Proof: Do Stack At Unchanged 51

Let's prove the following theorem:

if the following are true:

expression state at time 51 = "call_returned"
stack at time 51 = [ ]

then stack at time 52 = [ ]

Proof:

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Given

1	expression state at time 51 = "call_returned"
2	stack at time 51 = [ ]

Proof Table

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

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