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:

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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), [ ] ]
Proof Table
# 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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