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Moddb.lisp

Moddb-mod-totalinsts

Signature
(moddb-mod-totalinsts modidx moddb) → totalinsts
Arguments: modidx — Guard (natp modidx).; moddb — Guard (moddb-basics-ok moddb).
Returns: totalinsts — Type (natp totalinsts).

Definitions and Theorems

Function: moddb-mod-totalinsts

(defun moddb-mod-totalinsts (modidx moddb)
  (declare (xargs :stobjs (moddb)))
  (declare (xargs :guard (and (natp modidx)
                              (moddb-basics-ok moddb))))
  (declare (xargs :guard (< modidx (moddb->nmods moddb))))
  (let ((__function__ 'moddb-mod-totalinsts))
    (declare (ignorable __function__))
    (b* (((unless (mbt (< (lnfix modidx)
                          (moddb->nmods moddb))))
          0)
         ((stobj-get totalinsts)
          ((elab-mod (moddb->modsi modidx moddb)))
          (elab-mod->totalinsts elab-mod)))
      totalinsts)))

Theorem: natp-of-moddb-mod-totalinsts

(defthm natp-of-moddb-mod-totalinsts
  (b* ((totalinsts (moddb-mod-totalinsts modidx moddb)))
    (natp totalinsts))
  :rule-classes :type-prescription)

Theorem: moddb-mod-totalinsts-in-terms-of-instoffset

(defthm moddb-mod-totalinsts-in-terms-of-instoffset
 (implies
   (moddb-mods-ok moddb)
   (equal (moddb-mod-totalinsts modidx moddb)
          (moddb-mod-inst-instoffset (moddb-mod-ninsts modidx moddb)
                                     modidx moddb)))
 :rule-classes
 ((:definition
       :install-body nil
       :clique (moddb-mod-inst-instoffset moddb-mod-totalinsts)
       :controller-alist ((moddb-mod-inst-instoffset t t nil)
                          (moddb-mod-totalinsts t nil)))))

Theorem: moddb-mod-inst-instoffset-recursive

(defthm moddb-mod-inst-instoffset-recursive
 (implies
  (moddb-mods-ok moddb)
  (equal
   (moddb-mod-inst-instoffset instidx modidx moddb)
   (if (or (>= (nfix modidx)
               (nfix (moddb->nmods moddb)))
           (zp instidx)
           (zp (elab-mod$a-ninsts (moddb->modsi modidx moddb))))
       0
    (+
     (moddb-mod-inst-instoffset (1- instidx)
                                modidx moddb)
     (let*
      ((submod-idx
            (elab-mod$a->inst-modidx (1- instidx)
                                     (moddb->modsi modidx moddb))))
      (if (and (< submod-idx (nfix modidx))
               (<= (nfix instidx)
                   (elab-mod$a-ninsts (moddb->modsi modidx moddb))))
          (+ 1
             (moddb-mod-totalinsts submod-idx moddb))
        0))))))
 :rule-classes
 ((:definition
       :install-body nil
       :clique (moddb-mod-inst-instoffset moddb-mod-totalinsts)
       :controller-alist ((moddb-mod-inst-instoffset t t nil)
                          (moddb-mod-totalinsts t nil)))))

Theorem: moddb-mod-inst-instoffset-monotonic

(defthm moddb-mod-inst-instoffset-monotonic
  (implies (and (<= (nfix n) (nfix m))
                (moddb-mods-ok moddb))
           (<= (moddb-mod-inst-instoffset n modidx moddb)
               (moddb-mod-inst-instoffset m modidx moddb)))
  :rule-classes (:rewrite :linear))

Theorem: moddb-totalinsts-rewrite

(defthm moddb-totalinsts-rewrite
 (implies
  (< (nfix modidx)
     (nfix (moddb->nmods moddb)))
  (nat-equiv (g :totalinsts (nth modidx (nth *moddb->modsi* moddb)))
             (moddb-mod-totalinsts modidx moddb))))

Theorem: moddb-mod-totalinsts-of-nfix-modidx

(defthm moddb-mod-totalinsts-of-nfix-modidx
  (equal (moddb-mod-totalinsts (nfix modidx)
                               moddb)
         (moddb-mod-totalinsts modidx moddb)))

Theorem: moddb-mod-totalinsts-nat-equiv-congruence-on-modidx

(defthm moddb-mod-totalinsts-nat-equiv-congruence-on-modidx
  (implies (nat-equiv modidx modidx-equiv)
           (equal (moddb-mod-totalinsts modidx moddb)
                  (moddb-mod-totalinsts modidx-equiv moddb)))
  :rule-classes :congruence)

Theorem: moddb-mod-totalinsts-of-moddb-fix-moddb

(defthm moddb-mod-totalinsts-of-moddb-fix-moddb
  (equal (moddb-mod-totalinsts modidx (moddb-fix moddb))
         (moddb-mod-totalinsts modidx moddb)))

Theorem: moddb-mod-totalinsts-moddb-equiv-congruence-on-moddb

(defthm moddb-mod-totalinsts-moddb-equiv-congruence-on-moddb
  (implies (moddb-equiv moddb moddb-equiv)
           (equal (moddb-mod-totalinsts modidx moddb)
                  (moddb-mod-totalinsts modidx moddb-equiv)))
  :rule-classes :congruence)