Proof: Get Iterate State 10

Let's prove the following theorem:

if the following are true:

expression state at time 10 = "iterate_args"
arguments stack at time 10 = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ]

then expression state at time 11 = "begin_expr"

Proof:

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Given

1	expression state at time 10 = "iterate_args"
2	arguments stack at time 10 = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ]

Proof Table

#	Claim	Reason
1	expression state at time (10 + 1) = "begin_expr"	if expression state at time 10 = "iterate_args" and arguments stack at time 10 = [ [ "John", [ "Smith", [ 25, [ ] ] ] ], [ ] ], then expression state at time (10 + 1) = "begin_expr" (Iterate Arguments State Property)
2	10 + 1 = 11	10 + 1 = 11 (Fixed Value Statement)
3	expression state at time (10 + 1) = expression state at time 11	if 10 + 1 = 11, then expression state at time (10 + 1) = expression state at time 11 (Substitution)
4	expression state at time 11 = "begin_expr"	if expression state at time (10 + 1) = expression state at time 11 and expression state at time (10 + 1) = "begin_expr", then expression state at time 11 = "begin_expr" (Transitive Property of Equality Variation 2)

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