Compare Example Gt

Greater Than Example

Greater Than Substitution

Minimum Example 2

are Equal List Example

Find Number Example 2

Minimum Index Example

Pop Index Example 3

Reverse Example General

Pop Index Example 3 Extend

Minimum Index One

Reverse Empty List

Pop Index Base 2

Reverse List Two General

Reverse Two

Proof: Reverse Two

Let's prove the following theorem:

reverse of [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] = [ [ y, [ ] ], [ [ x, [ ] ], [ ] ] ]

Proof:

View as a tree | View dependent proofs | Try proving it

Proof Table

#	Claim	Reason
1	reverse of remaining stack [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] and already reversed stack [ ] = [ [ y, [ ] ], [ [ x, [ ] ], [ ] ] ]	reverse of remaining stack [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] and already reversed stack [ ] = [ [ y, [ ] ], [ [ x, [ ] ], [ ] ] ] (reverse_list_two_general)
2	reverse of [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] = reverse of remaining stack [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] and already reversed stack [ ]	reverse of [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] = reverse of remaining stack [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] and already reversed stack [ ] (Reversing a List Property 1)
3	reverse of [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] = [ [ y, [ ] ], [ [ x, [ ] ], [ ] ] ]	if reverse of [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] = reverse of remaining stack [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] and already reversed stack [ ] and reverse of remaining stack [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] and already reversed stack [ ] = [ [ y, [ ] ], [ [ x, [ ] ], [ ] ] ], then reverse of [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] = [ [ y, [ ] ], [ [ x, [ ] ], [ ] ] ] (Transitive Property of Equality)

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