Proof: Get Iterate End Parent 30

Let's prove the following theorem:

if the following are true:

expression state at time 30 = "iterate_args"
arguments stack at time 30 = [ [ ], [ ] ]
parent stack at time 30 = [ self."y" = 0, [ ] ]

then parent stack at time 31 = [ ]

Proof:

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Given

1	expression state at time 30 = "iterate_args"
2	arguments stack at time 30 = [ [ ], [ ] ]
3	parent stack at time 30 = [ self."y" = 0, [ ] ]

Proof Table

#	Claim	Reason
1	parent stack at time (30 + 1) = [ ]	if expression state at time 30 = "iterate_args" and arguments stack at time 30 = [ [ ], [ ] ] and parent stack at time 30 = [ self."y" = 0, [ ] ], then parent stack at time (30 + 1) = [ ] (Iterate Args Empty (3))
2	30 + 1 = 31	30 + 1 = 31 (Fixed Value Statement)
3	parent stack at time (30 + 1) = parent stack at time 31	if 30 + 1 = 31, then parent stack at time (30 + 1) = parent stack at time 31 (Substitution)
4	parent stack at time 31 = [ ]	if parent stack at time (30 + 1) = parent stack at time 31 and parent stack at time (30 + 1) = [ ], then parent stack at time 31 = [ ] (Transitive Property of Equality Variation 2)

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