Proof: Do Stack At Unchanged 15

Let's prove the following theorem:

if the following are true:

expression state at time 15 = "return"
stack at time 15 = [ ]

then stack at time 16 = [ ]

Proof:

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Given

1	expression state at time 15 = "return"
2	stack at time 15 = [ ]

Proof Table

#	Claim	Reason
1	stack at time (15 + 1) = stack at time 15	if expression state at time 15 = "return", then stack at time (15 + 1) = stack at time 15 (Return (8))
2	stack at time (15 + 1) = [ ]	if stack at time (15 + 1) = stack at time 15 and stack at time 15 = [ ], then stack at time (15 + 1) = [ ] (Transitive Property of Equality)
3	15 + 1 = 16	15 + 1 = 16 (Fixed Value Statement)
4	stack at time (15 + 1) = stack at time 16	if 15 + 1 = 16, then stack at time (15 + 1) = stack at time 16 (Substitution)
5	stack at time 16 = [ ]	if stack at time (15 + 1) = stack at time 16 and stack at time (15 + 1) = [ ], then stack at time 16 = [ ] (Transitive Property of Equality Variation 2)

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