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Russell's paradox: remove experiments
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Blaisorblade committed Feb 2, 2019
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Expand Up @@ -88,65 +88,6 @@ Section Russell.
iIntros "!>!>"; iSplit. iExact "HvHasA".
iExact "HnotRussellV".
Qed.

Lemma notRussellVOld: γ ⤇ (λ ρ v, russell_p ρ v) -∗ □ (russell_p [] v → False).
assert (Hclv: nclosed_vl (vobj [("A", dtysem [] γ)]) 0) by done.
assert (Hlook: vobj [("A", dtysem [] γ)] @ "A" ↘ dtysem [] γ) by (hnf; eauto).
iIntros "#Hγ !>". iIntros "#[HvHasA #HnotRussellV]".
iAssert (⟦ TSel (pv (vobj [("A", dtysem [] γ)])) "A" ⟧ [] v) as "#HrussellV".
2: {iApply "HnotRussellV". iApply "HrussellV". }

iSplitL => //. iRight.
iExists [], russell_p, (dtysem [] γ).
repeat (repeat iExists _ ; repeat iSplit => //).

(* iPoseProof "HvHasA" as "H'". *)
(* iDestruct "H'" as "[_ H1]". iDestruct "H1" as (d) "[% [% H2]]". *)
(* iDestruct "H2" as (φ σ) "[H3 #_]". iDestruct "H3" as (γ') "[% #Hlook']". *)
(* assert (γ' = γ ∧ σ = []) as [-> ->]. by objLookupDet; subst; injectHyps. *)

(* iAssert (▷ (φ [] v ≡ russell_p [] v))%I as "#Hag". *)
(* { iIntros; by iApply (saved_interp_agree_eta γ (λ a, φ a) (λ a, russell_p a) [] v). } *)
iIntros "!>!>".
(* repeat (repeat iExists _ ; repeat iSplit => //). *)
iSplit. iApply "HvHasA".
iApply "HnotRussellV".
Qed.


Lemma foo0: γ ⤇ (λ ρ v, russell_p ρ v) -∗ russell_p [] v.
assert (Hclv: nclosed_vl (vobj [("A", dtysem [] γ)]) 0) by done.
assert (Hlook: vobj [("A", dtysem [] γ)] @ "A" ↘ dtysem [] γ) by (hnf; eauto).
rewrite /v; iIntros "#Hγ"; (iEval cbn); iSplit => //.

- iSplit => //. repeat (repeat iExists _ ; repeat iSplit => //).
iModIntro; repeat iSplit; by iIntros "**"; try iModIntro.
-
iIntros "/= !>"; repeat iSplit =>//.
iIntros "#[% [[] | H]]".
iDestruct "H" as (σ φ d) "[% [H1 H2]]". iDestruct "H1" as (γ') "[-> Hγ']".
assert (γ' = γ ∧ σ = []) as [-> ->] by admit.
iAssert (▷ (φ [] v ≡ russell_p [] v))%I as "#Hag".
{ iIntros; by iApply (saved_interp_agree_eta γ (λ a, φ a) (λ a, russell_p a) [] v). }
Abort.

Lemma foo: γ ⤇ (λ ρ v, russell_p ρ v) -∗ ⟦TSel (pv v) "A"⟧ [] v.
assert (Hclv: nclosed_vl (vobj [("A", dtysem [] γ)]) 0) by done.
assert (Hlook: vobj [("A", dtysem [] γ)] @ "A" ↘ dtysem [] γ) by (hnf; eauto).
rewrite /v; iIntros "#Hγ"; (iEval cbn); iSplit => //; iRight.
iExists [], russell_p, (dtysem [] γ); iSplit => //.
iSplit. naive_solver.
rewrite /russell_p.
iIntros "!>!>"; iSplit.
iEval (cbn).
iSplit => //. repeat (repeat iExists _ ; repeat iSplit => //).
- iModIntro; repeat iSplit; by iIntros "**"; try iModIntro.
- iIntros "/= !>"; repeat iSplit =>//.
iIntros "#[% [[] | H]]".
iDestruct "H" as (σ Φ d) "[% [H1 H2]]". iDestruct "H1" as (γ') "[-> Hγ']".
assert (γ' = γ ∧ σ = []) as [-> ->] by admit.
Abort.

End Russell.

Section Sec.
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