Proof: Do Control Map At Unchanged 8

Let's prove the following theorem:

if the following are true:

expression state at time 8 = "return"
Control Map at time 8 = [ ]

then Control Map at time 9 = [ ]

Proof:

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Given

1	expression state at time 8 = "return"
2	Control Map at time 8 = [ ]

Proof Table

#	Claim	Reason
1	Control Map at time (8 + 1) = Control Map at time 8	if expression state at time 8 = "return", then Control Map at time (8 + 1) = Control Map at time 8 (Return (10))
2	Control Map at time (8 + 1) = [ ]	if Control Map at time (8 + 1) = Control Map at time 8 and Control Map at time 8 = [ ], then Control Map at time (8 + 1) = [ ] (Transitive Property of Equality)
3	8 + 1 = 9	8 + 1 = 9 (Fixed Value Statement)
4	Control Map at time (8 + 1) = Control Map at time 9	if 8 + 1 = 9, then Control Map at time (8 + 1) = Control Map at time 9 (Substitution)
5	Control Map at time 9 = [ ]	if Control Map at time (8 + 1) = Control Map at time 9 and Control Map at time (8 + 1) = [ ], then Control Map at time 9 = [ ] (Transitive Property of Equality Variation 2)

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