Proof: Find Number Example

Let's prove the following theorem:

Proof:

Proof Table

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

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