Proof: Do Expr At Unchanged 12

Let's prove the following theorem:

if the following are true:

expression state at time 12 = "begin_expr"
the expression at time 12 = Dog()

then the expression at time 13 = Dog()

Proof:

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Given

1	expression state at time 12 = "begin_expr"
2	the expression at time 12 = `Dog()`

Proof Table

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

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