Proof: Do Stack At Unchanged 19

Let's prove the following theorem:

if the following are true:

expression state at time 19 = "iterate_args"
stack at time 19 = [ ]

then stack at time 20 = [ ]

Proof:

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Given

1	expression state at time 19 = "iterate_args"
2	stack at time 19 = [ ]

Proof Table

#	Claim	Reason
1	stack at time (19 + 1) = stack at time 19	if expression state at time 19 = "iterate_args", then stack at time (19 + 1) = stack at time 19 (Iterate Insn (5))
2	stack at time (19 + 1) = [ ]	if stack at time (19 + 1) = stack at time 19 and stack at time 19 = [ ], then stack at time (19 + 1) = [ ] (Transitive Property of Equality)
3	19 + 1 = 20	19 + 1 = 20 (Fixed Value Statement)
4	stack at time (19 + 1) = stack at time 20	if 19 + 1 = 20, then stack at time (19 + 1) = stack at time 20 (Substitution)
5	stack at time 20 = [ ]	if stack at time (19 + 1) = stack at time 20 and stack at time (19 + 1) = [ ], then stack at time 20 = [ ] (Transitive Property of Equality Variation 2)

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