Proof: Do Variables At Unchanged 23

Let's prove the following theorem:

if the following are true:

expression state at time 23 = "return"
Variables Map at time 23 = [ ]

then Variables Map at time 24 = [ ]

Proof:

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Given

1	expression state at time 23 = "return"
2	Variables Map at time 23 = [ ]

Proof Table

#	Claim	Reason
1	Variables Map at time (23 + 1) = Variables Map at time 23	if expression state at time 23 = "return", then Variables Map at time (23 + 1) = Variables Map at time 23 (Return (5))
2	Variables Map at time (23 + 1) = [ ]	if Variables Map at time (23 + 1) = Variables Map at time 23 and Variables Map at time 23 = [ ], then Variables Map at time (23 + 1) = [ ] (Transitive Property of Equality)
3	23 + 1 = 24	23 + 1 = 24 (Fixed Value Statement)
4	Variables Map at time (23 + 1) = Variables Map at time 24	if 23 + 1 = 24, then Variables Map at time (23 + 1) = Variables Map at time 24 (Substitution)
5	Variables Map at time 24 = [ ]	if Variables Map at time (23 + 1) = Variables Map at time 24 and Variables Map at time (23 + 1) = [ ], then Variables Map at time 24 = [ ] (Transitive Property of Equality Variation 2)

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