Proof: Do Expr At Unchanged 43

Let's prove the following theorem:

if the following are true:

expression state at time 43 = "begin_expr"
the expression at time 43 = self."x" = __add__(self.x, 5)

then the expression at time 44 = self."x" = __add__(self.x, 5)

Proof:

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Given

1	expression state at time 43 = "begin_expr"
2	the expression at time 43 = self."x" = `__add__(self.x, 5)`

Proof Table

#	Claim	Reason
1	the expression at time (43 + 1) = the expression at time 43	if expression state at time 43 = "begin_expr", then the expression at time (43 + 1) = the expression at time 43 (Insn Count Begin Expression (1))
2	the expression at time (43 + 1) = self."x" = `__add__(self.x, 5)`	if the expression at time (43 + 1) = the expression at time 43 and the expression at time 43 = self."x" = `__add__(self.x, 5)`, then the expression at time (43 + 1) = self."x" = `__add__(self.x, 5)` (Transitive Property of Equality)
3	43 + 1 = 44	43 + 1 = 44 (Fixed Value Statement)
4	the expression at time (43 + 1) = the expression at time 44	if 43 + 1 = 44, then the expression at time (43 + 1) = the expression at time 44 (Substitution)
5	the expression at time 44 = self."x" = `__add__(self.x, 5)`	if the expression at time (43 + 1) = the expression at time 44 and the expression at time (43 + 1) = self."x" = `__add__(self.x, 5)`, then the expression at time 44 = self."x" = `__add__(self.x, 5)` (Transitive Property of Equality Variation 2)

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