Library functional_algebra.base

This module defines functions and notations shared by all of the modules in this package.
Copyright (C) 2018 Larry D. Lee Jr. <llee454@gmail.com>
This program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License along with this program. If not, see <https://www.gnu.org/licenses/>.
The following notations are introduced here to simplify sequences of algebraic rewrites which would otherwise be expressed as long sequences of eq_ind*.

Notation "A || B @ X 'by' E"
  := (eq_ind_r (fun X => B) A E) (at level 40, left associativity).

Notation "A || B @ X 'by' <- H"
  := (eq_ind_r (fun X => B) A (eq_sym H)) (at level 40, left associativity).

The following notation can be used to define equality assertions. These are like unittests in that they check that a given expression reduces to a given value.
Notation "A =:= B"
  := (eq_refl A : A = B) (at level 90).