Proof: Do Expr At Unchanged 18

Let's prove the following theorem:

if the following are true:

expression state at time 18 = "begin_expr"
the expression at time 18 = self."x" = 0

then the expression at time 19 = self."x" = 0

Proof:

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Given

1	expression state at time 18 = "begin_expr"
2	the expression at time 18 = self."x" = 0

Proof Table

#	Claim	Reason
1	the expression at time (18 + 1) = the expression at time 18	if expression state at time 18 = "begin_expr", then the expression at time (18 + 1) = the expression at time 18 (Insn Count Begin Expression (1))
2	the expression at time (18 + 1) = self."x" = 0	if the expression at time (18 + 1) = the expression at time 18 and the expression at time 18 = self."x" = 0, then the expression at time (18 + 1) = self."x" = 0 (Transitive Property of Equality)
3	18 + 1 = 19	18 + 1 = 19 (Fixed Value Statement)
4	the expression at time (18 + 1) = the expression at time 19	if 18 + 1 = 19, then the expression at time (18 + 1) = the expression at time 19 (Substitution)
5	the expression at time 19 = self."x" = 0	if the expression at time (18 + 1) = the expression at time 19 and the expression at time (18 + 1) = self."x" = 0, then the expression at time 19 = self."x" = 0 (Transitive Property of Equality Variation 2)

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