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:
Given
1 | expression state at time 60 = "begin_expr" |
---|---|
2 | the expression at time 60 = __mul__(self.age, 12) |
# | 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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