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- Replace `altP eqP` and `altP (_ =P _)` with `eqVneq`:
The improved `eqVneq` lemma (#351) is redesigned as a comparison predicate and
introduces a hypothesis in the form of `x != y` in the second case. Thus,
`case: (altP eqP)`, `case: (altP (x =P _))` and `case: (altP (x =P y))` idioms
can be replaced with `case: eqVneq`, `case: (eqVneq x)` and
`case: (eqVneq x y)` respectively. This replacement slightly simplifies and
reduces proof scripts.
- use `have [] :=` rather than `case` if it is better.
- `by apply:` -> `exact:`.
- `apply/lem1; apply/lem2` or `apply: lem1; apply: lem2` -> `apply/lem1/lem2`.
- `move/lem1; move/lem2` -> `move/lem1/lem2`.
- Remove `GRing.` prefix if applicable.
- `negbTE` -> `negPf`, `eq_refl` -> `eqxx` and `sym_equal` -> `esym`.
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Replaced the legacy generalised induction idiom with a more robust one
that does not rely on the `{-2}` numerical occurrence selector, using
either new helper lemmas `ubnP` and `ltnSE` or a specific `nat`
induction principle `ltn_ind`.
Added (non-strict in)equality induction helper lemmas
Added `ubnP[lg]?eq` helper lemmas that abstract an integer expression
along with some (in)equality, in preparation for some generalised
induction. Note that while `ubnPleq` is very similar to `ubnP` (indeed
`ubnP M` is basically `ubnPleq M.+1`), `ubnPgeq` is used to remember
that the inductive value remains below the initial one.
Used the change log to give notice to users to update the generalised
induction idioms in their proofs to one of the new forms before
Mathcomp 1.11.
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Initial properties of polynomials in R-algebras
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Like injectivity lemmas, instances of cancellation lemmas (whose
conclusion is `cancel ? ?`, `{in ?, cancel ? ?}`, `pcancel`, or
`ocancel`) are passed to
generic lemmas such as `canRL` or `canLR_in`. Thus such lemmas should
not have trailing on-demand implicits _just before_ the `cancel`
conclusion, as these would be inconvenient to insert (requiring
essentially an explicit eta-expansion).
We therefore use `Arguments` or `Prenex Implicits` directives to make
all such arguments maximally inserted implicits. We don’t, however make
other arguments implicit, so as not to spoil direct instantiation of
the lemmas (in, e.g., `rewrite -[y](invmK injf)`).
We have also tried to do this with lemmas whose statement matches a
`cancel`, i.e., ending in `forall x, g (E[x]) = x` (where pattern
unification will pick up `f = fun x => E[x]`).
We also adjusted implicits of a few stray injectivity
lemmas, and defined constants.
We provide a shorthand for reindexing a bigop with a permutation.
Finally we used the new implicit signatures to simplify proofs that
use injectivity or cancellation lemmas.
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This increases performance 10% - 15% for Coq v8.6.1 - v8.9.dev.
Tested on a Debain-based 16-core build server and
a Macbook Pro laptop with 2,3 GHz Intel Core i5.
| | Compilation time, old | Compilation | Speedup |
| | (mathcomp commit 967088a6f87) | time, new | |
| Coq 8.6.1 | 10min 33s | 9min 10s | 15% |
| Coq 8.7.2 | 10min 12s | 8min 50s | 15% |
| Coq 8.8.2 | 9min 39s | 8min 32s | 13% |
| Coq 8.9.dev(05d827c800544) | 9min 12s | 8min 16s | 11% |
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It seems Coq at some point fixed the problem `_ : Type` was
supposed to solve.
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See the discussion here:
https://github.com/math-comp/math-comp/pull/242#discussion_r233778114
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Default cloning requires a manifest field class.
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Type cast on head constant spoils projection registration (Coq misfeature).
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It's no more crashing but it's still way to long...
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