Proof: Find Number One Element Example

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	index of value x in [ x, [ ] ] = index of value x in [ x, [ ] ] with current index 0	index of value x in [ x, [ ] ] = index of value x in [ x, [ ] ] with current index 0 (Find Value Property)
2	x = x	x = x (Reflexive Property of Equality)
3	index of value x in [ x, [ ] ] with current index 0 = 0	if x = x, then index of value x in [ x, [ ] ] with current index 0 = 0 (Find Value Match Property)
4	index of value x in [ x, [ ] ] = 0	if index of value x in [ x, [ ] ] = index of value x in [ x, [ ] ] with current index 0 and index of value x in [ x, [ ] ] with current index 0 = 0, then index of value x in [ x, [ ] ] = 0 (Transitive Property of Equality)

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