Proof: Get Iterate Params 15

Let's prove the following theorem:

if the following are true:

expression state at time 15 = "iterate_args"
arguments stack at time 15 = [ [ "MX", [ "Mexico", [ ] ] ], [ [ ], [ ] ] ]

then arguments stack at time 16 = [ [ "Mexico", [ ] ], [ [ ], [ ] ] ]

Proof:

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Given

1	expression state at time 15 = "iterate_args"
2	arguments stack at time 15 = [ [ "MX", [ "Mexico", [ ] ] ], [ [ ], [ ] ] ]

Proof Table

#	Claim	Reason
1	arguments stack at time (15 + 1) = [ [ "Mexico", [ ] ], [ [ ], [ ] ] ]	if expression state at time 15 = "iterate_args" and arguments stack at time 15 = [ [ "MX", [ "Mexico", [ ] ] ], [ [ ], [ ] ] ], then arguments stack at time (15 + 1) = [ [ "Mexico", [ ] ], [ [ ], [ ] ] ] (Iterate Arguments Pop Property)
2	15 + 1 = 16	15 + 1 = 16 (Fixed Value Statement)
3	arguments stack at time (15 + 1) = arguments stack at time 16	if 15 + 1 = 16, then arguments stack at time (15 + 1) = arguments stack at time 16 (Substitution)
4	arguments stack at time 16 = [ [ "Mexico", [ ] ], [ [ ], [ ] ] ]	if arguments stack at time (15 + 1) = arguments stack at time 16 and arguments stack at time (15 + 1) = [ [ "Mexico", [ ] ], [ [ ], [ ] ] ], then arguments stack at time 16 = [ [ "Mexico", [ ] ], [ [ ], [ ] ] ] (Transitive Property of Equality Variation 2)

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