Proof: Do Variables At Unchanged 8

Let's prove the following theorem:

if the following are true:

expression state at time 8 = "begin_expr"
Variables Map at time 8 = [ ]

then Variables Map at time 9 = [ ]

Proof:

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Given

1	expression state at time 8 = "begin_expr"
2	Variables Map at time 8 = [ ]

Proof Table

#	Claim	Reason
1	Variables Map at time (8 + 1) = Variables Map at time 8	if expression state at time 8 = "begin_expr", then Variables Map at time (8 + 1) = Variables Map at time 8 (Insn Count Begin Expression (2))
2	Variables Map at time (8 + 1) = [ ]	if Variables Map at time (8 + 1) = Variables Map at time 8 and Variables Map at time 8 = [ ], then Variables Map at time (8 + 1) = [ ] (Transitive Property of Equality)
3	8 + 1 = 9	8 + 1 = 9 (Fixed Value Statement)
4	Variables Map at time (8 + 1) = Variables Map at time 9	if 8 + 1 = 9, then Variables Map at time (8 + 1) = Variables Map at time 9 (Substitution)
5	Variables Map at time 9 = [ ]	if Variables Map at time (8 + 1) = Variables Map at time 9 and Variables Map at time (8 + 1) = [ ], then Variables Map at time 9 = [ ] (Transitive Property of Equality Variation 2)

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