FDL - Step of Proof: exists_functionality_wrt

Step of Proof: exists_functionality_wrt_implies

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

1. S : Type
2. T : Type
3. P : S

4. Q : S

5. S = T
6.

x:S. P(x)

Q(x)
7.

x:S. P(x)

y:T. Q(y)

by ((((((D 7)

CollapseTHEN (With x (D 0)))

)

CollapseTHENM (HypBackchain))

)

CollapseTHEN (

C(Auto_aux (first_nat 1:n) ((first_nat 1:n),(first_nat 3:n)) (first_tok :t) inil_term)))

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