Proof: Do Expr At Unchanged 1
Let's prove the following theorem:
if the following are true:
- expression state at time 1 = "begin_expr"
- the expression at time 1 =
{"ES": "Estonia", "MX": "Mexico"}
then the expression at time 2 = {"ES": "Estonia", "MX": "Mexico"}
Proof:
Given
1 | expression state at time 1 = "begin_expr" |
---|---|
2 | the expression at time 1 = {"ES": "Estonia", "MX": "Mexico"} |
# | Claim | Reason |
---|---|---|
1 | the expression at time (1 + 1) = the expression at time 1 | if expression state at time 1 = "begin_expr", then the expression at time (1 + 1) = the expression at time 1 |
2 | the expression at time (1 + 1) = {"ES": "Estonia", "MX": "Mexico"} |
if the expression at time (1 + 1) = the expression at time 1 and the expression at time 1 = {"ES": "Estonia", "MX": "Mexico"} , then the expression at time (1 + 1) = {"ES": "Estonia", "MX": "Mexico"} |
3 | 1 + 1 = 2 | 1 + 1 = 2 |
4 | the expression at time (1 + 1) = the expression at time 2 | if 1 + 1 = 2, then the expression at time (1 + 1) = the expression at time 2 |
5 | the expression at time 2 = {"ES": "Estonia", "MX": "Mexico"} |
if the expression at time (1 + 1) = the expression at time 2 and the expression at time (1 + 1) = {"ES": "Estonia", "MX": "Mexico"} , then the expression at time 2 = {"ES": "Estonia", "MX": "Mexico"} |
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