Require Import Autosubst2.unscoped Autosubst2.syntax. Require Import fp_red logrel typing. From Hammer Require Import Tactics. Theorem fundamental_theorem : (forall Γ, ⊢ Γ -> ⊨ Γ) /\ (forall Γ a A, Γ ⊢ a ∈ A -> Γ ⊨ a ∈ A) /\ (forall Γ a b A, Γ ⊢ a ≡ b ∈ A -> Γ ⊨ a ≡ b ∈ A) /\ (forall Γ a b, Γ ⊢ a ≲ b -> Γ ⊨ a ≲ b). apply wt_mutual; eauto with sem; [hauto l:on use:SE_Pair]. Unshelve. all : exact 0. Qed. Lemma synsub_to_usub : forall Γ (a b : PTm), Γ ⊢ a ≲ b -> SN a /\ SN b /\ Sub.R a b. Proof. hauto lq:on rew:off use:fundamental_theorem, SemLEq_SN_Sub. Qed.