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Currently, the bidirectional entailment ⊣⊢ is defined as equality in order to use Lean's rw tactic to rewrite with bidirectional entailments in proofs inside the framework (e.g. in proofs of the derived laws).
https://github.com/larsk21/iris-lean/blob/bde762e5d24b2f3777b8c950dc5857b2e8f4f9c6/src/Iris/BI/DerivedConnectives.lean#L7

This requires the axiom equiv_entails, stating that equality is equal to entailments in both directions, which is used to resolve a bidirectional entailment (using an instance of AntiSymm).
https://github.com/larsk21/iris-lean/blob/bde762e5d24b2f3777b8c950dc5857b2e8f4f9c6/src/Iris/BI/Interface.lean#L108-L111

The axiom is however not true for all separation logics, which is why setoids and quotient types need to be used to instantiate the separation logic interface with such logics (see readme). This is, however, not a viable solution, since Lean's Setoid type does not support parameterized equivalances, such as ={n}= from the Iris separation logic.

There are at least two possible solutions:

1. As soon as Lean supports generalized rewriting, we should change the equality = to an equivalence ≡ and rewrite with that.
2. We could instead extend the tactic rw' included in this project (currently used for rewriting with preorders, such as ⊢) to support equivalences as well. This is less prefered, since it would probably require a backtracking search and should really be part of a general solution for generalized rewriting outside of this project. Also, rw' should be replaced with Lean's generalized rewriting in the future.

see also Rewriting congruent relations

The tactic implementations need to destruct expressions (Expr), which is currently done by hand, i.e. using methods like isAppOf and getAppArgs in Iris/Std/Expr.lean. Using expression quotations would presumably simplify this process. One package to check out is quote4.

Currently, the proof that the length of the hypothesis mask is equal to the length of the spatial context in the implementation of isplit (Tactics.lean) is required to be assigned to a separate variable first. If the proof is inlined at $h_length_eq, the error unknown free variable is shown.

This workaround should be removed as soon as lean4/#1415 is fixed.

let h_length_eq ← ``(by show $(quote mask.length) = $(quote lₛ) ; decide)
try evalTactic (← `(tactic|
  first
  | refine tac_sep_split $(quote mask) $h_length_eq _ ?Sep.left ?Sep.right
  | fail
))