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Finish the soundness and completeness proof of the subtyping algorithm

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Yiyun Liu 2025-03-06 20:42:08 -05:00
parent fe52d78ec5
commit 437c97455e
3 changed files with 179 additions and 10 deletions
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56
theories/executable.v
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@ -217,6 +217,62 @@ Scheme algo_ind := Induction for algo_dom Sort Prop
Combined Scheme algo_dom_mutual from algo_ind, algor_ind.
(* Inductive salgo_dom : PTm -> PTm -> Prop := *)
(* | S_UnivCong i j : *)
(* (* -------------------------- *) *)
(* salgo_dom (PUniv i) (PUniv j) *)
(* | S_PiCong A0 A1 B0 B1 : *)
(* salgo_dom_r A1 A0 -> *)
(* salgo_dom_r B0 B1 -> *)
(* (* ---------------------------- *) *)
(* salgo_dom (PBind PPi A0 B0) (PBind PPi A1 B1) *)
(* | S_SigCong A0 A1 B0 B1 : *)
(* salgo_dom_r A0 A1 -> *)
(* salgo_dom_r B0 B1 -> *)
(* (* ---------------------------- *) *)
(* salgo_dom (PBind PSig A0 B0) (PBind PSig A1 B1) *)
(* | S_NatCong : *)
(* salgo_dom PNat PNat *)
(* | S_NeuNeu a b : *)
(* ishne a -> *)
(* ishne b -> *)
(* algo_dom a b -> *)
(* (* ------------------- *) *)
(* salgo_dom *)
(* | S_Conf a b : *)
(* HRed.nf a -> *)
(* HRed.nf b -> *)
(* tm_conf a b -> *)
(* salgo_dom a b *)
(* with salgo_dom_r : PTm -> PTm -> Prop := *)
(* | S_NfNf a b : *)
(* salgo_dom a b -> *)
(* salgo_dom_r a b *)
(* | S_HRedL a a' b : *)
(* HRed.R a a' -> *)
(* salgo_dom_r a' b -> *)
(* (* ----------------------- *) *)
(* salgo_dom_r a b *)
(* | S_HRedR a b b' : *)
(* HRed.nf a -> *)
(* HRed.R b b' -> *)
(* salgo_dom_r a b' -> *)
(* (* ----------------------- *) *)
(* salgo_dom_r a b. *)
(* Scheme salgo_ind := Induction for salgo_dom Sort Prop *)
(* with algor_ind := Induction for salgo_dom_r Sort Prop. *)
Lemma hf_no_hred (a b : PTm) :
ishf a ->
HRed.R a b ->