Proof: Do Tab At Unchanged 31

Let's prove the following theorem:

if the following are true:

expression state at time 31 = "return"
the tab at time 31 = 0

then the tab at time 32 = 0

Proof:

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Given

1	expression state at time 31 = "return"
2	the tab at time 31 = 0

Proof Table

#	Claim	Reason
1	the tab at time (31 + 1) = the tab at time 31	if expression state at time 31 = "return", then the tab at time (31 + 1) = the tab at time 31 (Return (7))
2	the tab at time (31 + 1) = 0	if the tab at time (31 + 1) = the tab at time 31 and the tab at time 31 = 0, then the tab at time (31 + 1) = 0 (Transitive Property of Equality)
3	31 + 1 = 32	31 + 1 = 32 (Fixed Value Statement)
4	the tab at time (31 + 1) = the tab at time 32	if 31 + 1 = 32, then the tab at time (31 + 1) = the tab at time 32 (Substitution)
5	the tab at time 32 = 0	if the tab at time (31 + 1) = the tab at time 32 and the tab at time (31 + 1) = 0, then the tab at time 32 = 0 (Transitive Property of Equality Variation 2)

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