Proof: Get Begin Expr Parent 47

Let's prove the following theorem:

if the following are true:
  • expression state at time 47 = "begin_expr"
  • the expression at time 47 = self.x
  • parent stack at time 47 = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ]

then parent stack at time 48 = [ self.x, [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] ]

Proof:

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Given
1 expression state at time 47 = "begin_expr"
2 the expression at time 47 = self.x
3 parent stack at time 47 = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ]
Proof Table
# Claim Reason
1 parent stack at time (47 + 1) = [ self.x, parent stack at time 47 ] if expression state at time 47 = "begin_expr" and the expression at time 47 = self.x, then parent stack at time (47 + 1) = [ self.x, parent stack at time 47 ]
2 [ self.x, parent stack at time 47 ] = [ self.x, [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] ] if parent stack at time 47 = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ], then [ self.x, parent stack at time 47 ] = [ self.x, [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] ]
3 parent stack at time (47 + 1) = [ self.x, [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] ] if parent stack at time (47 + 1) = [ self.x, parent stack at time 47 ] and [ self.x, parent stack at time 47 ] = [ self.x, [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] ], then parent stack at time (47 + 1) = [ self.x, [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] ]
4 47 + 1 = 48 47 + 1 = 48
5 parent stack at time (47 + 1) = parent stack at time 48 if 47 + 1 = 48, then parent stack at time (47 + 1) = parent stack at time 48
6 parent stack at time 48 = [ self.x, [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] ] if parent stack at time (47 + 1) = parent stack at time 48 and parent stack at time (47 + 1) = [ self.x, [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] ], then parent stack at time 48 = [ self.x, [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] ]

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