Proof: Get Iterate Parent 10

Let's prove the following theorem:

if the following are true:

expression state at time 10 = "iterate_args"
arguments stack at time 10 = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ]
parent stack at time 10 = [ Person("John", "Smith", 25), [ ] ]

then parent stack at time 11 = [ Person("John", "Smith", 25), [ ] ]

Proof:

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Given

1	expression state at time 10 = "iterate_args"
2	arguments stack at time 10 = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ]
3	parent stack at time 10 = [ `Person("John", "Smith", 25)`, [ ] ]

Proof Table

#	Claim	Reason
1	parent stack at time (10 + 1) = parent stack at time 10	if expression state at time 10 = "iterate_args" and arguments stack at time 10 = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ], then parent stack at time (10 + 1) = parent stack at time 10 (Do Iterage Args (4))
2	parent stack at time (10 + 1) = [ `Person("John", "Smith", 25)`, [ ] ]	if parent stack at time (10 + 1) = parent stack at time 10 and parent stack at time 10 = [ `Person("John", "Smith", 25)`, [ ] ], then parent stack at time (10 + 1) = [ `Person("John", "Smith", 25)`, [ ] ] (Transitive Property of Equality)
3	10 + 1 = 11	10 + 1 = 11 (Fixed Value Statement)
4	parent stack at time (10 + 1) = parent stack at time 11	if 10 + 1 = 11, then parent stack at time (10 + 1) = parent stack at time 11 (Substitution)
5	parent stack at time 11 = [ `Person("John", "Smith", 25)`, [ ] ]	if parent stack at time (10 + 1) = parent stack at time 11 and parent stack at time (10 + 1) = [ `Person("John", "Smith", 25)`, [ ] ], then parent stack at time 11 = [ `Person("John", "Smith", 25)`, [ ] ] (Transitive Property of Equality Variation 2)

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