• Top
  • Documentation
  • Books
  • Boolean-reasoning
    • Ipasir
    • Aignet
    • Aig
    • Satlink
    • Truth
    • Ubdds
    • Bdd
    • Faig
    • Bed
    • 4v
      • 4v-sexprs
        • 4v-sexpr-vars
        • 4v-sexpr-eval
        • 4v-sexpr-to-faig
        • 4v-sexpr-restrict-with-rw
        • 4vs-constructors
        • 4v-sexpr-compose-with-rw
        • 4v-sexpr-restrict
        • 4v-sexpr-alist-extract
        • 4v-sexpr-compose
        • 4v-nsexpr-p
          • 4v-nsexpr-alist-p
          • 4v-nsexpr-p-4v-sexpr-compose
          • 4v-nsexpr-p-4v-sexpr-restrict
        • 4v-sexpr-purebool-p
        • 4v-sexpr-<=
        • Sfaig
        • Sexpr-equivs
        • 3v-syntax-sexprp
        • Sexpr-rewriting
        • 4v-sexpr-ind
        • 4v-alist-extract
      • 4v-monotonicity
      • 4v-operations
      • Why-4v-logic
      • 4v-<=
      • 4vp
      • 4vcases
      • 4v-fix
      • 4v-lookup
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• 4v-nsexpr-p
• 4v-sexpr-compose

4v-nsexpr-p-4v-sexpr-compose

Definitions and Theorems

Theorem: 4v-nsexpr-p-4v-sexpr-compose

(defthm 4v-nsexpr-p-4v-sexpr-compose
  (implies (4v-nsexpr-alist-p al)
           (nat-listp (4v-sexpr-vars (4v-sexpr-compose x al)))))

Theorem: 4v-nsexpr-list-p-4v-sexpr-compose-list

(defthm 4v-nsexpr-list-p-4v-sexpr-compose-list
 (implies
     (4v-nsexpr-alist-p al)
     (nat-listp (4v-sexpr-vars-list (4v-sexpr-compose-list x al)))))

Theorem: 4v-nsexpr-alist-p-4v-sexpr-compose-alist

(defthm 4v-nsexpr-alist-p-4v-sexpr-compose-alist
  (implies (4v-nsexpr-alist-p al)
           (4v-nsexpr-alist-p (4v-sexpr-compose-alist x al))))