Proof: Get Iterate State 14

Let's prove the following theorem:

if the following are true:

expression state at time 14 = "iterate_args"
arguments stack at time 14 = [ [ 7, [ 9, [ ] ] ], [ ] ]

then expression state at time 15 = "begin_expr"

Proof:

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Given

1	expression state at time 14 = "iterate_args"
2	arguments stack at time 14 = [ [ 7, [ 9, [ ] ] ], [ ] ]

Proof Table

#	Claim	Reason
1	expression state at time (14 + 1) = "begin_expr"	if expression state at time 14 = "iterate_args" and arguments stack at time 14 = [ [ 7, [ 9, [ ] ] ], [ ] ], then expression state at time (14 + 1) = "begin_expr" (Iterate Arguments State Property)
2	14 + 1 = 15	14 + 1 = 15 (Fixed Value Statement)
3	expression state at time (14 + 1) = expression state at time 15	if 14 + 1 = 15, then expression state at time (14 + 1) = expression state at time 15 (Substitution)
4	expression state at time 15 = "begin_expr"	if expression state at time (14 + 1) = expression state at time 15 and expression state at time (14 + 1) = "begin_expr", then expression state at time 15 = "begin_expr" (Transitive Property of Equality Variation 2)

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