Work on specification of RTLBlock generation

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+(*|
+..
+   Vericert: Verified high-level synthesis.
+   Copyright (C) 2020-2022 Yann Herklotz <yann@yannherklotz.com>
+
+   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/>.
+
+====================
+Decidable Equalities
+====================
+|*)
+
+Require compcert.backend.RTL.
+Require Import compcert.common.AST.
+Require Import compcert.lib.Maps.
+Require Import compcert.lib.Integers.
+Require Import compcert.lib.Floats.
+
+Require Import vericert.common.Vericertlib.
+Require Import vericert.hls.RTLBlockInstr.
+Require Import vericert.hls.RTLBlock.
+
+Lemma comparison_eq: forall (x y : comparison), {x = y} + {x <> y}.
+Proof.
+  decide equality.
+Defined.
+
+Lemma condition_eq: forall (x y : Op.condition), {x = y} + {x <> y}.
+Proof.
+  generalize comparison_eq; intro.
+  generalize Int.eq_dec; intro.
+  generalize Int64.eq_dec; intro.
+  decide equality.
+Defined.
+
+Lemma addressing_eq : forall (x y : Op.addressing), {x = y} + {x <> y}.
+Proof.
+  generalize Int.eq_dec; intro.
+  generalize AST.ident_eq; intro.
+  generalize Z.eq_dec; intro.
+  generalize Ptrofs.eq_dec; intro.
+  decide equality.
+Defined.
+
+Lemma typ_eq : forall (x y : AST.typ), {x = y} + {x <> y}.
+Proof.
+  decide equality.
+Defined.
+
+Lemma operation_eq: forall (x y : Op.operation), {x = y} + {x <> y}.
+Proof.
+  generalize Int.eq_dec; intro.
+  generalize Int64.eq_dec; intro.
+  generalize Float.eq_dec; intro.
+  generalize Float32.eq_dec; intro.
+  generalize AST.ident_eq; intro.
+  generalize condition_eq; intro.
+  generalize addressing_eq; intro.
+  generalize typ_eq; intro.
+  decide equality.
+Defined.
+
+Lemma memory_chunk_eq : forall (x y : AST.memory_chunk), {x = y} + {x <> y}.
+Proof.
+  decide equality.
+Defined.
+
+Lemma list_typ_eq: forall (x y : list AST.typ), {x = y} + {x <> y}.
+Proof.
+  generalize typ_eq; intro.
+  decide equality.
+Defined.
+
+Lemma option_typ_eq : forall (x y : option AST.typ), {x = y} + {x <> y}.
+Proof.
+  generalize typ_eq; intro.
+  decide equality.
+Defined.
+
+Lemma signature_eq: forall (x y : AST.signature), {x = y} + {x <> y}.
+Proof.
+  repeat decide equality.
+Defined.
+
+Lemma list_operation_eq : forall (x y : list Op.operation), {x = y} + {x <> y}.
+Proof.
+  generalize operation_eq; intro.
+  decide equality.
+Defined.
+
+Lemma list_pos_eq : forall (x y : list positive), {x = y} + {x <> y}.
+Proof.
+  generalize Pos.eq_dec; intros.
+  decide equality.
+Defined.
+
+Lemma sig_eq : forall (x y : AST.signature), {x = y} + {x <> y}.
+Proof.
+  repeat decide equality.
+Defined.
+
+Lemma instr_eq: forall (x y : instr), {x = y} + {x <> y}.
+Proof.
+  generalize Pos.eq_dec; intro.
+  generalize typ_eq; intro.
+  generalize Int.eq_dec; intro.
+  generalize memory_chunk_eq; intro.
+  generalize addressing_eq; intro.
+  generalize operation_eq; intro.
+  generalize condition_eq; intro.
+  generalize signature_eq; intro.
+  generalize list_operation_eq; intro.
+  generalize list_pos_eq; intro.
+  generalize AST.ident_eq; intro.
+  repeat decide equality.
+Defined.
+
+Lemma cf_instr_eq: forall (x y : cf_instr), {x = y} + {x <> y}.
+Proof.
+  generalize Pos.eq_dec; intro.
+  generalize typ_eq; intro.
+  generalize Int.eq_dec; intro.
+  generalize Int64.eq_dec; intro.
+  generalize Float.eq_dec; intro.
+  generalize Float32.eq_dec; intro.
+  generalize Ptrofs.eq_dec; intro.
+  generalize memory_chunk_eq; intro.
+  generalize addressing_eq; intro.
+  generalize operation_eq; intro.
+  generalize condition_eq; intro.
+  generalize signature_eq; intro.
+  generalize list_operation_eq; intro.
+  generalize list_pos_eq; intro.
+  generalize AST.ident_eq; intro.
+  repeat decide equality.
+Defined.
+
+Definition ceq {A: Type} (eqd: forall a b: A, {a = b} + {a <> b}) (a b: A): bool :=
+  if eqd a b then true else false.