Finish all cases
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1 changed files with 15 additions and 2 deletions
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@ -635,6 +635,16 @@ Proof.
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apply : InterpUniv_back_clos_star; eauto.
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apply : InterpUniv_back_clos_star; eauto.
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Qed.
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Qed.
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Lemma substing_RPar n m (A : Tm (S n)) ρ (B : Tm m) C :
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RPar.R B C ->
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RPar.R (subst_Tm (scons B ρ) A) (subst_Tm (scons C ρ) A).
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Proof. hauto lq:on inv:option use:RPar.morphing, RPar.refl. Qed.
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Lemma substing_RPars n m (A : Tm (S n)) ρ (B : Tm m) C :
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rtc RPar.R B C ->
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rtc RPar.R (subst_Tm (scons B ρ) A) (subst_Tm (scons C ρ) A).
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Proof. induction 1; hauto lq:on ctrs:rtc use:substing_RPar. Qed.
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Lemma ST_Proj2 n Γ (a : Tm n) A B :
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Lemma ST_Proj2 n Γ (a : Tm n) A B :
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Γ ⊨ a ∈ TBind TSig A B ->
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Γ ⊨ a ∈ TBind TSig A B ->
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Γ ⊨ Proj PR a ∈ subst_Tm (scons (Proj PL a) VarTm) B.
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Γ ⊨ Proj PR a ∈ subst_Tm (scons (Proj PL a) VarTm) B.
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@ -652,6 +662,9 @@ Proof.
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have hrr : RPar.R (Proj PR (Pair a0 b0)) b0 by hauto l:on use:RPar.ProjPair', RPar.refl.
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have hrr : RPar.R (Proj PR (Pair a0 b0)) b0 by hauto l:on use:RPar.ProjPair', RPar.refl.
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exists m, PB.
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exists m, PB.
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asimpl. split.
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asimpl. split.
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- admit.
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- have h : rtc RPar.R (Proj PL (subst_Tm ρ a)) a0 by eauto using @relations.rtc_r.
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have {}h : rtc RPar.R (subst_Tm (scons (Proj PL (subst_Tm ρ a)) ρ) B) (subst_Tm (scons a0 ρ) B) by eauto using substing_RPars.
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move : hPB. asimpl.
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eauto using InterpUnivN_back_preservation_star.
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- hauto lq:on use:@relations.rtc_r, InterpUniv_back_clos_star.
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- hauto lq:on use:@relations.rtc_r, InterpUniv_back_clos_star.
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Admitted.
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Qed.
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