Proof: Do Expr At Unchanged 54
Let's prove the following theorem:
if the following are true:
- expression state at time 54 = "begin_expr"
- the expression at time 54 =
p.age_in_months()
then the expression at time 55 = p.age_in_months()
Proof:
Given
1 | expression state at time 54 = "begin_expr" |
---|---|
2 | the expression at time 54 = p.age_in_months() |
# | Claim | Reason |
---|---|---|
1 | the expression at time (54 + 1) = the expression at time 54 | if expression state at time 54 = "begin_expr", then the expression at time (54 + 1) = the expression at time 54 |
2 | the expression at time (54 + 1) = p.age_in_months() |
if the expression at time (54 + 1) = the expression at time 54 and the expression at time 54 = p.age_in_months() , then the expression at time (54 + 1) = p.age_in_months() |
3 | 54 + 1 = 55 | 54 + 1 = 55 |
4 | the expression at time (54 + 1) = the expression at time 55 | if 54 + 1 = 55, then the expression at time (54 + 1) = the expression at time 55 |
5 | the expression at time 55 = p.age_in_months() |
if the expression at time (54 + 1) = the expression at time 55 and the expression at time (54 + 1) = p.age_in_months() , then the expression at time 55 = p.age_in_months() |
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