Proof: Reverse List Example 5

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] and already reversed stack [ ]	reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] and already reversed stack [ ] (Reversing a List Property 1)
2	reverse of remaining stack [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] and already reversed stack [ ] = reverse of remaining stack [ 2, [ 3, [ 4, [ ] ] ] ] and already reversed stack [ 1, [ ] ]	reverse of remaining stack [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] and already reversed stack [ ] = reverse of remaining stack [ 2, [ 3, [ 4, [ ] ] ] ] and already reversed stack [ 1, [ ] ] (Reversing a List Property 3)
3	reverse of remaining stack [ 2, [ 3, [ 4, [ ] ] ] ] and already reversed stack [ 1, [ ] ] = reverse of remaining stack [ 3, [ 4, [ ] ] ] and already reversed stack [ 2, [ 1, [ ] ] ]	reverse of remaining stack [ 2, [ 3, [ 4, [ ] ] ] ] and already reversed stack [ 1, [ ] ] = reverse of remaining stack [ 3, [ 4, [ ] ] ] and already reversed stack [ 2, [ 1, [ ] ] ] (Reversing a List Property 3)
4	reverse of remaining stack [ 3, [ 4, [ ] ] ] and already reversed stack [ 2, [ 1, [ ] ] ] = reverse of remaining stack [ 4, [ ] ] and already reversed stack [ 3, [ 2, [ 1, [ ] ] ] ]	reverse of remaining stack [ 3, [ 4, [ ] ] ] and already reversed stack [ 2, [ 1, [ ] ] ] = reverse of remaining stack [ 4, [ ] ] and already reversed stack [ 3, [ 2, [ 1, [ ] ] ] ] (Reversing a List Property 3)
5	reverse of remaining stack [ 4, [ ] ] and already reversed stack [ 3, [ 2, [ 1, [ ] ] ] ] = [ 4, [ 3, [ 2, [ 1, [ ] ] ] ] ]	reverse of remaining stack [ 4, [ ] ] and already reversed stack [ 3, [ 2, [ 1, [ ] ] ] ] = [ 4, [ 3, [ 2, [ 1, [ ] ] ] ] ] (Reversing a List Property 4)
6	reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 2, [ 3, [ 4, [ ] ] ] ] and already reversed stack [ 1, [ ] ]	if reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] and already reversed stack [ ] and reverse of remaining stack [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] and already reversed stack [ ] = reverse of remaining stack [ 2, [ 3, [ 4, [ ] ] ] ] and already reversed stack [ 1, [ ] ], then reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 2, [ 3, [ 4, [ ] ] ] ] and already reversed stack [ 1, [ ] ] (Transitive Property of Equality)
7	reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 3, [ 4, [ ] ] ] and already reversed stack [ 2, [ 1, [ ] ] ]	if reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 2, [ 3, [ 4, [ ] ] ] ] and already reversed stack [ 1, [ ] ] and reverse of remaining stack [ 2, [ 3, [ 4, [ ] ] ] ] and already reversed stack [ 1, [ ] ] = reverse of remaining stack [ 3, [ 4, [ ] ] ] and already reversed stack [ 2, [ 1, [ ] ] ], then reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 3, [ 4, [ ] ] ] and already reversed stack [ 2, [ 1, [ ] ] ] (Transitive Property of Equality)
8	reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 4, [ ] ] and already reversed stack [ 3, [ 2, [ 1, [ ] ] ] ]	if reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 3, [ 4, [ ] ] ] and already reversed stack [ 2, [ 1, [ ] ] ] and reverse of remaining stack [ 3, [ 4, [ ] ] ] and already reversed stack [ 2, [ 1, [ ] ] ] = reverse of remaining stack [ 4, [ ] ] and already reversed stack [ 3, [ 2, [ 1, [ ] ] ] ], then reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 4, [ ] ] and already reversed stack [ 3, [ 2, [ 1, [ ] ] ] ] (Transitive Property of Equality)
9	reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = [ 4, [ 3, [ 2, [ 1, [ ] ] ] ] ]	if reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = reverse of remaining stack [ 4, [ ] ] and already reversed stack [ 3, [ 2, [ 1, [ ] ] ] ] and reverse of remaining stack [ 4, [ ] ] and already reversed stack [ 3, [ 2, [ 1, [ ] ] ] ] = [ 4, [ 3, [ 2, [ 1, [ ] ] ] ] ], then reverse of [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = [ 4, [ 3, [ 2, [ 1, [ ] ] ] ] ] (Transitive Property of Equality)

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