FDL - Step of Proof: wellfounded_functionality_wrt

Step of Proof: wellfounded_functionality_wrt_implies

Inference at * 1 2 1 1
Iof proof for Lemma wellfounded functionality wrt implies:

1. T1 : Type
2. T2 : Type
3. r1 : T1

4. r2 : T2

5. T1 = T2
6.

x, y:T1. r1(x,y)

r2(x,y)
7. P : T2

8. j : T1
9.

k:T1. r1(k,j)

P(k)
10. k : T2
11. r2(k,j)

P(k)

by ((((BackThruHyp 9)

CollapseTHEN (Thin 9))

)

CollapseTHEN ((Auto_aux (first_nat 1:n

C) ((first_nat 1:n),(first_nat 4:n)) (first_tok :t) inil_term)))

C1:

C1: 9. k : T2

C1: 10. r2(k,j)

C1:

r1(k,j)

Definitions t T, P Q, x:A. B(x)