Proof: Minimum Index Example

Let's prove the following theorem:

index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ]

Proof:

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Proof Table

#	Claim	Reason
1	index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = index of value (minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = index of value (minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Minimum Index Of A List)
2	minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 0, [ ] ]	minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 0, [ ] ] (minimum_example_2)
3	index of value (minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	if minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 0, [ ] ], then index of value (minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Substitution)
4	index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ]	index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ] (find_number_example_2)
5	index of value (minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ]	if index of value (minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] and index of value [ 0, [ ] ] in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ], then index of value (minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ] (Transitive Property of Equality)
6	index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ]	if index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = index of value (minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] and index of value (minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) in [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ], then index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ] (Transitive Property of Equality)

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