Proof: Get Iterate Parent 29

Let's prove the following theorem:

if the following are true:

expression state at time 29 = "iterate_args"
arguments stack at time 29 = [ [ locations, [ "ES", [ "Spain", [ ] ] ] ], [ ] ]
parent stack at time 29 = [ __setitem__(locations, "ES", "Spain"), [ ] ]

then parent stack at time 30 = [ __setitem__(locations, "ES", "Spain"), [ ] ]

Proof:

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Given

1	expression state at time 29 = "iterate_args"
2	arguments stack at time 29 = [ [ locations, [ "ES", [ "Spain", [ ] ] ] ], [ ] ]
3	parent stack at time 29 = [ `__setitem__(locations, "ES", "Spain")`, [ ] ]

Proof Table

#	Claim	Reason
1	parent stack at time (29 + 1) = parent stack at time 29	if expression state at time 29 = "iterate_args" and arguments stack at time 29 = [ [ locations, [ "ES", [ "Spain", [ ] ] ] ], [ ] ], then parent stack at time (29 + 1) = parent stack at time 29 (Do Iterage Args (4))
2	parent stack at time (29 + 1) = [ `__setitem__(locations, "ES", "Spain")`, [ ] ]	if parent stack at time (29 + 1) = parent stack at time 29 and parent stack at time 29 = [ `__setitem__(locations, "ES", "Spain")`, [ ] ], then parent stack at time (29 + 1) = [ `__setitem__(locations, "ES", "Spain")`, [ ] ] (Transitive Property of Equality)
3	29 + 1 = 30	29 + 1 = 30 (Fixed Value Statement)
4	parent stack at time (29 + 1) = parent stack at time 30	if 29 + 1 = 30, then parent stack at time (29 + 1) = parent stack at time 30 (Substitution)
5	parent stack at time 30 = [ `__setitem__(locations, "ES", "Spain")`, [ ] ]	if parent stack at time (29 + 1) = parent stack at time 30 and parent stack at time (29 + 1) = [ `__setitem__(locations, "ES", "Spain")`, [ ] ], then parent stack at time 30 = [ `__setitem__(locations, "ES", "Spain")`, [ ] ] (Transitive Property of Equality Variation 2)

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