54 lines
1.1 KiB
Coq
54 lines
1.1 KiB
Coq
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From Coq Require Import Lists.List.
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Require Import Atom.
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Require Import Environment.
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Require Import Metatheory.
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Require Import debruijn.
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Require Import subtype.
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Require Import env.
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Require Import morph.
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Require Import subst_lemmas.
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Require Import typing.
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Lemma typing_inv_tabs : forall Γ t τ,
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(Γ |- [{ Λ t }] \is [< ∀ τ >]) ->
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forall L x, x `notin` L ->
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(Γ |- (expr_open_type (ty_fvar x) t) \is τ)
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.
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Proof.
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Admitted.
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Lemma typing_inv_abs : forall Γ σ t τ,
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(Γ |- [{ λ σ ↦ t }] \is [< σ -> τ >]) ->
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forall L x, x `notin` L ->
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((x,σ)::Γ |- (expr_open (ex_fvar x) t) \is τ)
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.
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Proof.
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Admitted.
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Lemma typing_inv_morph : forall Γ σ t τ,
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(Γ |- [{ λ σ ↦morph t }] \is [< σ ->morph τ >]) ->
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forall L x, x `notin` L ->
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((x,σ)::Γ |- (expr_open (ex_fvar x) t) \is τ)
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.
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Proof.
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intros.
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inversion H.
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subst.
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Admitted.
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Lemma typing_inv_let : forall Γ s σ t τ,
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(Γ |- s \is σ) ->
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(Γ |- [{ let s in t }] \is [< τ >]) ->
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forall L x, x `notin` L ->
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((x,σ)::Γ |- (expr_open (ex_fvar x) t) \is τ)
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.
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Proof.
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Admitted.
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