Proof: Minimum Example Three

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	[ 0, [ 1, [ ] ] ] is greater than [ 0, [ 0, [ ] ] ]	[ 0, [ 1, [ ] ] ] is greater than [ 0, [ 0, [ ] ] ] (greater_than_example_two)
2	minimum value of stack [ [ 0, [ 0, [ ] ] ], [ ] ] = [ 0, [ 0, [ ] ] ]	minimum value of stack [ [ 0, [ 0, [ ] ] ], [ ] ] = [ 0, [ 0, [ ] ] ] (Minimum Of A Single Element List)
3	[ 0, [ 1, [ ] ] ] is greater than (minimum value of stack [ [ 0, [ 0, [ ] ] ], [ ] ])	if [ 0, [ 1, [ ] ] ] is greater than [ 0, [ 0, [ ] ] ] and minimum value of stack [ [ 0, [ 0, [ ] ] ], [ ] ] = [ 0, [ 0, [ ] ] ], then [ 0, [ 1, [ ] ] ] is greater than (minimum value of stack [ [ 0, [ 0, [ ] ] ], [ ] ]) (Greater Than Substitution)
4	minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] = minimum value of stack [ [ 0, [ 0, [ ] ] ], [ ] ]	if [ 0, [ 1, [ ] ] ] is greater than (minimum value of stack [ [ 0, [ 0, [ ] ] ], [ ] ]), then minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] = minimum value of stack [ [ 0, [ 0, [ ] ] ], [ ] ] (Minimum Value (2))
5	minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] = [ 0, [ 0, [ ] ] ]	if minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] = minimum value of stack [ [ 0, [ 0, [ ] ] ], [ ] ] and minimum value of stack [ [ 0, [ 0, [ ] ] ], [ ] ] = [ 0, [ 0, [ ] ] ], then minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] = [ 0, [ 0, [ ] ] ] (Transitive Property of Equality)
6	[ 1, [ 1, [ ] ] ] is greater than [ 0, [ 0, [ ] ] ]	[ 1, [ 1, [ ] ] ] is greater than [ 0, [ 0, [ ] ] ] (greater_than_example_two_2)
7	[ 1, [ 1, [ ] ] ] is greater than (minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ])	if [ 1, [ 1, [ ] ] ] is greater than [ 0, [ 0, [ ] ] ] and minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] = [ 0, [ 0, [ ] ] ], then [ 1, [ 1, [ ] ] ] is greater than (minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ]) (Greater Than Substitution)
8	minimum value of stack [ [ 1, [ 1, [ ] ] ], [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] ] = minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ]	if [ 1, [ 1, [ ] ] ] is greater than (minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ]), then minimum value of stack [ [ 1, [ 1, [ ] ] ], [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] ] = minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] (Minimum Value (2))
9	minimum value of stack [ [ 1, [ 1, [ ] ] ], [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] ] = [ 0, [ 0, [ ] ] ]	if minimum value of stack [ [ 1, [ 1, [ ] ] ], [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] ] = minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] and minimum value of stack [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] = [ 0, [ 0, [ ] ] ], then minimum value of stack [ [ 1, [ 1, [ ] ] ], [ [ 0, [ 1, [ ] ] ], [ [ 0, [ 0, [ ] ] ], [ ] ] ] ] = [ 0, [ 0, [ ] ] ] (Transitive Property of Equality)

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