Proof: Minimum Example

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	[ 0, [ ] ] is less than [ 1, [ ] ]	[ 0, [ ] ] is less than [ 1, [ ] ] (less_than_example)
2	minimum value of stack [ [ 1, [ ] ], [ ] ] = [ 1, [ ] ]	minimum value of stack [ [ 1, [ ] ], [ ] ] = [ 1, [ ] ] (Minimum Of A Single Element List)
3	[ 1, [ ] ] = minimum value of stack [ [ 1, [ ] ], [ ] ]	if minimum value of stack [ [ 1, [ ] ], [ ] ] = [ 1, [ ] ], then [ 1, [ ] ] = minimum value of stack [ [ 1, [ ] ], [ ] ] (Symmetric Property of Equality)
4	[ 0, [ ] ] is less than [ 1, [ ] ] = [ 0, [ ] ] is less than (minimum value of stack [ [ 1, [ ] ], [ ] ])	if [ 1, [ ] ] = minimum value of stack [ [ 1, [ ] ], [ ] ], then [ 0, [ ] ] is less than [ 1, [ ] ] = [ 0, [ ] ] is less than (minimum value of stack [ [ 1, [ ] ], [ ] ]) (Substitution)
5	[ 0, [ ] ] is less than (minimum value of stack [ [ 1, [ ] ], [ ] ])	if [ 0, [ ] ] is less than [ 1, [ ] ] and [ 0, [ ] ] is less than [ 1, [ ] ] = [ 0, [ ] ] is less than (minimum value of stack [ [ 1, [ ] ], [ ] ]), then [ 0, [ ] ] is less than (minimum value of stack [ [ 1, [ ] ], [ ] ]) (Truth Propagation Property)
6	minimum value of stack [ [ 0, [ ] ], [ [ 1, [ ] ], [ ] ] ] = [ 0, [ ] ]	if [ 0, [ ] ] is less than (minimum value of stack [ [ 1, [ ] ], [ ] ]), then minimum value of stack [ [ 0, [ ] ], [ [ 1, [ ] ], [ ] ] ] = [ 0, [ ] ] (Minimum Value)

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