section 2 with infinite carrier

LICENSE

@@ -17,3 +17,24 @@ AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
+
+lib/LibTactics.v is part of the Software Foundations Sources and is governed by the following license:
+Copyright (c) 2016
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.

README.org

@@ -13,6 +13,10 @@ This project uses Autosubst ([[https://github.com/uds-psl/autosubst]]). It
 must be installed from the coq86-devel branch as described in the
 README of Autosubst.
 
+For inversion the inverts ... as tactic from lib/LibTactics.v is used,
+which is taken from the code of the Software Foundations book at
+[[https://softwarefoundations.cis.upenn.edu/]].
+
 * Building the project
 To build the project run
 =$ make=

_CoqProject

+-Q lib GQM.Lib
 -Q theories GQM
 -arg -w -arg -notation-overridden
 theories/CoqLib.v
@@ -19,3 +20,4 @@ theories/BAEA.v
 theories/FO.v
 theories/FODeduction.v
 theories/Section8.v
+lib/LibTactics.v
\ No newline at end of file

theories/BAE.v

@@ -34,9 +34,9 @@ Record bae := Bae {
   bae_bae_axioms : BaeAxioms bae_Top bae_Bot bae_Imp
 }.
 
-Notation "|[]|𝔹 a" := (bae_Box a) (at level 74, right associativity).
-Notation "a '->>𝔹' b" := (bae_Imp a b) (at level 77, right associativity).
-Definition bae_Neg(b : bae) := b ->>𝔹 bae_Bot b.
+Notation "|[]|𝔹 a" := (bae_Box _ a) (at level 74, right associativity).
+Notation "a '->>𝔹' b" := (bae_Imp _ a b) (at level 77, right associativity).
+Definition bae_Neg{B : bae}(b : bae_car B) := b ->>𝔹 bae_Bot B.
 Notation "'-!𝔹' b" := (bae_Neg b) (at level 73, right associativity).
 
 

theories/Base.v

@@ -6,6 +6,7 @@ Require Export Coq.Logic.FunctionalExtensionality.
 Require Export Coq.omega.Omega.
 Require Export GQM.CoqLib.
 Require Export Coq.Lists.List.
+Require Export GQM.Lib.LibTactics.
 Export ListNotations.
 
 Set Implicit Arguments.