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use apply tactic in ReificationFromGeneralizedArrow; not sure why this is required
[coq-hetmet.git]
/
src
/
NaturalDeduction.v
diff --git
a/src/NaturalDeduction.v
b/src/NaturalDeduction.v
index
407948b
..
5cf67db
100644
(file)
--- a/
src/NaturalDeduction.v
+++ b/
src/NaturalDeduction.v
@@
-182,6
+182,13
@@
Section Natural_Deduction.
| T_Branch a b => nd_prod (nd_id a) (nd_id b)
end.
| T_Branch a b => nd_prod (nd_id a) (nd_id b)
end.
+ Fixpoint nd_weak' (sl:Tree ??Judgment) : sl /⋯⋯/ [] :=
+ match sl as SL return SL /⋯⋯/ [] with
+ | T_Leaf None => nd_id0
+ | T_Leaf (Some x) => nd_weak x
+ | T_Branch a b => nd_prod (nd_weak' a) (nd_weak' b) ;; nd_cancelr
+ end.
+
Hint Constructors Structural.
Lemma nd_id_structural : forall sl, Structural (nd_id sl).
intros.
Hint Constructors Structural.
Lemma nd_id_structural : forall sl, Structural (nd_id sl).
intros.
@@
-189,6
+196,16
@@
Section Natural_Deduction.
destruct a; auto.
Defined.
destruct a; auto.
Defined.
+ Lemma weak'_structural : forall a, Structural (nd_weak' a).
+ intros.
+ induction a.
+ destruct a; auto.
+ simpl.
+ auto.
+ simpl.
+ auto.
+ Qed.
+
(* An equivalence relation on proofs which is sensitive only to the logical content of the proof -- insensitive to
* structural variations *)
Class ND_Relation :=
(* An equivalence relation on proofs which is sensitive only to the logical content of the proof -- insensitive to
* structural variations *)
Class ND_Relation :=
@@
-212,6
+229,9
@@
Section Natural_Deduction.
(* any two _structural_ proofs with the same hypotheses/conclusions must be considered equal *)
; ndr_structural_indistinguishable : forall `(f:a/⋯⋯/b)(g:a/⋯⋯/b), Structural f -> Structural g -> f===g
(* any two _structural_ proofs with the same hypotheses/conclusions must be considered equal *)
; ndr_structural_indistinguishable : forall `(f:a/⋯⋯/b)(g:a/⋯⋯/b), Structural f -> Structural g -> f===g
+
+ (* any two proofs of nothing are "equally good" *)
+ ; ndr_void_proofs_irrelevant : forall `(f:a/⋯⋯/[])(g:a/⋯⋯/[]), f === g
}.
(*
}.
(*