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          • Decoding-left-inverse
            • Decodex-of-encode-of-instr
            • Get-opcode-of-encode-of-instr
            • Get-funct3-of-encode-of-instr
            • Get-rd-of-encode-of-instr
            • Get-rs1-of-encode-of-instr
            • Get-fields-itype-of-encode-of-instr
            • Get-imm-itype-of-encode-of-instr
            • Get-rs2-of-encode-of-instr
            • Encode-injective
            • Get-fields-rtype-of-encode-of-instr
            • Get-funct7-of-encode-of-instr
            • Get-fields-utype-of-encode-of-instr
            • Decodex-of-encode
            • Get-imm-utype-of-encode-of-instr
            • Get-fields-stype-of-encode-of-instr
            • Get-fields-btype-of-encode-of-instr
            • Get-imm-stype-of-encode-of-instr
            • Get-imm-jtype-of-encode-of-instr
            • Get-imm-btype-of-encode-of-instr
            • Get-fields-jtype-of-encode-of-instr
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• Decoding-left-inverse

Decodex-of-encode-of-instr

Theorems about decodex applied to the encoding of different instructions.

Definitions and Theorems

Theorem: decodex-of-encode-of-instr-op-imm

(defthm decodex-of-encode-of-instr-op-imm
  (implies (instr-validp (instr-op-imm funct rd rs1 imm)
                         feat)
           (equal (decodex (encode (instr-op-imm funct rd rs1 imm)
                                   feat)
                           feat)
                  (instr-op-imm funct rd rs1 imm))))

Theorem: decodex-of-encode-of-instr-op-imms32

(defthm decodex-of-encode-of-instr-op-imms32
 (implies (instr-validp (instr-op-imms32 funct rd rs1 imm)
                        feat)
          (equal (decodex (encode (instr-op-imms32 funct rd rs1 imm)
                                  feat)
                          feat)
                 (instr-op-imms32 funct rd rs1 imm))))

Theorem: decodex-of-encode-of-instr-op-imms64

(defthm decodex-of-encode-of-instr-op-imms64
 (implies (instr-validp (instr-op-imms64 funct rd rs1 imm)
                        feat)
          (equal (decodex (encode (instr-op-imms64 funct rd rs1 imm)
                                  feat)
                          feat)
                 (instr-op-imms64 funct rd rs1 imm))))

Theorem: decodex-of-encode-of-instr-op-imm-32

(defthm decodex-of-encode-of-instr-op-imm-32
 (implies (instr-validp (instr-op-imm-32 funct rd rs1 imm)
                        feat)
          (equal (decodex (encode (instr-op-imm-32 funct rd rs1 imm)
                                  feat)
                          feat)
                 (instr-op-imm-32 funct rd rs1 imm))))

Theorem: decodex-of-encode-of-instr-op-imms-32

(defthm decodex-of-encode-of-instr-op-imms-32
  (implies
       (instr-validp (instr-op-imms-32 funct rd rs1 imm)
                     feat)
       (equal (decodex (encode (instr-op-imms-32 funct rd rs1 imm)
                               feat)
                       feat)
              (instr-op-imms-32 funct rd rs1 imm))))

Theorem: decodex-of-encode-of-instr-lui

(defthm decodex-of-encode-of-instr-lui
  (implies (instr-validp (instr-lui rd imm) feat)
           (equal (decodex (encode (instr-lui rd imm) feat)
                           feat)
                  (instr-lui rd imm))))

Theorem: decodex-of-encode-of-instr-auipc

(defthm decodex-of-encode-of-instr-auipc
  (implies (instr-validp (instr-auipc rd imm) feat)
           (equal (decodex (encode (instr-auipc rd imm) feat)
                           feat)
                  (instr-auipc rd imm))))

Theorem: decodex-of-encode-of-instr-op

(defthm decodex-of-encode-of-instr-op
  (implies (instr-validp (instr-op funct rd rs1 rs2)
                         feat)
           (equal (decodex (encode (instr-op funct rd rs1 rs2)
                                   feat)
                           feat)
                  (instr-op funct rd rs1 rs2))))

Theorem: decodex-of-encode-of-instr-op-32

(defthm decodex-of-encode-of-instr-op-32
  (implies (instr-validp (instr-op-32 funct rd rs1 rs2)
                         feat)
           (equal (decodex (encode (instr-op-32 funct rd rs1 rs2)
                                   feat)
                           feat)
                  (instr-op-32 funct rd rs1 rs2))))

Theorem: decodex-of-encode-of-instr-jal

(defthm decodex-of-encode-of-instr-jal
  (implies (instr-validp (instr-jal rd imm) feat)
           (equal (decodex (encode (instr-jal rd imm) feat)
                           feat)
                  (instr-jal rd imm))))

Theorem: decodex-of-encode-of-instr-jalr

(defthm decodex-of-encode-of-instr-jalr
  (implies (instr-validp (instr-jalr rd rs1 imm)
                         feat)
           (equal (decodex (encode (instr-jalr rd rs1 imm) feat)
                           feat)
                  (instr-jalr rd rs1 imm))))

Theorem: decodex-of-encode-of-instr-branch

(defthm decodex-of-encode-of-instr-branch
  (implies (instr-validp (instr-branch funct rs1 rs2 imm)
                         feat)
           (equal (decodex (encode (instr-branch funct rs1 rs2 imm)
                                   feat)
                           feat)
                  (instr-branch funct rs1 rs2 imm))))

Theorem: decodex-of-encode-of-instr-load

(defthm decodex-of-encode-of-instr-load
  (implies (instr-validp (instr-load funct rd rs1 imm)
                         feat)
           (equal (decodex (encode (instr-load funct rd rs1 imm)
                                   feat)
                           feat)
                  (instr-load funct rd rs1 imm))))

Theorem: decodex-of-encode-of-instr-store

(defthm decodex-of-encode-of-instr-store
  (implies (instr-validp (instr-store funct rs1 rs2 imm)
                         feat)
           (equal (decodex (encode (instr-store funct rs1 rs2 imm)
                                   feat)
                           feat)
                  (instr-store funct rs1 rs2 imm))))