Proof: Do Expr At Unchanged 9

Let's prove the following theorem:

if the following are true:

expression state at time 9 = "begin_expr"
the expression at time 9 = Person("John", "Smith", 25)

then the expression at time 10 = Person("John", "Smith", 25)

Proof:

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Given

1	expression state at time 9 = "begin_expr"
2	the expression at time 9 = `Person("John", "Smith", 25)`

Proof Table

#	Claim	Reason
1	the expression at time (9 + 1) = the expression at time 9	if expression state at time 9 = "begin_expr", then the expression at time (9 + 1) = the expression at time 9 (Insn Count Begin Expression (1))
2	the expression at time (9 + 1) = `Person("John", "Smith", 25)`	if the expression at time (9 + 1) = the expression at time 9 and the expression at time 9 = `Person("John", "Smith", 25)`, then the expression at time (9 + 1) = `Person("John", "Smith", 25)` (Transitive Property of Equality)
3	9 + 1 = 10	9 + 1 = 10 (Fixed Value Statement)
4	the expression at time (9 + 1) = the expression at time 10	if 9 + 1 = 10, then the expression at time (9 + 1) = the expression at time 10 (Substitution)
5	the expression at time 10 = `Person("John", "Smith", 25)`	if the expression at time (9 + 1) = the expression at time 10 and the expression at time (9 + 1) = `Person("John", "Smith", 25)`, then the expression at time 10 = `Person("John", "Smith", 25)` (Transitive Property of Equality Variation 2)

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