Proof: Sort Two

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ] = result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ]	result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ] = result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] (Sort List Property)
2	minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 0, [ ] ]	minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 0, [ ] ] (minimum_example_2)
3	[ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = [ [ 0, [ ] ], [ ] ]	if minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 0, [ ] ], then [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = [ [ 0, [ ] ], [ ] ] (Substitution)
4	index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ]	index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ] (minimum_index_example)
5	remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) = remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index [ 1, [ ] ]	if index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ], then remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) = remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index [ 1, [ ] ] (Substitution)
6	remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index [ 1, [ ] ] = [ [ 1, [ ] ], [ ] ]	remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index [ 1, [ ] ] = [ [ 1, [ ] ], [ ] ] (pop_index_example_3_extend)
7	remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) = [ [ 1, [ ] ], [ ] ]	if remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) = remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index [ 1, [ ] ] and remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index [ 1, [ ] ] = [ [ 1, [ ] ], [ ] ], then remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) = [ [ 1, [ ] ], [ ] ] (Transitive Property of Equality)
8	result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ]	if remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) = [ [ 1, [ ] ], [ ] ], then result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] (Substitution)
9	result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ]	if [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = [ [ 0, [ ] ], [ ] ], then result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ] (Substitution)
10	result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ]	if result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] and result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ], then result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ] (Transitive Property of Equality)
11	result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ] = result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ]	result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ] = result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] (Sort List Property)
12	index of the mininum value in stack [ [ 1, [ ] ], [ ] ] = [ 0, [ ] ]	index of the mininum value in stack [ [ 1, [ ] ], [ ] ] = [ 0, [ ] ] (minimum_index_one)
13	remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ]) = remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index [ 0, [ ] ]	if index of the mininum value in stack [ [ 1, [ ] ], [ ] ] = [ 0, [ ] ], then remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ]) = remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index [ 0, [ ] ] (Substitution)
14	remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index [ 0, [ ] ] = [ ]	remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index [ 0, [ ] ] = [ ] (pop_index_base_2)
15	remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ]) = [ ]	if remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ]) = remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index [ 0, [ ] ] and remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index [ 0, [ ] ] = [ ], then remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ]) = [ ] (Transitive Property of Equality)
16	result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ]	if remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ]) = [ ], then result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] (Substitution)
17	minimum value of stack [ [ 1, [ ] ], [ ] ] = [ 1, [ ] ]	minimum value of stack [ [ 1, [ ] ], [ ] ] = [ 1, [ ] ] (Minimum Of A Single Element List)
18	[ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	if minimum value of stack [ [ 1, [ ] ], [ ] ] = [ 1, [ ] ], then [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Substitution)
19	result of sorting [ ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	if [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], then result of sorting [ ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Substitution)
20	result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	if result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] and result of sorting [ ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], then result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Transitive Property of Equality)
21	result of sorting [ ] with sorted stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	result of sorting [ ] with sorted stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Sorted List Property)
22	result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	if result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] and result of sorting [ ] with sorted stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], then result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Transitive Property of Equality)
23	result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	if result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ] = result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] and result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], then result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Transitive Property of Equality)
24	result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	if result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ] and result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], then result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Transitive Property of Equality)
25	result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	if result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ] = result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] and result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], then result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Transitive Property of Equality)
26	result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = reverse of (result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ])	result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = reverse of (result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ]) (Sort Begin Property)
27	reverse of (result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ]) = reverse of [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]	if result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], then reverse of (result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ]) = reverse of [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] (Substitution)
28	reverse of [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 0, [ ] ], [ [ 1, [ ] ], [ ] ] ]	reverse of [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 0, [ ] ], [ [ 1, [ ] ], [ ] ] ] (reverse_two)
29	reverse of (result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ]) = [ [ 0, [ ] ], [ [ 1, [ ] ], [ ] ] ]	if reverse of (result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ]) = reverse of [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] and reverse of [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 0, [ ] ], [ [ 1, [ ] ], [ ] ] ], then reverse of (result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ]) = [ [ 0, [ ] ], [ [ 1, [ ] ], [ ] ] ] (Transitive Property of Equality)
30	result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 0, [ ] ], [ [ 1, [ ] ], [ ] ] ]	if result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = reverse of (result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ]) and reverse of (result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ]) = [ [ 0, [ ] ], [ [ 1, [ ] ], [ ] ] ], then result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 0, [ ] ], [ [ 1, [ ] ], [ ] ] ] (Transitive Property of Equality)

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