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authorGeorges Gonthier2018-12-13 12:55:43 +0100
committerGeorges Gonthier2018-12-13 12:55:43 +0100
commit0b1ea03dafcf36880657ba910eec28ab78ccd018 (patch)
tree60a84ff296299226d530dd0b495be24fd7675748 /plugin
parentfa9b7b19fc0409f3fdfa680e08f40a84594e8307 (diff)
Adjust implicits of cancellation lemmas
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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