44 lines
1.2 KiB
Coq
44 lines
1.2 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 transl_inv_let : forall Γ s s' σ t t' τ,
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(Γ |- s \is σ) ->
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(Γ |- [[ [{ let s in t }] \is τ ]] = [{ let s' in t' }]) ->
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forall L x, x `notin` L ->
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((x, σ) :: Γ |- [[expr_open [{$ x}] t \is τ]] = expr_open [{$ x}] t')
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.
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Proof.
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Admitted.
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Lemma transl_inv_abs : forall Γ σ e e' τ,
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(Γ |- [[ [{ λ σ ↦ e }] \is τ ]] = [{ λ σ ↦ e' }]) ->
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forall L x, x `notin` L ->
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((x, σ) :: Γ |- [[expr_open [{$ x}] e \is τ]] = expr_open [{$ x}] e')
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.
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Proof.
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Admitted.
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Lemma transl_inv_morph : forall Γ σ e e' τ,
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(Γ |- [[ [{ λ σ ↦morph e }] \is τ ]] = [{ λ σ ↦morph e' }]) ->
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forall L x, x `notin` L ->
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((x, σ) :: Γ |- [[expr_open [{$ x}] e \is τ]] = expr_open [{$ x}] e')
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.
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Proof.
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Admitted.
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Lemma transl_inv_tabs : forall Γ e e' τ,
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(Γ |- [[ [{ Λ e }] \is [< ∀ τ >] ]] = [{ Λ e' }]) ->
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forall L x, x `notin` L ->
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(Γ |- [[ (expr_open_type (ty_fvar x) e) \is τ]] = expr_open_type (ty_fvar x) e')
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.
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Proof.
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Admitted.
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