Proof: Get Iterate End Expr 31

Let's prove the following theorem:

if the following are true:

expression state at time 31 = "iterate_args"
arguments stack at time 31 = [ [ ], [ ] ]
parent stack at time 31 = [ self."first_name" = first_name, [ ] ]

then the expression at time 32 = self."first_name" = first_name

Proof:

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Given

1	expression state at time 31 = "iterate_args"
2	arguments stack at time 31 = [ [ ], [ ] ]
3	parent stack at time 31 = [ self."first_name" = first_name, [ ] ]

Proof Table

#	Claim	Reason
1	the expression at time (31 + 1) = self."first_name" = first_name	if expression state at time 31 = "iterate_args" and arguments stack at time 31 = [ [ ], [ ] ] and parent stack at time 31 = [ self."first_name" = first_name, [ ] ], then the expression at time (31 + 1) = self."first_name" = first_name (Iterate Arguments Finished Rule)
2	31 + 1 = 32	31 + 1 = 32 (Fixed Value Statement)
3	the expression at time (31 + 1) = the expression at time 32	if 31 + 1 = 32, then the expression at time (31 + 1) = the expression at time 32 (Substitution)
4	the expression at time 32 = self."first_name" = first_name	if the expression at time (31 + 1) = the expression at time 32 and the expression at time (31 + 1) = self."first_name" = first_name, then the expression at time 32 = self."first_name" = first_name (Transitive Property of Equality Variation 2)

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