[Merged by Bors] - feat: improvements to congr! and convert
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…lib4 into kmill_congr_fallback
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congr! and convert
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* There is now configuration for `congr!`, `convert`, and `convert_to` to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas. * `congr!` now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first. * There is now a new `HEq` congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality `⊢ ⟨a, x⟩ = ⟨b, y⟩` of sigma types, `congr!` turns this into goals `⊢ a = b` and `⊢ a = b → HEq x y` (note that `congr!` will also auto-introduce `a = b` for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does. * `congr!` (and hence `convert`) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of `congr` was being abused to unfold definitions. * With `set_option trace.congr! true` you can see what `congr!` sees when it is deciding on congruence lemmas. * There is also a bug fix in `convert_to` to do `using 1` when there is no `using` clause, to match its documentation. Note that `congr!` is more capable than `congr` at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a `using` clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the `typeEqs` option), which can help limit the depth automatically. There is also a predefined configuration that you can invoke with, for example, `convert (config := .unfoldSameFun) h`, that causes it to behave more like `congr`, including using default transparency when unfolding.
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congr! and convertcongr! and convert
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congr!,convert, andconvert_toto control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.congr!now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.HEqcongruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality⊢ ⟨a, x⟩ = ⟨b, y⟩of sigma types,congr!turns this into goals⊢ a = band⊢ a = b → HEq x y(note thatcongr!will also auto-introducea = bfor you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.congr!(and henceconvert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation ofcongrwas being abused to unfold definitions.set_option trace.congr! trueyou can see whatcongr!sees when it is deciding on congruence lemmas.convert_toto dousing 1when there is nousingclause, to match its documentation.Note that
congr!is more capable thancongrat finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with ausingclause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by thetypeEqsoption), which can help limit the depth automatically.There is also a predefined configuration that you can invoke with, for example,
convert (config := .unfoldSameFun) h, that causes it to behave more likecongr, including using default transparency when unfolding.