ND Rule [] [ Γ > Δ > [x@@lev] |- [y]@lev ] ->
ND Rule [ Γ > Δ > ant |- [x]@lev ] [ Γ > Δ > ant |- [y]@lev ].
intros.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanR ].
eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
eapply nd_comp; [ apply nd_rlecnac | idtac ].
apply nd_prod.
apply X.
eapply nd_rule.
eapply RArrange.
- apply RuCanR.
+ apply AuCanR.
Defined.
Definition precompose Γ Δ ec : forall a x y z lev,
eapply nd_comp; [ apply nd_rlecnac | idtac ].
apply nd_prod.
apply nd_id.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
apply ga_comp.
Defined.
[ Γ > Δ > a,,b |- [@ga_mk _ ec y z ]@lev ]
[ Γ > Δ > a,,([@ga_mk _ ec x y @@ lev],,b) |- [@ga_mk _ ec x z ]@lev ].
intros.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RLeft; eapply RExch ].
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCossa ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ALeft; eapply AExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuAssoc ].
apply precompose.
Defined.
ND Rule [] [ Γ > Δ > [] |- [@ga_mk _ ec x y ]@lev ] ->
ND Rule [] [ Γ > Δ > [@ga_mk _ ec y z @@ lev] |- [@ga_mk _ ec x z ]@lev ].
intros.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanL ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanL ].
eapply nd_comp; [ idtac | eapply postcompose_ ].
apply X.
Defined.
ND Rule [ Γ > Δ > Σ |- [@ga_mk Γ ec a b ]@lev ]
[ Γ > Δ > Σ |- [@ga_mk Γ ec (a,,c) (b,,c) ]@lev ].
intros.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanR ].
eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
eapply nd_comp; [ apply nd_rlecnac | idtac ].
apply nd_prod.
apply nd_id.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RuCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuCanR ].
apply ga_first.
Defined.
[ Γ > Δ > Σ |- [@ga_mk Γ ec a b ]@lev ]
[ Γ > Δ > Σ |- [@ga_mk Γ ec (c,,a) (c,,b) ]@lev ].
intros.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanR ].
eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
eapply nd_comp; [ apply nd_rlecnac | idtac ].
apply nd_prod.
apply nd_id.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RuCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuCanR ].
apply ga_second.
Defined.
[Γ > Δ > Σ |- [@ga_mk Γ ec (a,,x) b ]@l ]
[Γ > Δ > Σ,,[@ga_mk Γ ec [] a @@ l] |- [@ga_mk Γ ec x b ]@l ].
intros.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
apply nd_prod.
apply nd_prod.
apply postcompose.
apply ga_uncancell.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
apply precompose.
Defined.
(mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) B))
(mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) A)) ]@nil]
with
- | RId a => let case_RId := tt in ga_id _ _ _ _ _
- | RCanL a => let case_RCanL := tt in ga_uncancell _ _ _ _ _
- | RCanR a => let case_RCanR := tt in ga_uncancelr _ _ _ _ _
- | RuCanL a => let case_RuCanL := tt in ga_cancell _ _ _ _ _
- | RuCanR a => let case_RuCanR := tt in ga_cancelr _ _ _ _ _
- | RAssoc a b c => let case_RAssoc := tt in ga_assoc _ _ _ _ _ _ _
- | RCossa a b c => let case_RCossa := tt in ga_unassoc _ _ _ _ _ _ _
- | RExch a b => let case_RExch := tt in ga_swap _ _ _ _ _ _
- | RWeak a => let case_RWeak := tt in ga_drop _ _ _ _ _
- | RCont a => let case_RCont := tt in ga_copy _ _ _ _ _
- | RLeft a b c r' => let case_RLeft := tt in flatten _ _ r' ;; boost _ _ _ _ _ (ga_second _ _ _ _ _ _ _)
- | RRight a b c r' => let case_RRight := tt in flatten _ _ r' ;; boost _ _ _ _ _ (ga_first _ _ _ _ _ _ _)
- | RComp c b a r1 r2 => let case_RComp := tt in (fun r1' r2' => _) (flatten _ _ r1) (flatten _ _ r2)
+ | AId a => let case_AId := tt in ga_id _ _ _ _ _
+ | ACanL a => let case_ACanL := tt in ga_uncancell _ _ _ _ _
+ | ACanR a => let case_ACanR := tt in ga_uncancelr _ _ _ _ _
+ | AuCanL a => let case_AuCanL := tt in ga_cancell _ _ _ _ _
+ | AuCanR a => let case_AuCanR := tt in ga_cancelr _ _ _ _ _
+ | AAssoc a b c => let case_AAssoc := tt in ga_assoc _ _ _ _ _ _ _
+ | AuAssoc a b c => let case_AuAssoc := tt in ga_unassoc _ _ _ _ _ _ _
+ | AExch a b => let case_AExch := tt in ga_swap _ _ _ _ _ _
+ | AWeak a => let case_AWeak := tt in ga_drop _ _ _ _ _
+ | ACont a => let case_ACont := tt in ga_copy _ _ _ _ _
+ | ALeft a b c r' => let case_ALeft := tt in flatten _ _ r' ;; boost _ _ _ _ _ (ga_second _ _ _ _ _ _ _)
+ | ARight a b c r' => let case_ARight := tt in flatten _ _ r' ;; boost _ _ _ _ _ (ga_first _ _ _ _ _ _ _)
+ | AComp c b a r1 r2 => let case_AComp := tt in (fun r1' r2' => _) (flatten _ _ r1) (flatten _ _ r2)
end); clear flatten; repeat take_simplify; repeat drop_simplify; intros.
- destruct case_RComp.
+ destruct case_AComp.
set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) a)) as a' in *.
set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) b)) as b' in *.
set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) c)) as c' in *.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RCanL ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply ACanL ].
eapply nd_comp; [ idtac | eapply nd_rule; apply
(@RLet Γ Δ [] [] (@ga_mk _ (v2t ec) a' b') (@ga_mk _ (v2t ec) a' c')) ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
apply nd_prod.
apply r2'.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RuCanR ].
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RCanL ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AuCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply ACanL ].
eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
eapply nd_prod.
apply r1'.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
apply ga_comp.
Defined.
match r as R in Arrange A B return
Arrange (mapOptionTree (flatten_leveled_type ) (drop_lev _ A))
(mapOptionTree (flatten_leveled_type ) (drop_lev _ B)) with
- | RId a => let case_RId := tt in RId _
- | RCanL a => let case_RCanL := tt in RCanL _
- | RCanR a => let case_RCanR := tt in RCanR _
- | RuCanL a => let case_RuCanL := tt in RuCanL _
- | RuCanR a => let case_RuCanR := tt in RuCanR _
- | RAssoc a b c => let case_RAssoc := tt in RAssoc _ _ _
- | RCossa a b c => let case_RCossa := tt in RCossa _ _ _
- | RExch a b => let case_RExch := tt in RExch _ _
- | RWeak a => let case_RWeak := tt in RWeak _
- | RCont a => let case_RCont := tt in RCont _
- | RLeft a b c r' => let case_RLeft := tt in RLeft _ (flatten _ _ r')
- | RRight a b c r' => let case_RRight := tt in RRight _ (flatten _ _ r')
- | RComp a b c r1 r2 => let case_RComp := tt in RComp (flatten _ _ r1) (flatten _ _ r2)
+ | AId a => let case_AId := tt in AId _
+ | ACanL a => let case_ACanL := tt in ACanL _
+ | ACanR a => let case_ACanR := tt in ACanR _
+ | AuCanL a => let case_AuCanL := tt in AuCanL _
+ | AuCanR a => let case_AuCanR := tt in AuCanR _
+ | AAssoc a b c => let case_AAssoc := tt in AAssoc _ _ _
+ | AuAssoc a b c => let case_AuAssoc := tt in AuAssoc _ _ _
+ | AExch a b => let case_AExch := tt in AExch _ _
+ | AWeak a => let case_AWeak := tt in AWeak _
+ | ACont a => let case_ACont := tt in ACont _
+ | ALeft a b c r' => let case_ALeft := tt in ALeft _ (flatten _ _ r')
+ | ARight a b c r' => let case_ARight := tt in ARight _ (flatten _ _ r')
+ | AComp a b c r1 r2 => let case_AComp := tt in AComp (flatten _ _ r1) (flatten _ _ r2)
end) ant1 ant2 r); clear flatten; repeat take_simplify; repeat drop_simplify; intros.
Defined.
apply nd_rule.
apply RArrange.
induction r; simpl.
- apply RId.
- apply RCanL.
- apply RCanR.
- apply RuCanL.
- apply RuCanR.
- apply RAssoc.
- apply RCossa.
- apply RExch. (* TO DO: check for all-leaf trees here *)
- apply RWeak.
- apply RCont.
- apply RLeft; auto.
- apply RRight; auto.
- eapply RComp; [ apply IHr1 | apply IHr2 ].
+ apply AId.
+ apply ACanL.
+ apply ACanR.
+ apply AuCanL.
+ apply AuCanR.
+ apply AAssoc.
+ apply AuAssoc.
+ apply AExch. (* TO DO: check for all-leaf trees here *)
+ apply AWeak.
+ apply ACont.
+ apply ALeft; auto.
+ apply ARight; auto.
+ eapply AComp; [ apply IHr1 | apply IHr2 ].
apply flatten_arrangement.
apply r.
eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
apply nd_prod.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanL ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanL ].
eapply nd_comp; [ idtac | eapply postcompose_ ].
apply ga_uncancelr.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
eapply nd_comp; [ idtac | eapply precompose ].
apply pfb.
Defined.
apply y.
idtac.
clear y q.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
simpl.
eapply nd_comp; [ apply nd_llecnac | idtac ].
eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
destruct s.
simpl.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AExch ].
set (fun z z' => @RLet Γ Δ z (mapOptionTree flatten_leveled_type q') t z' nil) as q''.
eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
clear q''.
apply nd_prod.
apply nd_rule.
apply RArrange.
- eapply RComp; [ idtac | apply RCanR ].
- apply RLeft.
+ eapply AComp; [ idtac | apply ACanR ].
+ apply ALeft.
apply (@arrangeCancelEmptyTree _ _ _ _ e).
eapply nd_comp.
eapply (@RVar Γ Δ t nil).
apply nd_rule.
apply RArrange.
- eapply RComp.
- apply RuCanR.
- apply RLeft.
- apply RWeak.
+ eapply AComp.
+ apply AuCanR.
+ apply ALeft.
+ apply AWeak.
(*
eapply decide_tree_empty.
simpl.
apply nd_rule.
apply RArrange.
- apply RLeft.
- apply RWeak.
+ apply ALeft.
+ apply AWeak.
simpl.
apply nd_rule.
unfold take_lev.
simpl.
apply RArrange.
- apply RLeft.
- apply RWeak.
+ apply ALeft.
+ apply AWeak.
apply (Prelude_error "escapifying code with multi-leaf antecedents is not supported").
*)
Defined.
simpl.
drop_simplify.
simpl.
- apply RId.
+ apply AId.
simpl.
- apply RId.
- eapply RComp; [ idtac | apply RCanL ].
- eapply RComp; [ idtac | eapply RLeft; apply IHt2 ].
+ apply AId.
+ eapply AComp; [ idtac | apply ACanL ].
+ eapply AComp; [ idtac | eapply ALeft; apply IHt2 ].
Opaque drop_lev.
simpl.
Transparent drop_lev.
idtac.
drop_simplify.
- apply RRight.
+ apply ARight.
apply IHt1.
Defined.
simpl.
drop_simplify.
simpl.
- apply RId.
+ apply AId.
simpl.
- apply RId.
- eapply RComp; [ apply RuCanL | idtac ].
- eapply RComp; [ eapply RRight; apply IHt1 | idtac ].
+ apply AId.
+ eapply AComp; [ apply AuCanL | idtac ].
+ eapply AComp; [ eapply ARight; apply IHt1 | idtac ].
Opaque drop_lev.
simpl.
Transparent drop_lev.
idtac.
drop_simplify.
- apply RLeft.
+ apply ALeft.
apply IHt2.
Defined.
admit.
Qed.
- Definition flatten_proof :
+ Lemma drop_to_nothing : forall (Γ:TypeEnv) Σ (lev:HaskLevel Γ),
+ drop_lev lev (Σ @@@ lev) = mapTree (fun _ => None) (mapTree (fun _ => tt) Σ).
+ intros.
+ induction Σ.
+ destruct a; simpl.
+ drop_simplify.
+ auto.
+ drop_simplify.
+ auto.
+ simpl.
+ rewrite <- IHΣ1.
+ rewrite <- IHΣ2.
+ reflexivity.
+ Qed.
+
+ Definition flatten_skolemized_proof :
forall {h}{c},
ND SRule h c ->
ND Rule (mapOptionTree (flatten_judgment ) h) (mapOptionTree (flatten_judgment ) c).
| RAbsCo Γ Δ Σ κ σ σ₁ σ₂ lev => let case_RAbsCo := tt in _
| RApp Γ Δ Σ₁ Σ₂ tx te lev => let case_RApp := tt in _
| RLet Γ Δ Σ₁ Σ₂ σ₁ σ₂ lev => let case_RLet := tt in _
+ | RCut Γ Δ Σ Σ₁ Σ₁₂ Σ₂ Σ₃ l => let case_RCut := tt in _
+ | RLeft Γ Δ Σ₁ Σ₂ Σ l => let case_RLeft := tt in _
+ | RRight Γ Δ Σ₁ Σ₂ Σ l => let case_RRight := tt in _
| RWhere Γ Δ Σ₁ Σ₂ Σ₃ σ₁ σ₂ lev => let case_RWhere := tt in _
- | RJoin Γ p lri m x q l => let case_RJoin := tt in _
| RVoid _ _ l => let case_RVoid := tt in _
| RBrak Γ Δ t ec succ lev => let case_RBrak := tt in _
| REsc Γ Δ t ec succ lev => let case_REsc := tt in _
eapply nd_rule.
eapply RArrange.
simpl.
- apply RCanR.
+ apply ACanR.
apply boost.
simpl.
apply ga_curry.
apply flatten_coercion; auto.
apply (Prelude_error "RCast at level >0; casting inside of code brackets is currently not supported").
- destruct case_RJoin.
- simpl.
- destruct l;
- [ apply nd_rule; apply RJoin | idtac ];
- apply (Prelude_error "RJoin at depth >0").
-
destruct case_RApp.
simpl.
eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
apply nd_prod.
apply nd_id.
- eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply RCanL | idtac ].
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch (* okay *)].
+ eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply ACanL | idtac ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch (* okay *)].
apply precompose.
destruct case_RWhere.
eapply nd_comp; [ idtac | eapply precompose' ].
apply nd_rule.
apply RArrange.
- apply RLeft.
- apply RCanL.
+ apply ALeft.
+ apply ACanL.
+
+ destruct case_RCut.
+ simpl.
+ destruct l as [|ec lev]; simpl.
+ apply nd_rule.
+ replace (mapOptionTree flatten_leveled_type (Σ₁₂ @@@ nil)) with (mapOptionTree flatten_type Σ₁₂ @@@ nil).
+ apply RCut.
+ induction Σ₁₂; try destruct a; auto.
+ simpl.
+ rewrite <- IHΣ₁₂1.
+ rewrite <- IHΣ₁₂2.
+ reflexivity.
+ simpl; repeat drop_simplify.
+ simpl; repeat take_simplify.
+ simpl.
+ set (drop_lev (ec :: lev) (Σ₁₂ @@@ (ec :: lev))) as x1.
+ rewrite take_lemma'.
+ rewrite mapOptionTree_compose.
+ rewrite mapOptionTree_compose.
+ rewrite mapOptionTree_compose.
+ rewrite mapOptionTree_compose.
+ rewrite unlev_relev.
+ rewrite <- mapOptionTree_compose.
+ rewrite <- mapOptionTree_compose.
+ rewrite <- mapOptionTree_compose.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ].
+ apply nd_prod.
+ apply nd_id.
+ eapply nd_comp.
+ eapply nd_rule.
+ eapply RArrange.
+ eapply ALeft.
+ eapply ARight.
+ unfold x1.
+ rewrite drop_to_nothing.
+ apply arrangeCancelEmptyTree with (q:=(mapTree (fun _ : ??(HaskType Γ ★) => tt) Σ₁₂)).
+ admit. (* OK *)
+ eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply ALeft; eapply ACanL | idtac ].
+ set (mapOptionTree flatten_type Σ₁₂) as a.
+ set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₁)) as b.
+ set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₂)) as c.
+ set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₂)) as d.
+ set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ)) as e.
+ set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ)) as f.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ].
+ eapply nd_comp; [ apply nd_llecnac | idtac ].
+ apply nd_prod.
+ simpl.
+ eapply secondify.
+ apply ga_first.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ALeft; eapply AExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuAssoc ].
+ simpl.
+ apply precompose.
+
+ destruct case_RLeft.
+ simpl.
+ destruct l as [|ec lev].
+ simpl.
+ replace (mapOptionTree flatten_leveled_type (Σ @@@ nil)) with (mapOptionTree flatten_type Σ @@@ nil).
+ apply nd_rule.
+ apply RLeft.
+ induction Σ; try destruct a; auto.
+ simpl.
+ rewrite <- IHΣ1.
+ rewrite <- IHΣ2.
+ reflexivity.
+ repeat drop_simplify.
+ rewrite drop_to_nothing.
+ simpl.
+ eapply nd_comp.
+ Focus 2.
+ eapply nd_rule.
+ eapply RArrange.
+ eapply ARight.
+ apply arrangeUnCancelEmptyTree with (q:=(mapTree (fun _ : ??(HaskType Γ ★) => tt) Σ)).
+ admit (* FIXME *).
+ idtac.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuCanL ].
+ apply boost.
+ take_simplify.
+ simpl.
+ replace (take_lev (ec :: lev) (Σ @@@ (ec :: lev))) with (Σ @@@ (ec::lev)).
+ rewrite mapOptionTree_compose.
+ rewrite mapOptionTree_compose.
+ rewrite unlev_relev.
+ apply ga_second.
+ rewrite take_lemma'.
+ reflexivity.
+
+ destruct case_RRight.
+ simpl.
+ destruct l as [|ec lev].
+ simpl.
+ replace (mapOptionTree flatten_leveled_type (Σ @@@ nil)) with (mapOptionTree flatten_type Σ @@@ nil).
+ apply nd_rule.
+ apply RRight.
+ induction Σ; try destruct a; auto.
+ simpl.
+ rewrite <- IHΣ1.
+ rewrite <- IHΣ2.
+ reflexivity.
+ repeat drop_simplify.
+ rewrite drop_to_nothing.
+ simpl.
+ eapply nd_comp.
+ Focus 2.
+ eapply nd_rule.
+ eapply RArrange.
+ eapply ALeft.
+ apply arrangeUnCancelEmptyTree with (q:=(mapTree (fun _ : ??(HaskType Γ ★) => tt) Σ)).
+ admit (* FIXME *).
+ idtac.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuCanR ].
+ apply boost.
+ take_simplify.
+ simpl.
+ replace (take_lev (ec :: lev) (Σ @@@ (ec :: lev))) with (Σ @@@ (ec::lev)).
+ rewrite mapOptionTree_compose.
+ rewrite mapOptionTree_compose.
+ rewrite unlev_relev.
+ apply ga_first.
+ rewrite take_lemma'.
+ reflexivity.
destruct case_RVoid.
simpl.
set (mapOptionTree (flatten_type ○ unlev)(take_lev (ec :: nil) succ)) as succ_guest.
set (mapOptionTree flatten_type (take_arg_types_as_tree t)) as succ_args.
unfold empty_tree.
- eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply RLeft; apply tree_of_nothing | idtac ].
- eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply RCanR | idtac ].
+ eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply ALeft; apply tree_of_nothing | idtac ].
+ eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply ACanR | idtac ].
refine (ga_unkappa Γ Δ (v2t ec) nil _ _ _ _ ;; _).
eapply nd_comp; [ idtac | eapply arrange_brak ].
unfold succ_host.
unfold succ_guest.
eapply nd_rule.
eapply RArrange.
- apply RExch.
+ apply AExch.
apply (Prelude_error "found Brak at depth >0 indicating 3-level code; only two-level code is currently supported").
destruct case_SEsc.
take_simplify.
drop_simplify.
simpl.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RLeft; apply tree_of_nothing' ].
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ALeft; apply tree_of_nothing' ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanR ].
simpl.
rewrite take_lemma'.
rewrite unlev_relev.
set (mapOptionTree flatten_leveled_type (drop_lev (ec :: nil) succ)) as succ_host.
set (mapOptionTree flatten_type (take_arg_types_as_tree t)) as succ_args.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RuCanR ].
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RuCanR ].
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RCanL ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AuCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AuCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply ACanL ].
eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
apply nd_prod; [ idtac | eapply boost ].
induction x.
apply ga_id.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanL ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanL ].
simpl.
apply ga_join.
apply IHx1.
apply (Prelude_error "found Esc at depth >0 indicating 3-level code; only two-level code is currently supported").
Defined.
+ Definition flatten_proof :
+ forall {h}{c},
+ ND Rule h c ->
+ ND Rule h c.
+ apply (Prelude_error "sorry, non-skolemized flattening isn't implemented").
+ Defined.
+
Definition skolemize_and_flatten_proof :
forall {h}{c},
ND Rule h c ->
intros.
rewrite mapOptionTree_compose.
rewrite mapOptionTree_compose.
- apply flatten_proof.
+ apply flatten_skolemized_proof.
apply skolemize_proof.
apply X.
Defined.
projects / coq-hetmet.git / blobdiff