Proof: Do Stack At Unchanged 18

Let's prove the following theorem:

if the following are true:

expression state at time 18 = "return"
stack at time 18 = [ ]

then stack at time 19 = [ ]

Proof:

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Given

1	expression state at time 18 = "return"
2	stack at time 18 = [ ]

Proof Table

#	Claim	Reason
1	stack at time (18 + 1) = stack at time 18	if expression state at time 18 = "return", then stack at time (18 + 1) = stack at time 18 (Return (8))
2	stack at time (18 + 1) = [ ]	if stack at time (18 + 1) = stack at time 18 and stack at time 18 = [ ], then stack at time (18 + 1) = [ ] (Transitive Property of Equality)
3	18 + 1 = 19	18 + 1 = 19 (Fixed Value Statement)
4	stack at time (18 + 1) = stack at time 19	if 18 + 1 = 19, then stack at time (18 + 1) = stack at time 19 (Substitution)
5	stack at time 19 = [ ]	if stack at time (18 + 1) = stack at time 19 and stack at time (18 + 1) = [ ], then stack at time 19 = [ ] (Transitive Property of Equality Variation 2)

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