Proof: Find Number Example 2

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ]	index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] (Find Value Property)
2	not (1 = 0)	not (1 = 0) (Fixed Value Statement)
3	[1,[]] ≠ [0,[]]	if not (1 = 0), then [1,[]] ≠ [0,[]] (Not Equal Lists)
4	index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] = index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index (sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ])	if [1,[]] ≠ [0,[]], then index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] = index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index (sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ]) (Number is Not Found)
5	sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ] = [ 1, [ ] ]	sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ] = [ 1, [ ] ] (Add 0 and 1)
6	index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index (sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ]) = index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index [ 1, [ ] ]	if sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ] = [ 1, [ ] ], then index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index (sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ]) = index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index [ 1, [ ] ] (Substitution)
7	index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] = index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index [ 1, [ ] ]	if index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] = index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index (sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ]) and index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index (sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ]) = index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index [ 1, [ ] ], then index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] = index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index [ 1, [ ] ] (Transitive Property of Equality)
8	[0,[]] = [0,[]]	[0,[]] = [0,[]] (are_equal_list_example)
9	index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index [ 1, [ ] ] = [ 1, [ ] ]	if [0,[]] = [0,[]], then index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index [ 1, [ ] ] = [ 1, [ ] ] (Number is Found)
10	index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] = [ 1, [ ] ]	if index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] = index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index [ 1, [ ] ] and index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index [ 1, [ ] ] = [ 1, [ ] ], then index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] = [ 1, [ ] ] (Transitive Property of Equality)
11	index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ]	if index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] and index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with current index [ 0, [ ] ] = [ 1, [ ] ], then index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ] (Transitive Property of Equality)

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