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