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The Final Simplification in the Base Case (Step 0)

The Final Simplification in the Base Case (Step 0)

Subgoal *1/1' 
(IMPLIES (NOT (CONSP A)) 
         (EQUAL (APP (APP A B) C) 
                (APP A (APP B C)))). 

Click on the link above to replace (APP A B) by its definition. Note that the hypothesis (NOT (CONSP A)) allows us to simplify the IF in APP to its false branch this time.