Proof: Get Iterate Parent 54

Let's prove the following theorem:

if the following are true:
  • expression state at time 54 = "iterate_args"
  • arguments stack at time 54 = [ [ 5, [ ] ], [ [ ], [ ] ] ]
  • parent stack at time 54 = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ]

then parent stack at time 55 = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ]

Proof:

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Given
1 expression state at time 54 = "iterate_args"
2 arguments stack at time 54 = [ [ 5, [ ] ], [ [ ], [ ] ] ]
3 parent stack at time 54 = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ]
Proof Table
# Claim Reason
1 parent stack at time (54 + 1) = parent stack at time 54 if expression state at time 54 = "iterate_args" and arguments stack at time 54 = [ [ 5, [ ] ], [ [ ], [ ] ] ], then parent stack at time (54 + 1) = parent stack at time 54
2 parent stack at time (54 + 1) = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] if parent stack at time (54 + 1) = parent stack at time 54 and parent stack at time 54 = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ], then parent stack at time (54 + 1) = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ]
3 54 + 1 = 55 54 + 1 = 55
4 parent stack at time (54 + 1) = parent stack at time 55 if 54 + 1 = 55, then parent stack at time (54 + 1) = parent stack at time 55
5 parent stack at time 55 = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ] if parent stack at time (54 + 1) = parent stack at time 55 and parent stack at time (54 + 1) = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ], then parent stack at time 55 = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ]

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