• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • 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
      • Aleobft
      • Aleovm
      • Leo
        • Grammar
        • Early-version
          • Json2ast
          • Testing
          • Definition
            • Flattening
            • Abstract-syntax
            • Dynamic-semantics
              • Execution
                • Exec-expressions/statements
                • Init-for-loop
                • Exec-file-main
                • Update-variable-value-in-scope-list
                • Step-for-loop
                • Update-variable-value-in-scope
                • Expr-value-to-value
                • Exec-binary
                • Exec-expression
                • Init-vcscope-dinfo-call
                • Value?+denv
                • Exec-statement
                • End-of-for-loop-p
                • Expr-value
                • Evalue+denv
                • Write-location
                • Read-location
                • Exec-for-loop-iterations
                • Update-variable-value
                • Exec-unary
                • Values+denv
                • Init-vcscope-dinfo-loop
                • Extend-denv-with-structdecl
                • Exec-var/const
                • Valuemap+denv
                • Namevalue+denv
                • Extend-denv-with-fundecl
                • Ensure-boolean
                • Int+denv
                • Push-vcscope-dinfo
                • Extend-denv-with-topdecl-list
                • Exec-literal
                • Build-denv-from-file
                • Namevalue+denv-result
                • Extend-denv-with-topdecl
                • Evalue+denv-result
                • Value?+denv-result
                • Values+denv-result
                • Valuemap+denv-result
                  • Valuemap+denv-result-fix
                  • Valuemap+denv-result-equiv
                  • Valuemap+denv-result-ok
                  • Valuemap+denv-result-err
                  • Valuemap+denv-resultp
                  • Valuemap+denv-result-kind
                • Int+denv-result
                • Push-call-dinfo
                • Exec-print
                • Pop-vcscope-dinfo
                • Exec-if
                • Exec-function
                • Pop-call-dinfo
                • Exec-statement-list
                • Exec-block
                • Exec-struct-init-list
                • Exec-struct-init
                • Exec-expression-list
              • Values
              • Dynamic-environments
              • Arithmetic-operations
              • Curve-parameterization
              • Shift-operations
              • Errors
              • Value-expressions
              • Locations
              • Input-execution
              • Edwards-bls12-generator
              • Equality-operations
              • Logical-operations
              • Program-execution
              • Ordering-operations
              • Bitwise-operations
              • Literal-evaluation
              • Type-maps-for-struct-components
              • Output-execution
              • Tuple-operations
              • Struct-operations
            • Compilation
            • Static-semantics
            • Concrete-syntax
    • 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

• Valuemap+denv-result

Valuemap+denv-result-equiv

Basic equivalence relation for valuemap+denv-result structures.

Definitions and Theorems

Function: valuemap+denv-result-equiv$inline

(defun valuemap+denv-result-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (valuemap+denv-resultp acl2::x)
                              (valuemap+denv-resultp acl2::y))))
  (equal (valuemap+denv-result-fix acl2::x)
         (valuemap+denv-result-fix acl2::y)))

Theorem: valuemap+denv-result-equiv-is-an-equivalence

(defthm valuemap+denv-result-equiv-is-an-equivalence
  (and (booleanp (valuemap+denv-result-equiv x y))
       (valuemap+denv-result-equiv x x)
       (implies (valuemap+denv-result-equiv x y)
                (valuemap+denv-result-equiv y x))
       (implies (and (valuemap+denv-result-equiv x y)
                     (valuemap+denv-result-equiv y z))
                (valuemap+denv-result-equiv x z)))
  :rule-classes (:equivalence))

Theorem: valuemap+denv-result-equiv-implies-equal-valuemap+denv-result-fix-1

(defthm
 valuemap+denv-result-equiv-implies-equal-valuemap+denv-result-fix-1
 (implies (valuemap+denv-result-equiv acl2::x x-equiv)
          (equal (valuemap+denv-result-fix acl2::x)
                 (valuemap+denv-result-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: valuemap+denv-result-fix-under-valuemap+denv-result-equiv

(defthm valuemap+denv-result-fix-under-valuemap+denv-result-equiv
  (valuemap+denv-result-equiv (valuemap+denv-result-fix acl2::x)
                              acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-valuemap+denv-result-fix-1-forward-to-valuemap+denv-result-equiv

(defthm
 equal-of-valuemap+denv-result-fix-1-forward-to-valuemap+denv-result-equiv
 (implies (equal (valuemap+denv-result-fix acl2::x)
                 acl2::y)
          (valuemap+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-valuemap+denv-result-fix-2-forward-to-valuemap+denv-result-equiv

(defthm
 equal-of-valuemap+denv-result-fix-2-forward-to-valuemap+denv-result-equiv
 (implies (equal acl2::x
                 (valuemap+denv-result-fix acl2::y))
          (valuemap+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: valuemap+denv-result-equiv-of-valuemap+denv-result-fix-1-forward

(defthm
   valuemap+denv-result-equiv-of-valuemap+denv-result-fix-1-forward
 (implies
      (valuemap+denv-result-equiv (valuemap+denv-result-fix acl2::x)
                                  acl2::y)
      (valuemap+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: valuemap+denv-result-equiv-of-valuemap+denv-result-fix-2-forward

(defthm
   valuemap+denv-result-equiv-of-valuemap+denv-result-fix-2-forward
 (implies
     (valuemap+denv-result-equiv acl2::x
                                 (valuemap+denv-result-fix acl2::y))
     (valuemap+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)