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|
; Milawa - A Reflective Theorem Prover
; Copyright (C) 2005-2009 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.com/
;
; License: (An MIT/X11-style license)
;
; 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.
;
; Original author: Jared Davis <jared@kookamara.com>
(in-package "MILAWA")
(include-book "pequal-list")
(%interactive)
(%autoadmit build.pequal-from-equal-list)
(%autoprove len-of-build.pequal-from-equal-list
(%cdr-induction x)
(%restrict default build.pequal-from-equal-list (equal x 'x)))
(%autoprove forcing-logic.appeal-listp-of-build.pequal-from-equal-list
(%cdr-induction x)
(%restrict default build.pequal-from-equal-list (equal x 'x)))
(%autoprove forcing-logic.strip-conclusions-of-build.pequal-from-equal-list
(%cdr-induction x)
(%restrict default build.pequal-from-equal-list (equal x 'x)))
(%autoprove forcing-logic.proof-listp-of-build.pequal-from-equal-list
(%cdr-induction x)
(%restrict default build.pequal-from-equal-list (equal x 'x)))
(%autoadmit build.disjoined-pequal-from-equal-list)
(%autoprove len-of-build.disjoined-pequal-from-equal-list
(%cdr-induction x)
(%restrict default build.disjoined-pequal-from-equal-list (equal x 'x)))
(%autoprove forcing-logic.appeal-listp-of-build.disjoined-pequal-from-equal-list
(%cdr-induction x)
(%restrict default build.disjoined-pequal-from-equal-list (equal x 'x)))
(%autoprove forcing-logic.strip-conclusions-of-build.disjoined-pequal-from-equal-list
(%cdr-induction x)
(%restrict default build.disjoined-pequal-from-equal-list (equal x 'x)))
(%autoprove forcing-logic.proof-listp-of-build.disjoined-pequal-from-equal-list
(%cdr-induction x)
(%restrict default build.disjoined-pequal-from-equal-list (equal x 'x)))
(%autoadmit build.equal-by-args)
(encapsulate
()
(local (%enable default build.equal-by-args axiom-equal-when-same))
(%autoprove build.equal-by-args-under-iff)
(%autoprove forcing-logic.appealp-of-build.equal-by-args)
(%autoprove forcing-logic.conclusion-of-build.equal-by-args)
(%autoprove forcing-logic.proofp-of-build.equal-by-args))
(%autoadmit build.disjoined-equal-by-args)
(encapsulate
()
(local (%enable default build.disjoined-equal-by-args axiom-equal-when-same))
(%autoprove build.disjoined-equal-by-args-under-iff)
(%autoprove forcing-logic.appealp-of-build.disjoined-equal-by-args)
(%autoprove forcing-logic.conclusion-of-build.disjoined-equal-by-args)
(%autoprove forcing-logic.proofp-of-build.disjoined-equal-by-args))
(%autoadmit build.equal-by-args-aux-okp)
(%autoprove build.equal-by-args-aux-okp-removal
(%autoinduct build.equal-by-args-aux-okp)
(%splitlimit 8)
(%auto :strategy (cleanup split urewrite crewrite))
(%restrict default build.equal-by-args-aux-okp (equal proofs 'proofs)))
(%autoadmit build.equal-by-args-okp)
(%autoprove booleanp-of-build.equal-by-args-aux-okp
(%autoinduct build.equal-by-args-aux-okp)
(%splitlimit 8)
(%restrict default build.equal-by-args-aux-okp (equal proofs 'proofs)))
(%autoprove booleanp-of-build.equal-by-args-okp
(%enable default build.equal-by-args-okp))
(%autoprove build.equal-by-args-okp-of-logic.appeal-identity
(%enable default build.equal-by-args-okp))
(%autoprove lemma-1-for-soundness-of-build.equal-by-args-okp
(%enable default build.equal-by-args-okp))
(%autoprove lemma-2-for-soundness-of-build.equal-by-args-okp
(%enable default build.equal-by-args-okp))
(%autoprove lemma-3-for-soundness-of-build.equal-by-args-okp
(%enable default build.equal-by-args-okp))
(%autoprove forcing-soundness-of-build.equal-by-args-okp
(%enable default
lemma-1-for-soundness-of-build.equal-by-args-okp
lemma-2-for-soundness-of-build.equal-by-args-okp
lemma-3-for-soundness-of-build.equal-by-args-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (build.equal-by-args (logic.function-name (first (logic.function-args (logic.=lhs (logic.conclusion x)))))
(logic.provable-list-witness (logic.strip-conclusions (logic.subproofs x))
axioms thms atbl))))))
(%autoadmit build.disjoined-equal-by-args-aux-okp)
(%autoprove build.disjoined-equal-by-args-aux-okp-removal
(%autoinduct build.disjoined-equal-by-args-aux-okp)
(%splitlimit 8)
(%disable default
trichotomy-of-<
antisymmetry-of-<
not-equal-when-less
not-equal-when-less-two
logic.termp-when-logic.formulap
logic.formulap-when-logic.termp
same-length-prefixes-equal-cheap
aggressive-equal-of-logic.pequals
aggressive-equal-of-logic.pors
aggressive-equal-of-logic.pnots)
(%disable default logic.vlhs-of-logic.conclusion-of-car-when-all-equalp)
(%auto :strategy (cleanup split urewrite crewrite))
(%restrict default build.disjoined-equal-by-args-aux-okp (equal proofs 'proofs)))
(%autoadmit build.disjoined-equal-by-args-okp)
(%autoprove booleanp-of-build.disjoined-equal-by-args-aux-okp
(%autoinduct build.disjoined-equal-by-args-aux-okp)
(%splitlimit 8)
(%restrict default build.disjoined-equal-by-args-aux-okp (equal proofs 'proofs)))
(%autoprove booleanp-of-build.disjoined-equal-by-args-okp
(%enable default build.disjoined-equal-by-args-okp))
(%autoprove build.disjoined-equal-by-args-okp-of-logic.appeal-identity
(%enable default build.disjoined-equal-by-args-okp))
(%autoprove lemma-1-for-soundness-of-build.disjoined-equal-by-args-okp
(%enable default build.disjoined-equal-by-args-okp)
(%disable default
aggressive-equal-of-logic.pequals
aggressive-equal-of-logic.pors
aggressive-equal-of-logic.pnots))
(%autoprove lemma-2-for-soundness-of-build.disjoined-equal-by-args-okp
(%enable default build.disjoined-equal-by-args-okp)
(%disable default
aggressive-equal-of-logic.pequals
aggressive-equal-of-logic.pors
aggressive-equal-of-logic.pnots))
(%autoprove lemma-3-for-soundness-of-build.disjoined-equal-by-args-okp
(%enable default build.disjoined-equal-by-args-okp)
(%disable default
aggressive-equal-of-logic.pequals
aggressive-equal-of-logic.pors
aggressive-equal-of-logic.pnots))
(%autoprove forcing-soundness-of-build.disjoined-equal-by-args-okp
(%enable default
lemma-1-for-soundness-of-build.disjoined-equal-by-args-okp
lemma-2-for-soundness-of-build.disjoined-equal-by-args-okp
lemma-3-for-soundness-of-build.disjoined-equal-by-args-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (build.disjoined-equal-by-args
(logic.function-name (first (logic.function-args (logic.=lhs (logic.vrhs (logic.conclusion x))))))
(logic.vlhs (logic.conclusion x))
(logic.provable-list-witness (logic.strip-conclusions (logic.subproofs x))
axioms thms atbl))))))
|
