We show that
1+...+n
equals
n(n+1)/2
.
We want to prove
( N : Nat) sum(N) + sum(N) = N * s N
We use induction on
N
to prove this goal. For this, we use the induction scheme based on signature
{0,s}
for
Nat.
Induction requires that we do the following:
Base case: prove assertion for
N = 0
.
Show
sum(0) + sum(0) == 0 * s 0
by reduction.
Induction case: prove assertion for
N = s N0
assume it for
N = N0
.
This page was generated by Kumo on Fri Jul 02 14:09:10 PDT 1999.