(* (c) Copyright 2006-2015 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) Require Import mathcomp.ssreflect.ssreflect. Axiom daemon : False. Ltac myadmit := case: daemon. Ltac T1 x := match goal with |- _ => set t := (x in X in _ = X) end. Ltac T2 x := first [set t := (x in RHS)]. Ltac T3 x := first [set t := (x in Y in _ = Y)|idtac]. Ltac T4 x := set t := (x in RHS);idtac. Ltac T5 x := match goal with |- _ => set t := (x in RHS) | |- _ => idtac end. From mathcomp Require Import ssrbool ssrnat. Lemma foo x y : x.+1 = y + x.+1. set t := (_.+1 in RHS). match goal with |- x.+1 = y + t => rewrite /t {t} end. set t := (x in RHS). match goal with |- x.+1 = y + t.+1 => rewrite /t {t} end. set t := (x in _ = x). match goal with |- x.+1 = t => rewrite /t {t} end. set t := (x in X in _ = X). match goal with |- x.+1 = y + t.+1 => rewrite /t {t} end. set t := (x in RHS). match goal with |- x.+1 = y + t.+1 => rewrite /t {t} end. set t := (y + (1 + x) as X in _ = X). match goal with |- x.+1 = t => rewrite /t addSn add0n {t} end. set t := x.+1. match goal with |- t = y + t => rewrite /t {t} end. set t := (x).+1. match goal with |- t = y + t => rewrite /t {t} end. set t := ((x).+1 in X in _ = X). match goal with |- x.+1 = y + t => rewrite /t {t} end. set t := (x.+1 in RHS). match goal with |- x.+1 = y + t => rewrite /t {t} end. T1 (x.+1). match goal with |- x.+1 = y + t => rewrite /t {t} end. T2 (x.+1). match goal with |- x.+1 = y + t => rewrite /t {t} end. T3 (x.+1). match goal with |- x.+1 = y + t => rewrite /t {t} end. T4 (x.+1). match goal with |- x.+1 = y + t => rewrite /t {t} end. T5 (x.+1). match goal with |- x.+1 = y + t => rewrite /t {t} end. rewrite [RHS]addnC. match goal with |- x.+1 = x.+1 + y => rewrite -[RHS]addnC end. rewrite -[in RHS](@subnK 1 x.+1) //. match goal with |- x.+1 = y + (x.+1 - 1 + 1) => rewrite subnK // end. have H : x.+1 = y by myadmit. set t := _.+1 in H |- *. match goal with H : t = y |- t = y + t => rewrite /t {t} in H * end. set t := (_.+1 in X in _ + X) in H |- *. match goal with H : x.+1 = y |- x.+1 = y + t => rewrite /t {t} in H * end. set t := 0. match goal with t := 0 |- x.+1 = y + x.+1 => clear t end. set t := y + _. match goal with |- x.+1 = t => rewrite /t {t} end. set t : nat := 0. clear t. set t : nat := (x in RHS). match goal with |- x.+1 = y + t.+1 => rewrite /t {t} end. set t : nat := RHS. match goal with |- x.+1 = t => rewrite /t {t} end. (* set t := 0 + _. *) (* set t := (x).+1 in X in _ + X in H |-. *) (* set t := (x).+1 in X in _ = X.*) Admitted.