DEFINITION not_void_abst()
TYPE =
not (eq B Void Abst)
BODY =
we must prove not (eq B Void Abst)
or equivalently (eq B Void Abst)→False
suppose H: eq B Void Abst
(H0)
we proceed by induction on H to prove <λ:B.Prop> CASE Abst OF Abbr⇒False | Abst⇒False | Void⇒True
case refl_equal : ⇒
the thesis becomes <λ:B.Prop> CASE Void OF Abbr⇒False | Abst⇒False | Void⇒True
consider I
we proved True
<λ:B.Prop> CASE Void OF Abbr⇒False | Abst⇒False | Void⇒True
<λ:B.Prop> CASE Abst OF Abbr⇒False | Abst⇒False | Void⇒True
end of H0
consider H0
we proved <λ:B.Prop> CASE Abst OF Abbr⇒False | Abst⇒False | Void⇒True
that is equivalent to False
we proceed by induction on the previous result to prove False
we proved False
we proved (eq B Void Abst)→False
that is equivalent to not (eq B Void Abst)