Proof: Get Begin Expr Parent 45
Let's prove the following theorem:
if the following are true:
- expression state at time 45 = "begin_expr"
- the expression at time 45 =
__add__(self.x, 5)
- parent stack at time 45 = [ self."x" =
__add__(self.x, 5)
, [ ] ]
then parent stack at time 46 = [ __add__(self.x, 5)
, [ self."x" = __add__(self.x, 5)
, [ ] ] ]
Proof:
Given
1 | expression state at time 45 = "begin_expr" |
---|---|
2 | the expression at time 45 = __add__(self.x, 5) |
3 | parent stack at time 45 = [ self."x" = __add__(self.x, 5) , [ ] ] |
# | Claim | Reason |
---|---|---|
1 | parent stack at time (45 + 1) = [ __add__(self.x, 5) , parent stack at time 45 ] |
if expression state at time 45 = "begin_expr" and the expression at time 45 = __add__(self.x, 5) , then parent stack at time (45 + 1) = [ __add__(self.x, 5) , parent stack at time 45 ] |
2 | [ __add__(self.x, 5) , parent stack at time 45 ] = [ __add__(self.x, 5) , [ self."x" = __add__(self.x, 5) , [ ] ] ] |
if parent stack at time 45 = [ self."x" = __add__(self.x, 5) , [ ] ], then [ __add__(self.x, 5) , parent stack at time 45 ] = [ __add__(self.x, 5) , [ self."x" = __add__(self.x, 5) , [ ] ] ] |
3 | parent stack at time (45 + 1) = [ __add__(self.x, 5) , [ self."x" = __add__(self.x, 5) , [ ] ] ] |
if parent stack at time (45 + 1) = [ __add__(self.x, 5) , parent stack at time 45 ] and [ __add__(self.x, 5) , parent stack at time 45 ] = [ __add__(self.x, 5) , [ self."x" = __add__(self.x, 5) , [ ] ] ], then parent stack at time (45 + 1) = [ __add__(self.x, 5) , [ self."x" = __add__(self.x, 5) , [ ] ] ] |
4 | 45 + 1 = 46 | 45 + 1 = 46 |
5 | parent stack at time (45 + 1) = parent stack at time 46 | if 45 + 1 = 46, then parent stack at time (45 + 1) = parent stack at time 46 |
6 | parent stack at time 46 = [ __add__(self.x, 5) , [ self."x" = __add__(self.x, 5) , [ ] ] ] |
if parent stack at time (45 + 1) = parent stack at time 46 and parent stack at time (45 + 1) = [ __add__(self.x, 5) , [ self."x" = __add__(self.x, 5) , [ ] ] ], then parent stack at time 46 = [ __add__(self.x, 5) , [ self."x" = __add__(self.x, 5) , [ ] ] ] |
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