Iof proof for Lemma nat ind a:
1. P :
{k}
2. P(0)
3.
i:
. P(i - 1) 
P(i)
4. i :
P(i)
by ((((((D 4)
CollapseTHENM (IntInd 4))
)
CollapseTHENM (D 0)))
CollapseTHENA (
C(Auto_aux (first_nat 1:n) ((first_nat 1:n),(first_nat 3:n)) (first_tok :t) inil_term)))
C1:
C1: 4. i : 
C1: 5. i < 0
C1: 6. ((i+1) 
0 ) P(i+1)
C1: 7. i 0
C1: P(i)
C2:
C2: 4. 0 0
C2: P(0)
C3:
C3: 4. i :
C3: 5. 0 < i
C3: 6. ((i - 1) 0 ) P(i - 1)
C3: 7. i 0
C3: P(i)
C.
T