Proof: Do Tab At Unchanged 15

Let's prove the following theorem:

if the following are true:

expression state at time 15 = "return"
the tab at time 15 = 0

then the tab at time 16 = 0

Proof:

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Given

1	expression state at time 15 = "return"
2	the tab at time 15 = 0

Proof Table

#	Claim	Reason
1	the tab at time (15 + 1) = the tab at time 15	if expression state at time 15 = "return", then the tab at time (15 + 1) = the tab at time 15 (Return (7))
2	the tab at time (15 + 1) = 0	if the tab at time (15 + 1) = the tab at time 15 and the tab at time 15 = 0, then the tab at time (15 + 1) = 0 (Transitive Property of Equality)
3	15 + 1 = 16	15 + 1 = 16 (Fixed Value Statement)
4	the tab at time (15 + 1) = the tab at time 16	if 15 + 1 = 16, then the tab at time (15 + 1) = the tab at time 16 (Substitution)
5	the tab at time 16 = 0	if the tab at time (15 + 1) = the tab at time 16 and the tab at time (15 + 1) = 0, then the tab at time 16 = 0 (Transitive Property of Equality Variation 2)

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