Proof: Get Iterate Expr 13

Let's prove the following theorem:

if the following are true:

expression state at time 13 = "iterate_args"
arguments stack at time 13 = [ [ "Smith", [ 25, [ ] ] ], [ ] ]

then the expression at time 14 = "Smith"

Proof:

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Given

1	expression state at time 13 = "iterate_args"
2	arguments stack at time 13 = [ [ "Smith", [ 25, [ ] ] ], [ ] ]

Proof Table

#	Claim	Reason
1	the expression at time (13 + 1) = "Smith"	if expression state at time 13 = "iterate_args" and arguments stack at time 13 = [ [ "Smith", [ 25, [ ] ] ], [ ] ], then the expression at time (13 + 1) = "Smith" (Iterate Arguments Expression Property)
2	13 + 1 = 14	13 + 1 = 14 (Fixed Value Statement)
3	the expression at time (13 + 1) = the expression at time 14	if 13 + 1 = 14, then the expression at time (13 + 1) = the expression at time 14 (Substitution)
4	the expression at time 14 = "Smith"	if the expression at time (13 + 1) = the expression at time 14 and the expression at time (13 + 1) = "Smith", then the expression at time 14 = "Smith" (Transitive Property of Equality Variation 2)

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