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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 "depth-3-special")
(%interactive)
(%autoadmit clause.lift-term1)
(defmacro %clause.lift-term1-induction (x)
`(%induct (rank ,x)
((logic.constantp ,x)
nil)
((logic.variablep ,x)
nil)
((logic.functionp ,x)
(((,x (first (logic.function-args ,x))))
((,x (second (logic.function-args ,x))))
((,x (third (logic.function-args ,x))))))
((logic.lambdap ,x)
nil)
((and (not (logic.constantp ,x))
(not (logic.variablep ,x))
(not (logic.functionp ,x))
(not (logic.lambdap ,x)))
nil)))
(local (%disable default
same-length-prefixes-equal-cheap
logic.termp-when-logic.formulap))
(%autoprove forcing-logic.termp-of-clause.lift-term1
(%clause.lift-term1-induction x)
(%restrict default clause.lift-term1 (equal x 'x))
(%disable default
expensive-arithmetic-rules
type-set-like-rules))
(%autoprove forcing-logic.term-atblp-of-clause.lift-term1
(%clause.lift-term1-induction x)
(%restrict default clause.lift-term1 (equal x 'x))
(%disable default
expensive-arithmetic-rules
type-set-like-rules))
(%autoprove clause.lift-term1-when-no-clause.unlifted-subterms
(%clause.lift-term1-induction x)
(%restrict default clause.lift-term1 (equal x 'x))
(%disable default
expensive-arithmetic-rules
type-set-like-rules))
(%autoprove forcing-clause.depth-of-clause.factor-strong)
(local (%enable default forcing-clause.depth-of-clause.factor-strong))
(%autoprove lemma-for-clause.depth-decreases-in-lambda-case
(%disable default clause.deepest-weakly-deeper-than-any-member)
(%use (%instance (%thm clause.deepest-weakly-deeper-than-any-member)
(x (logic.lambda-actuals x))
(a (clause.deepest-after-factoring (logic.lambda-actuals x) assignment)))))
(%autoprove lemma2-for-clause.depth-decreases-in-lambda-case
(%disable default
expensive-arithmetic-rules
type-set-like-rules
clause.simple-term-listp-of-domain-of-clause.cases
disjoint-from-nonep-of-domain-of-clause.cases
lemma-for-clause.depth-decreases-in-lambda-case)
(%use (%instance (%thm lemma-for-clause.depth-decreases-in-lambda-case)
(assignment (clause.special-assignment x (clause.cases (clause.simple-tests-list (logic.lambda-actuals x)) nil)))))
(%use (%instance (%thm clause.simple-term-listp-of-domain-of-clause.cases)
(x (clause.special-assignment x (clause.cases (clause.simple-tests-list (logic.lambda-actuals x)) nil)))
(cases (clause.simple-tests-list (logic.lambda-actuals x)))
(assignment nil)))
(%use (%instance (%thm disjoint-from-nonep-of-domain-of-clause.cases)
(x (clause.special-assignment x (clause.cases (clause.simple-tests-list (logic.lambda-actuals x)) nil)))
(cases (clause.simple-tests-list (logic.lambda-actuals x)))
(set (clause.term-paths-list (logic.lambda-actuals x)))
(assignment nil))))
(%autoprove clause.depth-decreases-in-lambda-case
(%enable default
clause.depth-list-redefinition
lemma2-for-clause.depth-decreases-in-lambda-case)
(%disable default
expensive-arithmetic-rules
type-set-like-rules))
(%autoprove lemma-for-clause.depth-decreases-in-logic.functionp-case
(%disable default clause.deepest-weakly-deeper-than-any-member)
(%use (%instance (%thm clause.deepest-weakly-deeper-than-any-member)
(x (logic.function-args x))
(a (clause.deepest-after-factoring (logic.function-args x) assignment)))))
(%autoprove lemma2-for-clause.depth-decreases-in-logic.functionp-case
(%disable default
clause.simple-term-listp-of-domain-of-clause.cases
disjoint-from-nonep-of-domain-of-clause.cases
lemma-for-clause.depth-decreases-in-logic.functionp-case
type-set-like-rules
expensive-arithmetic-rules)
(%use (%instance (%thm lemma-for-clause.depth-decreases-in-logic.functionp-case)
(assignment (clause.special-assignment x (clause.cases (clause.simple-tests-list (logic.function-args x)) nil)))))
(%use (%instance (%thm clause.simple-term-listp-of-domain-of-clause.cases)
(x (clause.special-assignment x (clause.cases (clause.simple-tests-list (logic.function-args x)) nil)))
(cases (clause.simple-tests-list (logic.function-args x)))
(assignment nil)))
(%use (%instance (%thm disjoint-from-nonep-of-domain-of-clause.cases)
(x (clause.special-assignment x (clause.cases (clause.simple-tests-list (logic.function-args x)) nil)))
(cases (clause.simple-tests-list (logic.function-args x)))
(set (clause.term-paths-list (logic.function-args x)))
(assignment nil))))
(%autoprove clause.depth-decreases-in-non-if-logic.functionp-case
(%disable default
expensive-arithmetic-rules
type-set-like-rules
clause.simple-termp-when-bad-args-logic.functionp
clause.unlifted-subterms-when-bad-args-logic.functionp)
(%enable default
clause.depth-list-redefinition
lemma2-for-clause.depth-decreases-in-logic.functionp-case))
(%autoprove clause.depth-decreases-in-bad-args-logic.functionp-case
(%enable default
clause.depth-list-redefinition
lemma2-for-clause.depth-decreases-in-logic.functionp-case))
(%autoprove clause.lift-term1-makes-progress
(%clause.lift-term1-induction x)
(%auto :strategy (cleanup split urewrite))
(%disable default
expensive-arithmetic-rules
type-set-like-rules)
(%crewrite default)
(%auto :strategy (cleanup split urewrite))
(%restrict default definition-of-clause.depth (equal x 'x))
(%restrict default clause.lift-term1 (equal x 'x))
(%enable default
clause.depth-decreases-in-bad-args-logic.functionp-case
clause.depth-decreases-in-non-if-logic.functionp-case
clause.depth-decreases-in-lambda-case)
(%disable default
expensive-arithmetic-rules-two
clause.depth-list-when-length-three)
(%crewrite default)
(%auto :strategy (cleanup split urewrite))
(%crewrite default)
(%auto :strategy (cleanup split urewrite))
(%enable default
clause.depth-list-when-length-three
expensive-arithmetic-rules
expensive-arithmetic-rules-two
type-set-like-rules))
|
