Proof: Get Iterate State 4

Let's prove the following theorem:

if the following are true:

expression state at time 4 = "iterate_args"
arguments stack at time 4 = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ]

then expression state at time 5 = "begin_expr"

Proof:

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Given

1	expression state at time 4 = "iterate_args"
2	arguments stack at time 4 = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ]

Proof Table

#	Claim	Reason
1	expression state at time (4 + 1) = "begin_expr"	if expression state at time 4 = "iterate_args" and arguments stack at time 4 = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ], then expression state at time (4 + 1) = "begin_expr" (Iterate Arguments State Property)
2	4 + 1 = 5	4 + 1 = 5 (Fixed Value Statement)
3	expression state at time (4 + 1) = expression state at time 5	if 4 + 1 = 5, then expression state at time (4 + 1) = expression state at time 5 (Substitution)
4	expression state at time 5 = "begin_expr"	if expression state at time (4 + 1) = expression state at time 5 and expression state at time (4 + 1) = "begin_expr", then expression state at time 5 = "begin_expr" (Transitive Property of Equality Variation 2)

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