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AdmissibilityPreservation.v を追加 #68

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c0fcd89
Add AdmissibilityPreservation.v.
cedretaber Oct 14, 2025
99d7df5
AdmissibleDirs_sublist_rule を仮定して AdmissibleDirsStep_preserve を証明.
cedretaber Oct 14, 2025
19c8958
改行を合わせた.
cedretaber Oct 14, 2025
67aee5f
不要なコメントを削除.
cedretaber Oct 14, 2025
6fb84b6
rocq と equations のバージョンを固定.
cedretaber Oct 29, 2025
cb04bf4
全部バージョンを指定した.
cedretaber Oct 29, 2025
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1 change: 1 addition & 0 deletions _CoqProject
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Expand Up @@ -3,6 +3,7 @@ theories/Dec.v
theories/Eq.v
theories/ListExt.v
theories/PrimitiveSegment.v
theories/AdmissibilityPreservation.v
theories/Main.v
theories/Example2.v
theories/Example3.v
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7 changes: 5 additions & 2 deletions coq-scurve.opam
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Expand Up @@ -8,8 +8,11 @@ dev-repo: "git+https://github.com/proof-ninja/coq-scurve"


depends: [
"rocq-prover"
"rocq-equations"
"rocq-prover" {>= "9.0.0" & < "9.1~"}
"rocq-core" {>= "9.0.0" & < "9.1~"}
"rocq-runtime" {>= "9.0.0" & < "9.1~"}
"coq-core" {>= "9.0.0" & < "9.1~"}
"rocq-equations" {>= "1.3" & < "1.4~"}
]

authors: [
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28 changes: 28 additions & 0 deletions theories/AdmissibilityPreservation.v
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@@ -0,0 +1,28 @@
Require Import Admissible.
Require Import Reduction.

(* 補題: Ruleを部分リストに適用しても許容性が保たれる *)
Axiom AdmissibleDirs_sublist_rule: forall l ds ds' r,
Rule ds ds' -> AdmissibleDirs (l ++ ds ++ r) -> AdmissibleDirs (l ++ ds' ++ r).

Lemma AdmissibleDirsStep_preserve ds ds' : AdmissibleDirs ds -> ReduceDirStep ds ds' -> AdmissibleDirs ds'.
Proof.
intros AD RDS.
(* ReduceDirStep の定義から、l, r, es, es' と Rule es es' が存在する *)
inversion RDS as [l r es es' HRule Hds Hds'].
(* ds = l ++ es ++ r, ds' = l ++ es' ++ r である *)
subst ds ds'.
eapply AdmissibleDirs_sublist_rule; eauto.
Qed.

Lemma AdmissibleDirs_preserve ds ds': AdmissibleDirs ds -> ReduceDir ds ds' -> AdmissibleDirs ds'.
Proof.
intros AD RD.
induction RD as [ds | ds ds' ds'' RDS RD IHRD].
- (* RDRefl: ds = ds なので自明 *)
exact AD.
- (* RDTrans: ds -> ds' -> ds'' の場合 *)
apply AdmissibleDirsStep_preserve with (ds := ds) in RDS; [|exact AD].
apply IHRD.
exact RDS.
Qed.
3 changes: 0 additions & 3 deletions theories/Admissible.v
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Expand Up @@ -68,9 +68,6 @@ Qed.

Definition reduced ds dsr:= ReduceDir ds dsr /\ ~ CanReduceDirStep dsr.

Lemma AdmissibleDirs_preserve ds ds': AdmissibleDirs ds -> ReduceDir ds ds' -> AdmissibleDirs ds'.
Admitted.

Axiom inadmissible_rotation_dif_four: forall ds, Z.abs(rotation_difference ds) >= 4 -> ~ AdmissibleDirs ds.

Lemma repeat_dif_P n: rotation_difference (repeat Plus n) = Z.of_nat n.
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