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We are switich away from De Bruijn indices because
1) it's hard to read terms with De Bruijn indices
2) they are making lots of things slower

A new formulation allows for doing more work inside HOSL.

Γ ⊨ e ≤log≤ e' : τ <=>
∀ Δ vvs ρ,
  spec_ctx ρ -∗
  □ ⟦ Γ ⟧* Δ vvs -∗
  ⟦ τ ⟧ₑ Δ (e.[env_subst (vvs.*1)], e'.[env_subst (vvs.*2)])

sans examples

The case of lam and case expressions that before required the terms to be
well-typed now require terms to be closed.

Separated definition context and context refinement from soundness_binary file.

We used to have:

(λ x, b) a ->β b[a/x]

But now we have:

(λ f x, b) a ->β b[a/x, (λ f x, b)/f]