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Abstract-syntax-rename

Ident-rename

Signature
(ident-rename ident subst) → fty::result
Arguments: ident — Guard (identp ident).; subst — Guard (ident-ident-alistp subst).
Returns: fty::result — Type (identp fty::result).

Definitions and Theorems

Function: ident-rename

(defun ident-rename (ident subst)
  (declare (xargs :guard (and (identp ident)
                              (ident-ident-alistp subst))))
  (declare (ignorable ident subst))
  (let ((__function__ 'ident-rename))
    (declare (ignorable __function__))
    (ident-ident-subst ident subst)))

Theorem: identp-of-ident-rename

(defthm identp-of-ident-rename
  (b* ((fty::result (ident-rename ident subst)))
    (identp fty::result))
  :rule-classes :rewrite)

Theorem: ident-rename-of-ident-fix-ident

(defthm ident-rename-of-ident-fix-ident
  (equal (ident-rename (ident-fix ident) subst)
         (ident-rename ident subst)))

Theorem: ident-rename-ident-equiv-congruence-on-ident

(defthm ident-rename-ident-equiv-congruence-on-ident
  (implies (c$::ident-equiv ident ident-equiv)
           (equal (ident-rename ident subst)
                  (ident-rename ident-equiv subst)))
  :rule-classes :congruence)

Theorem: ident-rename-of-ident-ident-alist-fix-subst

(defthm ident-rename-of-ident-ident-alist-fix-subst
  (equal (ident-rename ident (ident-ident-alist-fix subst))
         (ident-rename ident subst)))

Theorem: ident-rename-ident-ident-alist-equiv-congruence-on-subst

(defthm ident-rename-ident-ident-alist-equiv-congruence-on-subst
  (implies (ident-ident-alist-equiv subst subst-equiv)
           (equal (ident-rename ident subst)
                  (ident-rename ident subst-equiv)))
  :rule-classes :congruence)