* Initial invocation: - Patience on me to gain peace and perfection! -
*)
-include "ground_2/star.ma".
-include "basic_2/notation.ma".
+include "ground_2/lib/star.ma".
+include "basic_2/notation/constructors/item0_0.ma".
+include "basic_2/notation/constructors/snitem2_2.ma".
(* ATOMIC ARITY *************************************************************)
| APair: aarity → aarity → aarity (* binary aarity construction *)
.
-interpretation "aarity construction (atomic)"
+interpretation "atomic arity construction (atomic)"
'Item0 = AAtom.
-interpretation "aarity construction (binary)"
+interpretation "atomic arity construction (binary)"
'SnItem2 A1 A2 = (APair A1 A2).
(* Basic inversion lemmas ***************************************************)
#A #B elim B -B
[ #H destruct
| #Y #X #IHY #_ #H destruct
- -H >e0 in e1; normalize (**) (* destruct: one quality is not simplified, the destucted equality is not erased *)
+ -H >e0 in e1; normalize (**) (* destruct: one quality is not simplified, the destructed equality is not erased *)
/2 width=1/
]
qed-.
#B #A elim A -A
[ #H destruct
| #Y #X #_ #IHX #H destruct
- -H (**) (* destruct: the destucted equality is not erased *)
+ -H (**) (* destruct: the destructed equality is not erased *)
/2 width=1/
]
qed-.
(* Basic properties *********************************************************)
-lemma aarity_eq_dec: ∀A1,A2:aarity. Decidable (A1 = A2).
+lemma eq_aarity_dec: ∀A1,A2:aarity. Decidable (A1 = A2).
#A1 elim A1 -A1
[ #A2 elim A2 -A2 /2 width=1/
#B2 #A2 #_ #_ @or_intror #H destruct