Proof: Get Iterate Parent 32

Let's prove the following theorem:

if the following are true:

expression state at time 32 = "iterate_args"
arguments stack at time 32 = [ [ "ES", [ "Spain", [ ] ] ], [ ] ]
parent stack at time 32 = [ __setitem__(locations, "ES", "Spain"), [ ] ]

then parent stack at time 33 = [ __setitem__(locations, "ES", "Spain"), [ ] ]

Proof:

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Given

1	expression state at time 32 = "iterate_args"
2	arguments stack at time 32 = [ [ "ES", [ "Spain", [ ] ] ], [ ] ]
3	parent stack at time 32 = [ `__setitem__(locations, "ES", "Spain")`, [ ] ]

Proof Table

#	Claim	Reason
1	parent stack at time (32 + 1) = parent stack at time 32	if expression state at time 32 = "iterate_args" and arguments stack at time 32 = [ [ "ES", [ "Spain", [ ] ] ], [ ] ], then parent stack at time (32 + 1) = parent stack at time 32 (Do Iterage Args (4))
2	parent stack at time (32 + 1) = [ `__setitem__(locations, "ES", "Spain")`, [ ] ]	if parent stack at time (32 + 1) = parent stack at time 32 and parent stack at time 32 = [ `__setitem__(locations, "ES", "Spain")`, [ ] ], then parent stack at time (32 + 1) = [ `__setitem__(locations, "ES", "Spain")`, [ ] ] (Transitive Property of Equality)
3	32 + 1 = 33	32 + 1 = 33 (Fixed Value Statement)
4	parent stack at time (32 + 1) = parent stack at time 33	if 32 + 1 = 33, then parent stack at time (32 + 1) = parent stack at time 33 (Substitution)
5	parent stack at time 33 = [ `__setitem__(locations, "ES", "Spain")`, [ ] ]	if parent stack at time (32 + 1) = parent stack at time 33 and parent stack at time (32 + 1) = [ `__setitem__(locations, "ES", "Spain")`, [ ] ], then parent stack at time 33 = [ `__setitem__(locations, "ES", "Spain")`, [ ] ] (Transitive Property of Equality Variation 2)

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