Proof: Get Iterate End Parent 21

Let's prove the following theorem:

if the following are true:

expression state at time 21 = "iterate_args"
arguments stack at time 21 = [ [ ], [ [ ], [ ] ] ]
parent stack at time 21 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

then parent stack at time 22 = [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ]

Proof:

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Given

1	expression state at time 21 = "iterate_args"
2	arguments stack at time 21 = [ [ ], [ [ ], [ ] ] ]
3	parent stack at time 21 = [ entry "MX": "Mexico", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ]

Proof Table

#	Claim	Reason
1	parent stack at time (21 + 1) = [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ]	if expression state at time 21 = "iterate_args" and arguments stack at time 21 = [ [ ], [ [ ], [ ] ] ] and parent stack at time 21 = [ entry "MX": "Mexico", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ], then parent stack at time (21 + 1) = [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] (Iterate Args Empty (3))
2	21 + 1 = 22	21 + 1 = 22 (Fixed Value Statement)
3	parent stack at time (21 + 1) = parent stack at time 22	if 21 + 1 = 22, then parent stack at time (21 + 1) = parent stack at time 22 (Substitution)
4	parent stack at time 22 = [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ]	if parent stack at time (21 + 1) = parent stack at time 22 and parent stack at time (21 + 1) = [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ], then parent stack at time 22 = [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] (Transitive Property of Equality Variation 2)

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