Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
3cf7fdcbe0
This PR adds `T.ctor.noConfusion` declarations, which are
specializations of `T.noConfusion` to equalities between `T.ctor`. The
point is to avoid reducing the `T.noConfusionType` construction every
time we use `injection` or a similar tactic.
```lean
Vec.cons.noConfusion.{u_1, u} {α : Type u} (P : Sort u_1) {n : Nat}
(x : α) (xs : Vec α n) (x' : α) (xs' : Vec α n)
(h : Vec.cons x xs = Vec.cons x' xs')
(k : n = n → x = x' → xs ≍ xs' → P) : P
```
The constructions are not as powerful as `T.noConfusion` when the
indices of the inductive type are not just constructor parameters (or
constructor applications of these parameters), so the full
`T.noConfusion` construction is still needed as a fallback.
It may seem costly to generate these eagerly, but given that we eagerly
generate injectivity theorems already, and we will use them there, it
seems reasonable for now.
To further reduce the cost, we only generate them for constructors with
fields (for others, the `T.noConfusion` theorem doesn't provide any
information), and we use `macro_inline` to prevent the compiler from
creating code for these, given that the compiler has special support for
`T.noConfusion` that we want it to use).
An earlier version of this PR also removed trivial equations and
un-HEq-ed others, leading to
```
(k : x = x' → xs = xs' → P)
```
in the example above. I backed out of that change, as it makes it harder
for tactics like `injectivity` to know how often to `intro`, so better
to keep things uniform.
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