Proof: Do Variables At Unchanged 12

Let's prove the following theorem:

if the following are true:

expression state at time 12 = "begin_expr"
Variables Map at time 12 = [ ]

then Variables Map at time 13 = [ ]

Proof:

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Given

1	expression state at time 12 = "begin_expr"
2	Variables Map at time 12 = [ ]

Proof Table

#	Claim	Reason
1	Variables Map at time (12 + 1) = Variables Map at time 12	if expression state at time 12 = "begin_expr", then Variables Map at time (12 + 1) = Variables Map at time 12 (Insn Count Begin Expression (2))
2	Variables Map at time (12 + 1) = [ ]	if Variables Map at time (12 + 1) = Variables Map at time 12 and Variables Map at time 12 = [ ], then Variables Map at time (12 + 1) = [ ] (Transitive Property of Equality)
3	12 + 1 = 13	12 + 1 = 13 (Fixed Value Statement)
4	Variables Map at time (12 + 1) = Variables Map at time 13	if 12 + 1 = 13, then Variables Map at time (12 + 1) = Variables Map at time 13 (Substitution)
5	Variables Map at time 13 = [ ]	if Variables Map at time (12 + 1) = Variables Map at time 13 and Variables Map at time (12 + 1) = [ ], then Variables Map at time 13 = [ ] (Transitive Property of Equality Variation 2)

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