(* biteq: equivalence of bitvector rewrites.
 * Copyright (C) 2022  Yann Herklotz
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU 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 General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <https://www.gnu.org/licenses/>.
 *)

Lemma modusponens: forall (P Q: Prop), P -> (P -> Q) -> Q.
Proof. auto. Qed.

Ltac exploit x :=
    refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _ _) _)
 || refine (modusponens _ _ (x _ _ _) _)
 || refine (modusponens _ _ (x _ _) _)
 || refine (modusponens _ _ (x _) _).