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Lucid

Vl-initial-lucidcheck

Signature
(vl-initial-lucidcheck x ss st) → new-st
Arguments: x — Guard (vl-initial-p x).; ss — Guard (vl-scopestack-p ss).; st — Guard (vl-lucidstate-p st).
Returns: new-st — Type (vl-lucidstate-p new-st).

Definitions and Theorems

Function: vl-initial-lucidcheck

(defun vl-initial-lucidcheck (x ss st)
  (declare (xargs :guard (and (vl-initial-p x)
                              (vl-scopestack-p ss)
                              (vl-lucidstate-p st))))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-initial-lucidcheck))
    (declare (ignorable __function__))
    (b* ((x (vl-initial-fix x))
         (ss (vl-scopestack-fix ss))
         (st (vl-lucidstate-fix st)))
      (b* (((vl-initial x))
           (ctx (vl-lucid-ctx ss x)))
        (vl-stmt-lucidcheck x.stmt ss st ctx)))))

Theorem: vl-lucidstate-p-of-vl-initial-lucidcheck

(defthm vl-lucidstate-p-of-vl-initial-lucidcheck
  (b* ((new-st (vl-initial-lucidcheck x ss st)))
    (vl-lucidstate-p new-st))
  :rule-classes :rewrite)

Theorem: vl-initial-lucidcheck-of-vl-initial-fix-x

(defthm vl-initial-lucidcheck-of-vl-initial-fix-x
  (equal (vl-initial-lucidcheck (vl-initial-fix x)
                                ss st)
         (vl-initial-lucidcheck x ss st)))

Theorem: vl-initial-lucidcheck-vl-initial-equiv-congruence-on-x

(defthm vl-initial-lucidcheck-vl-initial-equiv-congruence-on-x
  (implies (vl-initial-equiv x x-equiv)
           (equal (vl-initial-lucidcheck x ss st)
                  (vl-initial-lucidcheck x-equiv ss st)))
  :rule-classes :congruence)

Theorem: vl-initial-lucidcheck-of-vl-scopestack-fix-ss

(defthm vl-initial-lucidcheck-of-vl-scopestack-fix-ss
  (equal (vl-initial-lucidcheck x (vl-scopestack-fix ss)
                                st)
         (vl-initial-lucidcheck x ss st)))

Theorem: vl-initial-lucidcheck-vl-scopestack-equiv-congruence-on-ss

(defthm vl-initial-lucidcheck-vl-scopestack-equiv-congruence-on-ss
  (implies (vl-scopestack-equiv ss ss-equiv)
           (equal (vl-initial-lucidcheck x ss st)
                  (vl-initial-lucidcheck x ss-equiv st)))
  :rule-classes :congruence)

Theorem: vl-initial-lucidcheck-of-vl-lucidstate-fix-st

(defthm vl-initial-lucidcheck-of-vl-lucidstate-fix-st
  (equal (vl-initial-lucidcheck x ss (vl-lucidstate-fix st))
         (vl-initial-lucidcheck x ss st)))

Theorem: vl-initial-lucidcheck-vl-lucidstate-equiv-congruence-on-st

(defthm vl-initial-lucidcheck-vl-lucidstate-equiv-congruence-on-st
  (implies (vl-lucidstate-equiv st st-equiv)
           (equal (vl-initial-lucidcheck x ss st)
                  (vl-initial-lucidcheck x ss st-equiv)))
  :rule-classes :congruence)