• 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
        • Circuits
          • Circuits-pfcs
          • Circuits-r1cs
          • Field-div-flagged
          • Boolean-assert-true
          • Field-inv-flagged
          • Boolean-assert
          • Field-div-unchecked
          • Field-neq
          • Boolean-not
          • Boolean-assert-all
          • Boolean-if
          • Field-if
          • Boolean-xor
          • Boolean-or
          • Boolean-nor
          • Boolean-and
          • Boolean-nand
          • Boolean-neq
          • Boolean-eq
          • Field-div-checked
          • Field-inv-checked
          • Boolean-assert-neq
          • Boolean-assert-eq
          • Field-eq
          • Field-assert-neq
          • Field-assert-eq
            • Field-assert-eq-correctness
            • Field-assert-eq-lifting
            • Field-assert-eq-circuit
            • Field-assert-eq-spec
          • Field-mul
          • Field-sub
          • Field-square
          • Field-neg
          • Field-double
          • Field-add
        • Language
      • Leo
    • 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

• Field-assert-eq

Field-assert-eq-lifting

Lifting of the circuit to a predicate.

Definitions and Theorems

Theorem: field-assert-eq-pred-suff

(defthm field-assert-eq-pred-suff
  (implies (and (pfield::fep z prime)
                (and (field-eq-pred x y z prime)
                     (boolean-assert-true-pred z prime)))
           (field-assert-eq-pred x y prime)))

Theorem: definition-satp-to-field-assert-eq-pred

(defthm definition-satp-to-field-assert-eq-pred
 (implies
  (and
   (equal
        (pfcs::lookup-definition '(:simple "field_assert_eq")
                                 pfcs::defs)
        '(:definition
              (name :simple "field_assert_eq")
              (pfcs::para (:simple "x") (:simple "y"))
              (pfcs::body (:relation (:simple "field_eq")
                                     ((:var (:simple "x"))
                                      (:var (:simple "y"))
                                      (:var (:simple "z"))))
                          (:relation (:simple "boolean_assert_true")
                                     ((:var (:simple "z")))))))
   (equal
    (pfcs::lookup-definition '(:simple "boolean_assert_true")
                             pfcs::defs)
    '(:definition
          (name :simple "boolean_assert_true")
          (pfcs::para (:simple "x"))
          (pfcs::body (:equal (:mul (:var (:simple "x")) (:const 1))
                              (:const 1)))))
   (equal
     (pfcs::lookup-definition '(:simple "field_eq")
                              pfcs::defs)
     '(:definition (name :simple "field_eq")
                   (pfcs::para (:simple "x")
                               (:simple "y")
                               (:simple "z"))
                   (pfcs::body (:relation (:simple "field_neq")
                                          ((:var (:simple "x"))
                                           (:var (:simple "y"))
                                           (:var (:simple "w"))))
                               (:relation (:simple "boolean_not")
                                          ((:var (:simple "w"))
                                           (:var (:simple "z")))))))
   (equal
     (pfcs::lookup-definition '(:simple "boolean_not")
                              pfcs::defs)
     '(:definition
           (name :simple "boolean_not")
           (pfcs::para (:simple "x") (:simple "y"))
           (pfcs::body
                (:equal (:mul (:sub (:const 1) (:var (:simple "x")))
                              (:const 1))
                        (:var (:simple "y"))))))
   (equal
    (pfcs::lookup-definition '(:simple "field_neq")
                             pfcs::defs)
    '(:definition
          (name :simple "field_neq")
          (pfcs::para (:simple "x")
                      (:simple "y")
                      (:simple "z"))
          (pfcs::body
               (:equal (:mul (:sub (:var (:simple "x"))
                                   (:var (:simple "y")))
                             (:var (:simple "w")))
                       (:var (:simple "z")))
               (:equal (:mul (:sub (:var (:simple "x"))
                                   (:var (:simple "y")))
                             (:sub (:const 1) (:var (:simple "z"))))
                       (:const 0)))))
   (pfield::fep x prime)
   (pfield::fep y prime)
   (primep prime))
  (equal (pfcs::definition-satp '(:simple "field_assert_eq")
                                pfcs::defs (list x y)
                                prime)
         (field-assert-eq-pred x y prime))))