Proof: Do Stack At Unchanged 30

Let's prove the following theorem:

if the following are true:

expression state at time 30 = "begin_expr"
stack at time 30 = [ ]

then stack at time 31 = [ ]

Proof:

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Given

1	expression state at time 30 = "begin_expr"
2	stack at time 30 = [ ]

Proof Table

#	Claim	Reason
1	stack at time (30 + 1) = stack at time 30	if expression state at time 30 = "begin_expr", then stack at time (30 + 1) = stack at time 30 (Insn Count Begin Expression (5))
2	stack at time (30 + 1) = [ ]	if stack at time (30 + 1) = stack at time 30 and stack at time 30 = [ ], then stack at time (30 + 1) = [ ] (Transitive Property of Equality)
3	30 + 1 = 31	30 + 1 = 31 (Fixed Value Statement)
4	stack at time (30 + 1) = stack at time 31	if 30 + 1 = 31, then stack at time (30 + 1) = stack at time 31 (Substitution)
5	stack at time 31 = [ ]	if stack at time (30 + 1) = stack at time 31 and stack at time (30 + 1) = [ ], then stack at time 31 = [ ] (Transitive Property of Equality Variation 2)

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