Prove that n + 3 = succ (succ(succ(n)) for any n e N (succ(sucec(succ(n))) Prove that...

   

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Prove that n + 3 = succ (succ(succ(n)) for any n e N (succ(sucec(succ(n))) Prove that n + 4 = succ CC for any n E N .CC Addition is a mapping N x N → N defined by a recurrence (recursive, iterative) definition: (Eq1) (Vn E N) [n + 0 = n ] (Eq2) (Vn, m e N) [ n + succ(m) = succ(n + m) ] Example: (Theorem) Prove that n+1 = succ(n) Proof: n +1 = n + succ(0) = succ(n + 0) by definition of 1 using (Eq2) using (Eq1) = succ(n) Prove that n + 3 = succ (succ(succ(n)) for any n e N (succ(sucec(succ(n))) Prove that n + 4 = succ CC for any n E N .CC Addition is a mapping N x N → N defined by a recurrence (recursive, iterative) definition: (Eq1) (Vn E N) [n + 0 = n ] (Eq2) (Vn, m e N) [ n + succ(m) = succ(n + m) ] Example: (Theorem) Prove that n+1 = succ(n) Proof: n +1 = n + succ(0) = succ(n + 0) by definition of 1 using (Eq2) using (Eq1) = succ(n)