DEFINITION csubc_arity_conf()
TYPE =
∀g:G.∀c1:C.∀c2:C.(csubc g c1 c2)→∀t:T.∀a:A.(arity g c1 t a)→(arity g c2 t a)
BODY =
assume g: G
assume c1: C
assume c2: C
suppose H: csubc g c1 c2
assume t: T
assume a: A
suppose H0: arity g c1 t a
by (csubc_csuba . . . H)
we proved csuba g c1 c2
by (csuba_arity . . . . H0 . previous)
we proved arity g c2 t a
we proved ∀g:G.∀c1:C.∀c2:C.(csubc g c1 c2)→∀t:T.∀a:A.(arity g c1 t a)→(arity g c2 t a)