• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Set
      • C
      • Soft
      • Bv
      • Imp-language
      • Ethereum
      • Event-macros
      • Java
      • Riscv
      • Bitcoin
      • Zcash
      • Yul
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
        • Process-syntheto-toplevel-fn
        • Translation
        • Language
          • Static-semantics
          • Abstract-syntax
          • Outcome
          • Abstract-syntax-operations
            • Subst-expression-fns
            • Field-list-to-typed-variable-list
            • Negate-expression
            • Get-function-definition-in-function-definitions
            • Get-function-definition
            • Get-type-definition-in-type-definitions
            • Get-type-definition
            • Get-function-specification
            • Get-type-subset
            • Get-alternative-product
            • Direct-supertype
            • Get-function-header-in-list
            • Equate-expression-lists
            • Get-field-type
            • Get-theorem
            • Get-defined-type-names-in-type-definitions
            • Disjoin-expressions
            • Conjoin-expressions
            • Get-type-product
            • Binary-op-nonstrictp
            • Get-type-sum
            • Get-defined-type-names
            • Equate-expressions
            • Field-to-typed-variable
            • Subst-expression
            • Binary-op-strictp
            • Initializer-list-from-flds-vals
            • Typed-variable-list->-expression-variable-list
            • Typed-variable-list->-expression
            • Variable-substitution
            • Local-variables
            • Identifier-list-names
            • Functions-called
            • Subst-expression-list
            • Subst-branch-list
            • Subst-branch
          • Outcome-list
          • Outcomes
        • Process-syntheto-toplevel
        • Shallow-embedding
      • File-io-light
      • Cryptography
      • Number-theory
      • Axe
      • Lists-light
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Abstract-syntax-operations

Equate-expression-lists

Construct a list of equalities between two lists of expressions, element-wise.

Signature

(equate-expression-lists lefts rights) → equalities

Arguments

lefts — Guard (expression-listp lefts).

rights — Guard (expression-listp rights).

Returns

equalities — Type (expression-listp equalities).

Definitions and Theorems

Function: equate-expression-lists

(defun equate-expression-lists (lefts rights)
  (declare (xargs :guard (and (expression-listp lefts)
                              (expression-listp rights))))
  (declare (xargs :guard (= (len lefts) (len rights))))
  (let ((__function__ 'equate-expression-lists))
    (declare (ignorable __function__))
    (cond ((endp lefts) nil)
          (t (cons (equate-expressions (car lefts)
                                       (car rights))
                   (equate-expression-lists (cdr lefts)
                                            (cdr rights)))))))

Theorem: expression-listp-of-equate-expression-lists

(defthm expression-listp-of-equate-expression-lists
  (b* ((equalities (equate-expression-lists lefts rights)))
    (expression-listp equalities))
  :rule-classes :rewrite)

Theorem: equate-expression-lists-of-expression-list-fix-lefts

(defthm equate-expression-lists-of-expression-list-fix-lefts
  (equal (equate-expression-lists (expression-list-fix lefts)
                                  rights)
         (equate-expression-lists lefts rights)))

Theorem: equate-expression-lists-expression-list-equiv-congruence-on-lefts

(defthm
  equate-expression-lists-expression-list-equiv-congruence-on-lefts
  (implies (expression-list-equiv lefts lefts-equiv)
           (equal (equate-expression-lists lefts rights)
                  (equate-expression-lists lefts-equiv rights)))
  :rule-classes :congruence)

Theorem: equate-expression-lists-of-expression-list-fix-rights

(defthm equate-expression-lists-of-expression-list-fix-rights
 (equal (equate-expression-lists lefts (expression-list-fix rights))
        (equate-expression-lists lefts rights)))

Theorem: equate-expression-lists-expression-list-equiv-congruence-on-rights

(defthm
 equate-expression-lists-expression-list-equiv-congruence-on-rights
 (implies (expression-list-equiv rights rights-equiv)
          (equal (equate-expression-lists lefts rights)
                 (equate-expression-lists lefts rights-equiv)))
 :rule-classes :congruence)