• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
      • Proof-support
      • Semantics
      • Lifting
      • R1cs-subset
      • Well-formedness
      • Abstract-syntax
        • Syntax-abstraction
        • Abstract-syntax-trees
        • Abstract-syntax-operations
        • Convenience-constructors
          • Constraint/constraintlist-p
          • Pfdef
          • Constraint/constraintlist-listp
            • Constraint/constraintlist-listp-basics
          • Pfname
          • Yyyjoin
          • Pf+
          • Pf*
          • Pfnames
          • Pfmon
          • Pf=
          • Pfconst
          • Pfcall
          • Pfvar
      • Concrete-syntax
      • R1cs-bridge
      • Parser-interface
    • Legacy-defrstobj
    • C
    • Proof-checker-array
    • Soft
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Ethereum
    • Leftist-trees
    • Java
    • Riscv
    • Taspi
    • Bitcoin
    • Zcash
    • Des
    • X86isa
    • Sha-2
    • Yul
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Axe
    • Poseidon
    • Where-do-i-place-my-book
    • Aleo
    • Bigmems
    • Builtins
    • Execloader
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Community
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Constraint/constraintlist-listp

Constraint/constraintlist-listp-basics

Basic theorems about constraint/constraintlist-listp, generated by std::deflist.

Definitions and Theorems

Theorem: constraint/constraintlist-listp-of-cons

(defthm constraint/constraintlist-listp-of-cons
  (equal (constraint/constraintlist-listp (cons acl2::a acl2::x))
         (and (constraint/constraintlist-p acl2::a)
              (constraint/constraintlist-listp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: constraint/constraintlist-listp-of-cdr-when-constraint/constraintlist-listp

(defthm
 constraint/constraintlist-listp-of-cdr-when-constraint/constraintlist-listp
 (implies (constraint/constraintlist-listp (double-rewrite acl2::x))
          (constraint/constraintlist-listp (cdr acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: constraint/constraintlist-listp-when-not-consp

(defthm constraint/constraintlist-listp-when-not-consp
  (implies (not (consp acl2::x))
           (equal (constraint/constraintlist-listp acl2::x)
                  (not acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: constraint/constraintlist-p-of-car-when-constraint/constraintlist-listp

(defthm
 constraint/constraintlist-p-of-car-when-constraint/constraintlist-listp
 (implies (constraint/constraintlist-listp acl2::x)
          (constraint/constraintlist-p (car acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: true-listp-when-constraint/constraintlist-listp-compound-recognizer

(defthm
 true-listp-when-constraint/constraintlist-listp-compound-recognizer
 (implies (constraint/constraintlist-listp acl2::x)
          (true-listp acl2::x))
 :rule-classes :compound-recognizer)

Theorem: constraint/constraintlist-listp-of-list-fix

(defthm constraint/constraintlist-listp-of-list-fix
  (implies (constraint/constraintlist-listp acl2::x)
           (constraint/constraintlist-listp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: constraint/constraintlist-listp-of-rev

(defthm constraint/constraintlist-listp-of-rev
  (equal (constraint/constraintlist-listp (rev acl2::x))
         (constraint/constraintlist-listp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: constraint/constraintlist-listp-of-append

(defthm constraint/constraintlist-listp-of-append
  (equal (constraint/constraintlist-listp (append acl2::a acl2::b))
         (and (constraint/constraintlist-listp (list-fix acl2::a))
              (constraint/constraintlist-listp acl2::b)))
  :rule-classes ((:rewrite)))