason
1	stack at time (31 + 1) = stack at time 31	if expression state at time 31 = "return", then stack at time (31 + 1) = stack at time 31 (Return (8))
2	stack at time (31 + 1) = [ ]	if stack at time (31 + 1) = stack at time 31 and stack at time 31 = [ ], then stack at time (31 + 1) = [ ] (Transitive Property of Equality)
3	31 + 1 = 32	31 + 1 = 32 (Fixed Value Statement)
4	stack at time (31 + 1) = stack at time 32	if 31 + 1 = 32, then stack at time (31 + 1) = stack at time 32 (Substitution)
5	stack at time 32 = [ ]	if stack at time (31 + 1) = stack at time 32 and stack at time (31 + 1) = [ ], then stack at time 32 = [ ] (Transitive Property of Equality Variation 2)

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