Proof: Do Variables At Unchanged 15

Let's prove the following theorem:

if the following are true:

expression state at time 15 = "return"
Variables Map at time 15 = [ ]

then Variables Map at time 16 = [ ]

Proof:

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Given

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

Proof Table

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

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