Proof: Get Begin Expr Parent 43

Let's prove the following theorem:

if the following are true:
  • expression state at time 43 = "begin_expr"
  • the expression at time 43 = self."x" = __add__(self.x, 5)
  • parent stack at time 43 = [ ]

then parent stack at time 44 = [ self."x" = __add__(self.x, 5), [ ] ]

Proof:

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Given
1 expression state at time 43 = "begin_expr"
2 the expression at time 43 = self."x" = __add__(self.x, 5)
3 parent stack at time 43 = [ ]
Proof Table
# Claim Reason
1 parent stack at time (43 + 1) = [ self."x" = __add__(self.x, 5), parent stack at time 43 ] if expression state at time 43 = "begin_expr" and the expression at time 43 = self."x" = __add__(self.x, 5), then parent stack at time (43 + 1) = [ self."x" = __add__(self.x, 5), parent stack at time 43 ]
2 [ self."x" = __add__(self.x, 5), parent stack at time 43 ] = [ self."x" = __add__(self.x, 5), [ ] ] if parent stack at time 43 = [ ], then [ self."x" = __add__(self.x, 5), parent stack at time 43 ] = [ self."x" = __add__(self.x, 5), [ ] ]
3 parent stack at time (43 + 1) = [ self."x" = __add__(self.x, 5), [ ] ] if parent stack at time (43 + 1) = [ self."x" = __add__(self.x, 5), parent stack at time 43 ] and [ self."x" = __add__(self.x, 5), parent stack at time 43 ] = [ self."x" = __add__(self.x, 5), [ ] ], then parent stack at time (43 + 1) = [ self."x" = __add__(self.x, 5), [ ] ]
4 43 + 1 = 44 43 + 1 = 44
5 parent stack at time (43 + 1) = parent stack at time 44 if 43 + 1 = 44, then parent stack at time (43 + 1) = parent stack at time 44
6 parent stack at time 44 = [ self."x" = __add__(self.x, 5), [ ] ] if parent stack at time (43 + 1) = parent stack at time 44 and parent stack at time (43 + 1) = [ self."x" = __add__(self.x, 5), [ ] ], then parent stack at time 44 = [ self."x" = __add__(self.x, 5), [ ] ]

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