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For context, in mathlib Lex α is a type wrapper. Lex (α × β) is the type of lexicographically ordered pairs (with a global LT instance, etc.).
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mathlib3 SHA: 1fc36cc9c8264e6e81253f88be7fb2cb6c92d76a porting notes: there are several issues here that should probably be fixed before this gets merged 1. `Prod.Lex` is not protect in core, so when you have this namespace open and try to refer to `Lex`, Lean finds `Prod.Lex` instead of `_root_.Lex`. This is not a huge deal since we have notation `α ×ₗ β`, but we should probably ask for it to be protected in core. See leanprover/lean4#1895 2. on the declarations `toLex_mono` and `toLex_strictMono`, Lean sees right through the type synonym `α ×ₗ β` to `α × β` and uses the wrong `Preorder` instance, which is why I had to provide them manually. I think this is a bug and should be fixed, otherwise it will cause loads of other issues down the road (for other type synonyms) and the errors will be hard to diagnose. EDIT: Hopefully leanprover/lean4#1891 will provide a fix. 3. I had to provide the definitions of `min` and `max` for the `LinearOrder` instance manually because in Lean 4 we have the classes `Min` and `Max` which have no counterpart in Lean 3. In this case it's a bit annoying because `ite` requires decidability, so I effectively had to provide that three times in this instance declaration. Surely there should be a better way? Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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mathlib3 SHA: 1fc36cc9c8264e6e81253f88be7fb2cb6c92d76a porting notes: there are several issues here that should probably be fixed before this gets merged 1. `Prod.Lex` is not protect in core, so when you have this namespace open and try to refer to `Lex`, Lean finds `Prod.Lex` instead of `_root_.Lex`. This is not a huge deal since we have notation `α ×ₗ β`, but we should probably ask for it to be protected in core. See leanprover/lean4#1895 2. on the declarations `toLex_mono` and `toLex_strictMono`, Lean sees right through the type synonym `α ×ₗ β` to `α × β` and uses the wrong `Preorder` instance, which is why I had to provide them manually. I think this is a bug and should be fixed, otherwise it will cause loads of other issues down the road (for other type synonyms) and the errors will be hard to diagnose. EDIT: Hopefully leanprover/lean4#1891 will provide a fix. 3. I had to provide the definitions of `min` and `max` for the `LinearOrder` instance manually because in Lean 4 we have the classes `Min` and `Max` which have no counterpart in Lean 3. In this case it's a bit annoying because `ite` requires decidability, so I effectively had to provide that three times in this instance declaration. Surely there should be a better way? Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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mathlib4 also defines a
Lex, and in porting people have encountered collisions with this one whenProdis open. ProtectingProd.Lexin core is not essential, but would be convenient for mathlib4.