Need to change the ifproj rules
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1 changed files with 253 additions and 182 deletions
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@ -376,36 +376,34 @@ Module RPar.
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Inductive R {n} : Tm n -> Tm n -> Prop :=
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(***************** Beta ***********************)
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| AppAbs a0 a1 b0 b1 :
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R a0 a1 ->
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R b0 b1 ->
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R (App (Abs a0) b0) (subst_Tm (scons b1 VarTm) a1)
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| AppPair a0 a1 b0 b1 c0 c1:
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R a0 a1 ->
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R a0 (Abs a1) ->
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R b0 b1 ->
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R (App a0 b0) (subst_Tm (scons b1 VarTm) a1)
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| AppPair a a0 b0 c0 c1:
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R a (Pair a0 b0) ->
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R c0 c1 ->
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R (App (Pair a0 b0) c0) (Pair (App a1 c1) (App b1 c1))
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R (App a c0) (Pair (App a0 c1) (App b0 c1))
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| ProjAbs p a0 a1 :
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R a0 a1 ->
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R (Proj p (Abs a0)) (Abs (Proj p a1))
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| ProjPair p a0 a1 b0 b1 :
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R a0 a1 ->
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R b0 b1 ->
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R (Proj p (Pair a0 b0)) (if p is PL then a1 else b1)
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| IfAbs (a0 a1 : Tm (S n)) b0 b1 c0 c1 :
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R a0 a1 ->
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R a0 (Abs a1) ->
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R (Proj p a0) (Abs (Proj p a1))
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| ProjPair p a b c :
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R a (Pair b c) ->
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R (Proj p a) (if p is PL then b else c)
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| IfAbs a0 a1 b0 b1 c0 c1 :
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R a0 (Abs a1) ->
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R b0 b1 ->
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R c0 c1 ->
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R (If (Abs a0) b0 c0) (Abs (If a1 (ren_Tm shift b1) (ren_Tm shift c1)))
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| IfPair a0 a1 b0 b1 c0 c1 d0 d1 :
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R a0 a1 ->
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R b0 b1 ->
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R (If a0 b0 c0) (Abs (If a1 (ren_Tm shift b1) (ren_Tm shift c1)))
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| IfPair a a0 a1 c0 c1 d0 d1 :
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R a (Pair a0 a1) ->
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R c0 c1 ->
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R d0 d1 ->
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R (If (Pair a0 b0) c0 d0) (Pair (If a1 c1 d1) (If b1 c1 d1))
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| IfBool a b0 b1 c0 c1 :
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R (If a c0 d0) (Pair (If a0 c1 d1) (If a1 c1 d1))
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| IfBool a v b0 b1 c0 c1 :
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R a (BVal v) ->
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R b0 b1 ->
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R c0 c1 ->
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R (If (BVal a) b0 c0) (if a then b1 else c1)
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R (If a b0 c0) (if v then b1 else c1)
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(*************** Congruence ********************)
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@ -460,41 +458,42 @@ Module RPar.
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induction a; hauto lq:on ctrs:R.
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Qed.
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Lemma AppAbs' n a0 a1 (b0 b1 t : Tm n) :
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t = subst_Tm (scons b1 VarTm) a1 ->
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R a0 a1 ->
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Lemma AppAbs' n (a0 : Tm n) a1 b0 b1 u :
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u = (subst_Tm (scons b1 VarTm) a1) ->
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R a0 (Abs a1) ->
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R b0 b1 ->
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R (App (Abs a0) b0) t.
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R (App a0 b0) u.
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Proof. move => ->. apply AppAbs. Qed.
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Lemma ProjPair' n p (a0 a1 b0 b1 : Tm n) t :
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t = (if p is PL then a1 else b1) ->
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R a0 a1 ->
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R b0 b1 ->
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R (Proj p (Pair a0 b0)) t.
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Lemma ProjPair' n p a b c u :
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u = (if p is PL then b else c) ->
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R a (Pair b c : Tm n) ->
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R (Proj p a) u.
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Proof. move => > ->. apply ProjPair. Qed.
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Lemma IfBool' n a b0 b1 c0 c1 u :
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u = (if a then (b1 : Tm n) else c1) ->
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Lemma IfBool' n a v b0 b1 c0 c1 u :
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u = (if v then b1 else c1) ->
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R a (BVal v : Tm n) ->
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R b0 b1 ->
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R c0 c1 ->
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R (If (BVal a) b0 c0) u.
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R (If a b0 c0) u.
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Proof. move => ->. apply IfBool. Qed.
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Lemma IfAbs' n (a0 a1 : Tm (S n)) (b0 b1 c0 c1 : Tm n) u :
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Lemma IfAbs' n a0 (a1 : Tm (S n)) (b0 b1 c0 c1 : Tm n) u :
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u = (Abs (If a1 (ren_Tm shift b1) (ren_Tm shift c1))) ->
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@R (S n) a0 a1 ->
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@R n a0 (Abs a1) ->
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R b0 b1 ->
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R c0 c1 ->
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R (If (Abs a0) b0 c0) u.
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R (If a0 b0 c0) u.
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Proof. move => ->. apply IfAbs. Qed.
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Lemma renaming n m (a b : Tm n) (ξ : fin n -> fin m) :
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R a b -> R (ren_Tm ξ a) (ren_Tm ξ b).
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Proof.
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move => h. move : m ξ.
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elim : n a b /h; try solve [(move => *; apply : AppAbs'; eauto; by asimpl) | (move => *; apply : IfAbs'; eauto; by asimpl)].
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elim : n a b /h => //=; try solve [(move => *; apply : AppAbs'; eauto; rewrite -/ren_Tm;by asimpl) |
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(move => *; apply : IfBool'; eauto; rewrite -/ren_Tm; hauto lq:on) |
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(move => *; apply : IfAbs'; eauto; rewrite -/ren_Tm; by asimpl)].
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all : try qauto ctrs:R use:ProjPair', IfBool'.
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Qed.
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@ -520,17 +519,18 @@ Module RPar.
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Proof.
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move => + h. move : m ρ0 ρ1.
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elim : n a b /h.
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- move => *.
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- move => /= *.
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apply : AppAbs'; eauto using morphing_up.
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by asimpl.
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- hauto lq:on ctrs:R.
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- hauto lq:on ctrs:R use:morphing_up.
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- hauto lq:on ctrs:R use:ProjPair' use:morphing_up.
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- move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc m ρ0 ρ1 hρ /=.
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- move => /= *.
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apply : IfAbs'; eauto using morphing_up.
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by asimpl.
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- hauto lq:on ctrs:R.
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- hauto lq:on ctrs:R use:IfBool' use:morphing_up.
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- move => n a v b0 b1 c0 c1 ha iha hb ihb hc ihc m ρ0 ρ1 hρ /=.
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eapply IfBool' with (v := v); qauto l:on.
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- hauto lq:on ctrs:R use:morphing_up.
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- hauto lq:on ctrs:R use:morphing_up.
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- hauto lq:on ctrs:R use:morphing_up.
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@ -585,145 +585,145 @@ Module RPar.
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Lemma antirenaming n m (a : Tm n) (b : Tm m) (ρ : fin n -> Tm m) :
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(forall i, var_or_bot (ρ i)) ->
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R (subst_Tm ρ a) b -> exists b0, R a b0 /\ subst_Tm ρ b0 = b.
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Proof.
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move E : (subst_Tm ρ a) => u hρ h.
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move : n ρ hρ a E. elim : m u b/h.
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- move => n a0 a1 b0 b1 ha iha hb ihb m ρ hρ []//=;
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first by antiimp.
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move => c c0 [+ ?]. subst.
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case : c => //=; first by antiimp.
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move => c [?]. subst.
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spec_refl.
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have /var_or_bot_up hρ' := hρ.
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move : iha hρ' => /[apply] iha.
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move : ihb hρ => /[apply] ihb.
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spec_refl.
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move : iha => [c1][ih0]?. subst.
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move : ihb => [c2][ih1]?. subst.
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eexists. split.
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apply AppAbs; eauto.
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by asimpl.
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- move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc m ρ hρ []//=;
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first by antiimp.
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move => []//=; first by antiimp.
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move => t t0 t1 [*]. subst.
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have {}/iha := hρ => iha.
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have {}/ihb := hρ => ihb.
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have {}/ihc := hρ => ihc.
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spec_refl.
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move : iha => [? [*]].
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move : ihb => [? [*]].
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move : ihc => [? [*]].
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eexists. split.
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apply AppPair; hauto. subst.
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by asimpl.
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- move => n p a0 a1 ha iha m ρ hρ []//=;
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first by antiimp.
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move => p0 []//= t [*]; first by antiimp. subst.
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have /var_or_bot_up {}/iha := hρ => iha.
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spec_refl. move : iha => [b0 [? ?]]. subst.
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eexists. split. apply ProjAbs; eauto. by asimpl.
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- move => n p a0 a1 b0 b1 ha iha hb ihb m ρ hρ []//=;
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first by antiimp.
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move => p0 []//=; first by antiimp. move => t t0[*].
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subst.
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have {}/iha := (hρ) => iha.
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have {}/ihb := (hρ) => ihb.
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spec_refl.
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move : iha => [b0 [? ?]].
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move : ihb => [c0 [? ?]]. subst.
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eexists. split. by eauto using ProjPair.
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hauto q:on.
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- move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc m ρ hρ []//=; first by antiimp.
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move => + b2 c2 [+ *]. subst. case => //=; first by antiimp.
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move => a [*]. subst.
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have /var_or_bot_up hρ' := hρ.
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move : iha hρ' => /[apply] iha.
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move : ihb (hρ) => /[apply] ihb.
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move : ihc hρ => /[apply] ihc.
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spec_refl.
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move : iha => [a0 [ha0 ?]]. subst.
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move : ihb => [b0 [hb0 ?]]. subst.
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move : ihc => [c0 [hc0 ?]]. subst.
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exists (Abs (If a0 (ren_Tm shift b0) (ren_Tm shift c0))). split.
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hauto lq:on ctrs:R.
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by asimpl.
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- move => n a0 a1 b0 b1 c0 c1 d0 d1 ha iha hb ihb hc ihc hd ihd m ρ hρ []//=; first by antiimp.
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move => a2 b2 c2 [+ *]. subst. case : a2 => //=; first by antiimp.
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move => a3 b3 [*]. subst.
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have {}/iha := (hρ) => iha.
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have {}/ihb := (hρ) => ihb.
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have {}/ihc := (hρ) => ihc.
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spec_refl.
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hauto lq:on ctrs:R.
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- move => n a b0 b1 c0 c1 hb ihb hc ihc m ρ hρ []//=; first by antiimp.
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move => t t0 t1 [h *]. subst.
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case : t h => //=; first by antiimp.
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move => b [*]. subst.
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have {}/ihb := (hρ) => ihb.
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have {}/ihc := (hρ) => ihc.
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spec_refl.
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hauto q:on use:IfBool.
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- move => n i m ρ hρ []//=.
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hauto l:on.
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- move => n a0 a1 ha iha m ρ hρ []//=; first by antiimp.
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move => t [*]. subst.
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have /var_or_bot_up {}/iha := hρ => iha.
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spec_refl.
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move :iha => [b0 [? ?]]. subst.
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eexists. split. by apply AbsCong; eauto.
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by asimpl.
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- move => n a0 a1 b0 b1 ha iha hb ihb m ρ hρ []//=;
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first by antiimp.
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move => t t0 [*]. subst.
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have {}/iha := (hρ) => iha.
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have {}/ihb := (hρ) => ihb.
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spec_refl.
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move : iha => [b0 [? ?]]. subst.
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move : ihb => [c0 [? ?]]. subst.
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eexists. split. by apply AppCong; eauto.
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done.
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- move => n a0 a1 b0 b1 ha iha hb ihb m ρ hρ []//=;
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first by antiimp.
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move => t t0[*]. subst.
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have {}/iha := (hρ) => iha.
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have {}/ihb := (hρ) => ihb.
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spec_refl.
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move : iha => [b0 [? ?]]. subst.
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move : ihb => [c0 [? ?]]. subst.
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eexists. split. by apply PairCong; eauto.
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by asimpl.
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- move => n p a0 a1 ha iha m ρ hρ []//=;
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first by antiimp.
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move => p0 t [*]. subst.
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have {}/iha := (hρ) => iha.
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spec_refl.
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move : iha => [b0 [? ?]]. subst.
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eexists. split. apply ProjCong; eauto. reflexivity.
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- move => n p A0 A1 B0 B1 ha iha hB ihB m ρ hρ []//=;
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first by antiimp.
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move => ? t t0 [*]. subst.
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have {}/iha := (hρ) => iha.
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have /var_or_bot_up {}/ihB := (hρ) => ihB.
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spec_refl.
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move : iha => [b0 [? ?]].
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move : ihB => [c0 [? ?]]. subst.
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eexists. split. by apply BindCong; eauto.
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by asimpl.
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- hauto q:on ctrs:R inv:Tm.
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- move => n i n0 ρ hρ []//=; first by antiimp.
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hauto l:on.
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- move => n m ρ hρ []//=; first by antiimp.
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hauto lq:on ctrs:R.
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- move => n b m ρ hρ []//; first by antiimp.
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hauto lq:on ctrs:R.
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- move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc m ρ hρ []//=; first by antiimp.
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move => t t0 t1 [*]. subst.
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have {}/iha := (hρ) => iha.
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have {}/ihb := (hρ) => ihb.
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have {}/ihc := (hρ) => ihc.
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spec_refl.
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hauto lq:on ctrs:R.
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(* Proof. *)
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(* move E : (subst_Tm ρ a) => u hρ h. *)
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(* move : n ρ hρ a E. elim : m u b/h. *)
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(* - move => n a0 a1 b0 b1 ha iha hb ihb m ρ hρ []//=; *)
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(* first by antiimp. *)
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(* move => c c0 [+ ?]. subst. *)
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(* case : c => //=; first by antiimp. *)
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(* move => c [?]. subst. *)
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(* spec_refl. *)
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(* have /var_or_bot_up hρ' := hρ. *)
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(* move : iha hρ' => /[apply] iha. *)
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(* move : ihb hρ => /[apply] ihb. *)
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(* spec_refl. *)
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(* move : iha => [c1][ih0]?. subst. *)
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(* move : ihb => [c2][ih1]?. subst. *)
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(* eexists. split. *)
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(* apply AppAbs; eauto. *)
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(* by asimpl. *)
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(* - move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc m ρ hρ []//=; *)
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(* first by antiimp. *)
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(* move => []//=; first by antiimp. *)
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(* move => t t0 t1 [*]. subst. *)
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(* have {}/iha := hρ => iha. *)
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(* have {}/ihb := hρ => ihb. *)
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(* have {}/ihc := hρ => ihc. *)
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(* spec_refl. *)
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(* move : iha => [? [*]]. *)
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(* move : ihb => [? [*]]. *)
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(* move : ihc => [? [*]]. *)
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(* eexists. split. *)
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(* apply AppPair; hauto. subst. *)
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(* by asimpl. *)
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(* - move => n p a0 a1 ha iha m ρ hρ []//=; *)
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(* first by antiimp. *)
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(* move => p0 []//= t [*]; first by antiimp. subst. *)
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(* have /var_or_bot_up {}/iha := hρ => iha. *)
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(* spec_refl. move : iha => [b0 [? ?]]. subst. *)
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(* eexists. split. apply ProjAbs; eauto. by asimpl. *)
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(* - move => n p a0 a1 b0 b1 ha iha hb ihb m ρ hρ []//=; *)
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(* first by antiimp. *)
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(* move => p0 []//=; first by antiimp. move => t t0[*]. *)
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(* subst. *)
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(* have {}/iha := (hρ) => iha. *)
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(* have {}/ihb := (hρ) => ihb. *)
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(* spec_refl. *)
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(* move : iha => [b0 [? ?]]. *)
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(* move : ihb => [c0 [? ?]]. subst. *)
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(* eexists. split. by eauto using ProjPair. *)
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(* hauto q:on. *)
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(* - move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc m ρ hρ []//=; first by antiimp. *)
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(* move => + b2 c2 [+ *]. subst. case => //=; first by antiimp. *)
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(* move => a [*]. subst. *)
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(* have /var_or_bot_up hρ' := hρ. *)
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(* move : iha hρ' => /[apply] iha. *)
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(* move : ihb (hρ) => /[apply] ihb. *)
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(* move : ihc hρ => /[apply] ihc. *)
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(* spec_refl. *)
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(* move : iha => [a0 [ha0 ?]]. subst. *)
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(* move : ihb => [b0 [hb0 ?]]. subst. *)
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(* move : ihc => [c0 [hc0 ?]]. subst. *)
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(* exists (Abs (If a0 (ren_Tm shift b0) (ren_Tm shift c0))). split. *)
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(* hauto lq:on ctrs:R. *)
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(* by asimpl. *)
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(* - move => n a0 a1 b0 b1 c0 c1 d0 d1 ha iha hb ihb hc ihc hd ihd m ρ hρ []//=; first by antiimp. *)
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(* move => a2 b2 c2 [+ *]. subst. case : a2 => //=; first by antiimp. *)
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(* move => a3 b3 [*]. subst. *)
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(* have {}/iha := (hρ) => iha. *)
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(* have {}/ihb := (hρ) => ihb. *)
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(* have {}/ihc := (hρ) => ihc. *)
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||||
(* spec_refl. *)
|
||||
(* hauto lq:on ctrs:R. *)
|
||||
(* - move => n a b0 b1 c0 c1 hb ihb hc ihc m ρ hρ []//=; first by antiimp. *)
|
||||
(* move => t t0 t1 [h *]. subst. *)
|
||||
(* case : t h => //=; first by antiimp. *)
|
||||
(* move => b [*]. subst. *)
|
||||
(* have {}/ihb := (hρ) => ihb. *)
|
||||
(* have {}/ihc := (hρ) => ihc. *)
|
||||
(* spec_refl. *)
|
||||
(* hauto q:on use:IfBool. *)
|
||||
(* - move => n i m ρ hρ []//=. *)
|
||||
(* hauto l:on. *)
|
||||
(* - move => n a0 a1 ha iha m ρ hρ []//=; first by antiimp. *)
|
||||
(* move => t [*]. subst. *)
|
||||
(* have /var_or_bot_up {}/iha := hρ => iha. *)
|
||||
(* spec_refl. *)
|
||||
(* move :iha => [b0 [? ?]]. subst. *)
|
||||
(* eexists. split. by apply AbsCong; eauto. *)
|
||||
(* by asimpl. *)
|
||||
(* - move => n a0 a1 b0 b1 ha iha hb ihb m ρ hρ []//=; *)
|
||||
(* first by antiimp. *)
|
||||
(* move => t t0 [*]. subst. *)
|
||||
(* have {}/iha := (hρ) => iha. *)
|
||||
(* have {}/ihb := (hρ) => ihb. *)
|
||||
(* spec_refl. *)
|
||||
(* move : iha => [b0 [? ?]]. subst. *)
|
||||
(* move : ihb => [c0 [? ?]]. subst. *)
|
||||
(* eexists. split. by apply AppCong; eauto. *)
|
||||
(* done. *)
|
||||
(* - move => n a0 a1 b0 b1 ha iha hb ihb m ρ hρ []//=; *)
|
||||
(* first by antiimp. *)
|
||||
(* move => t t0[*]. subst. *)
|
||||
(* have {}/iha := (hρ) => iha. *)
|
||||
(* have {}/ihb := (hρ) => ihb. *)
|
||||
(* spec_refl. *)
|
||||
(* move : iha => [b0 [? ?]]. subst. *)
|
||||
(* move : ihb => [c0 [? ?]]. subst. *)
|
||||
(* eexists. split. by apply PairCong; eauto. *)
|
||||
(* by asimpl. *)
|
||||
(* - move => n p a0 a1 ha iha m ρ hρ []//=; *)
|
||||
(* first by antiimp. *)
|
||||
(* move => p0 t [*]. subst. *)
|
||||
(* have {}/iha := (hρ) => iha. *)
|
||||
(* spec_refl. *)
|
||||
(* move : iha => [b0 [? ?]]. subst. *)
|
||||
(* eexists. split. apply ProjCong; eauto. reflexivity. *)
|
||||
(* - move => n p A0 A1 B0 B1 ha iha hB ihB m ρ hρ []//=; *)
|
||||
(* first by antiimp. *)
|
||||
(* move => ? t t0 [*]. subst. *)
|
||||
(* have {}/iha := (hρ) => iha. *)
|
||||
(* have /var_or_bot_up {}/ihB := (hρ) => ihB. *)
|
||||
(* spec_refl. *)
|
||||
(* move : iha => [b0 [? ?]]. *)
|
||||
(* move : ihB => [c0 [? ?]]. subst. *)
|
||||
(* eexists. split. by apply BindCong; eauto. *)
|
||||
(* by asimpl. *)
|
||||
(* - hauto q:on ctrs:R inv:Tm. *)
|
||||
(* - move => n i n0 ρ hρ []//=; first by antiimp. *)
|
||||
(* hauto l:on. *)
|
||||
(* - move => n m ρ hρ []//=; first by antiimp. *)
|
||||
(* hauto lq:on ctrs:R. *)
|
||||
(* - move => n b m ρ hρ []//; first by antiimp. *)
|
||||
(* hauto lq:on ctrs:R. *)
|
||||
(* - move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc m ρ hρ []//=; first by antiimp. *)
|
||||
(* move => t t0 t1 [*]. subst. *)
|
||||
(* have {}/iha := (hρ) => iha. *)
|
||||
(* have {}/ihb := (hρ) => ihb. *)
|
||||
(* have {}/ihc := (hρ) => ihc. *)
|
||||
(* spec_refl. *)
|
||||
(* hauto lq:on ctrs:R. *)
|
||||
Admitted.
|
||||
|
||||
Function tstar {n} (a : Tm n) :=
|
||||
|
|
@ -761,7 +761,78 @@ Module RPar.
|
|||
apply tstar_ind => {n a}.
|
||||
- hauto lq:on inv:RPar.R ctrs:RPar.R.
|
||||
- hauto lq:on inv:RPar.R ctrs:RPar.R.
|
||||
- hauto lq:on use:RPar.cong, RPar.refl ctrs:RPar.R inv:RPar.R.
|
||||
- move => n a a0 b ? ih a1 eq ih2 b0. subst.
|
||||
elim /inv => //= _.
|
||||
+ move => a2 a3 b1 b2 h0 h1 [*]. subst.
|
||||
apply cong; eauto.
|
||||
apply ih in h0.
|
||||
elim /inv : h0 => //=.
|
||||
scongruence.
|
||||
+ move => a2 a3 b1 c0 c1 h0 h1 [*]. subst.
|
||||
move /ih : h0.
|
||||
elim /inv => //=. scongruence.
|
||||
+ hauto l:on use:AppAbs.
|
||||
- move => n a a0 b ? ih a1 c e ih' h2 b0.
|
||||
elim /inv => //= _.
|
||||
+ move => a2 a3 b1 b2 ha hb [*]. subst.
|
||||
have {}/ih := ha.
|
||||
elim /inv => //=. scongruence.
|
||||
+ move => a2 b3 b1 c0 c1 + + [*]. subst.
|
||||
move /ih. elim/inv=>//=. move => ? a2 a3 b0 b2 ha hb [*]. subst.
|
||||
apply PairCong; eauto;
|
||||
apply AppCong; eauto; scongruence.
|
||||
+ hauto l:on use:AppPair.
|
||||
- move => n a a0 b ? ih c ? hc iha ihb. subst.
|
||||
move => b0. elim /inv => //=.
|
||||
+ qblast.
|
||||
+ qblast.
|
||||
+ hauto lq:on ctrs:R.
|
||||
- hauto lq:on ctrs:R inv:R.
|
||||
- move => n a p a0 ? ih a1 b h ?. subst.
|
||||
move => b0. elim /inv => //= _.
|
||||
+ sauto.
|
||||
+ sauto.
|
||||
+ move => p a2 a3 h0 [*]. subst.
|
||||
have {}/ih := h0.
|
||||
rewrite h. sfirstorder use:ProjPair'.
|
||||
- move => n a p a0 ? ih a1 b ih2 p0 ?. subst.
|
||||
case : p0 => //= _ b0.
|
||||
elim /inv=>//=.
|
||||
+ sauto.
|
||||
+ sauto.
|
||||
+ move => h p a2 a3 h0 [*]. subst.
|
||||
have {}/ih := h0.
|
||||
rewrite ih2. sfirstorder use:ProjPair'.
|
||||
- sauto use:ProjAbs.
|
||||
- move => n a p a0 ? ih ? ? h. subst.
|
||||
move => h0 b.
|
||||
elim /inv => //=.
|
||||
+ sauto use:ProjAbs.
|
||||
+ scrush use:ProjAbs.
|
||||
+ sauto lq:on use:ProjAbs.
|
||||
- hauto lq:on ctrs:R inv:R.
|
||||
- hauto lq:on ctrs:R inv:R.
|
||||
- hauto lq:on ctrs:R inv:R.
|
||||
- hauto lq:on ctrs:R inv:R.
|
||||
- hauto lq:on ctrs:R inv:R.
|
||||
- move => n a a0 b c ? ih v eq ? hh. subst.
|
||||
move => b0. elim /inv => //= _.
|
||||
+ sauto q:on.
|
||||
+ sauto q:on.
|
||||
+ sauto.
|
||||
+ move => a1 a2 b1 b2 c0 c1 ha hb hc [*]. subst.
|
||||
apply ih in ha. apply hh in hb.
|
||||
apply : IfBool'; eauto; cycle 1.
|
||||
hauto q:on.
|
||||
sfirstorder use:refl.
|
||||
sfirstorder.
|
||||
+ move => a1 a2 b1 b2 c0 c1 d0 d1 ha hb hc hd [*]. subst.
|
||||
have {}/ih : R (App a1 b1) (App a2 b2) by eauto using AppCong.
|
||||
rewrite eq.
|
||||
elim /inv => //= _.
|
||||
move => a0 a3 b0 b3 ha0 hb0 [*]. subst.
|
||||
|
||||
|
||||
- hauto lq:on rew:off ctrs:RPar.R inv:RPar.R.
|
||||
- hauto lq:on rew:off inv:RPar.R ctrs:RPar.R.
|
||||
- hauto lq:on rew:off inv:RPar.R ctrs:RPar.R.
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue