Proof: Do Expr At Unchanged 60

Let's prove the following theorem:

if the following are true:
  • expression state at time 60 = "begin_expr"
  • the expression at time 60 = __mul__(self.age, 12)

then the expression at time 61 = __mul__(self.age, 12)

Proof:

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Given
1 expression state at time 60 = "begin_expr"
2 the expression at time 60 = __mul__(self.age, 12)
Proof Table
# Claim Reason
1 the expression at time (60 + 1) = the expression at time 60 if expression state at time 60 = "begin_expr", then the expression at time (60 + 1) = the expression at time 60
2 the expression at time (60 + 1) = __mul__(self.age, 12) if the expression at time (60 + 1) = the expression at time 60 and the expression at time 60 = __mul__(self.age, 12), then the expression at time (60 + 1) = __mul__(self.age, 12)
3 60 + 1 = 61 60 + 1 = 61
4 the expression at time (60 + 1) = the expression at time 61 if 60 + 1 = 61, then the expression at time (60 + 1) = the expression at time 61
5 the expression at time 61 = __mul__(self.age, 12) if the expression at time (60 + 1) = the expression at time 61 and the expression at time (60 + 1) = __mul__(self.age, 12), then the expression at time 61 = __mul__(self.age, 12)

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