GitLab

This patch was created using

  find -name *.v | xargs -L 1 awk -i inplace '{from = 0} /^From/{ from = 1; ever_from = 1} { if (from == 0 && seen == 0 && ever_from == 1) { print "Set Default Proof Using \"Type*\"."; seen = 1 } }1 '

and some minor manual editing

The previous commit is not really necesarry anymore, but my proof
for UIP of types with decidable equality is a bit more general, so
I won't revert it.

Also cleanup the file a bit.

Thanks to Amin Timany for the suggestion.

simplify_equality        => simplify_eq
simplify_equality'       => simplify_eq/=
simplify_map_equality    => simplify_map_eq
simplify_map_equality'   => simplify_map_eq/=
simplify_option_equality => simplify_option_eq
simplify_list_equality   => simplify_list_eq
f_equal'                 => f_equal/=

The /= suffixes (meaning: do simpl) are inspired by ssreflect.

Also, make our redefinition of done more robust under different
orders of Importing modules.

Also do some minor clean up.

This reverts commit 24fa20e5.

Although these symmetric variants sometimes look "better", they
are really annoying and should IMHO never be used:

1.) For lemmas there is now a choice between >= and <=. Since there is
no longer a canonical choice, it is very easy to introduce a lot of
inconsistencies in statements of lemmas.

2.) For automation the situation becomes annoying, you have to built in
stuff for both >= and <=. That is very error-prone.

3.) For N and Z the notions x <= y and y >= x are not even convertible!
That means that done/by does not solve x <= y if you have y >= x and if
avoids you applying certain lemmas.