- Definition partition {Γ}{ec:HaskEC Γ} Σ :
- Σ ≈ ((dropEC ec Σ),, (takeEC ec Σ +@@@+ ec)).
- admit.
- Defined.
+ refine ((fix factor a b (arr:Arrange a b) :=
+ match arr as R in Arrange A B return
+ { c : _ & (c,,A) ≈ B }
+ with
+ | AId a => let case_AId := tt in _
+ | ACanL a => let case_ACanL := tt in _
+ | ACanR a => let case_ACanR := tt in _
+ | AuCanL a => let case_AuCanL := tt in _
+ | AuCanR a => let case_AuCanR := tt in _
+ | AAssoc a b c => let case_AAssoc := tt in _
+ | AuAssoc a b c => let case_AuAssoc := tt in _
+ | AExch a b => let case_AExch := tt in _
+ | AWeak a => let case_AWeak := tt in _
+ | ACont a => let case_ACont := tt in _
+ | ALeft a b c r' => let case_ALeft := tt in (fun r'' => _) (factor _ _ r')
+ | ARight a b c r' => let case_ARight := tt in (fun r'' => _) (factor _ _ r')
+ | AComp a b c r1 r2 => let case_AComp := tt in (fun r1' r2' => _) (factor _ _ r1) (factor _ _ r2)
+ end)); clear factor; intros.
+
+ destruct case_AId.
+ exists []. apply PCanL.
+
+ destruct case_ACanL.
+ exists [].
+ eapply PComp.
+ apply PCanL.
+ apply PCanL.
+
+ destruct case_ACanR.
+ exists [].
+ eapply PComp.
+ apply PCanL.
+ apply PCanR.
+
+ destruct case_AuCanL.
+ exists [].
+ apply PRight.
+ apply PId.
+
+ destruct case_AuCanR.
+ exists [].
+ apply PExch.
+
+ destruct case_AAssoc.
+ exists [].
+ eapply PComp.
+ eapply PCanL.
+ apply PAssoc.
+
+ destruct case_AuAssoc.
+ exists [].
+ eapply PComp.
+ eapply PCanL.
+ apply PuAssoc.
+
+ destruct case_AExch.
+ exists [].
+ eapply PComp.
+ eapply PCanL.
+ apply PExch.
+
+ destruct case_AWeak.
+ exists a0.
+ eapply PCanR.
+
+ destruct case_ACont.
+ exists [].
+ eapply PComp.
+ eapply PCanL.
+ eapply PComp.
+ eapply PLeft.
+ eapply
+
+ Defined.