(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.(** * Abstract syntax *)

(** Integer registers.  X0 is treated specially because it always reads 
  as zero and is never used as a destination of an instruction. *)

Inductive ireg: Type :=
  | X1:  ireg | X2:  ireg | X3:  ireg | X4:  ireg | X5:  ireg
  | X6:  ireg | X7:  ireg | X8:  ireg | X9:  ireg | X10: ireg
  | X11: ireg | X12: ireg | X13: ireg | X14: ireg | X15: ireg
  | X16: ireg | X17: ireg | X18: ireg | X19: ireg | X20: ireg
  | X21: ireg | X22: ireg | X23: ireg | X24: ireg | X25: ireg
  | X26: ireg | X27: ireg | X28: ireg | X29: ireg | X30: ireg
  | X31: ireg.Inductive ireg0: Type :=
  | X0: ireg0 | X: ireg -> ireg0.Inductive ireg0: Type :=
  | X0: ireg0 | X: ireg -> ireg0.Inductive ireg0: Type :=
  | X0: ireg0 | X: ireg -> ireg0.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.(** Floating-point registers *)

Inductive freg: Type :=
  | F0: freg  | F1: freg  | F2: freg  | F3: freg
  | F4: freg  | F5: freg  | F6: freg  | F7: freg
  | F8: freg  | F9: freg  | F10: freg | F11: freg
  | F12: freg | F13: freg | F14: freg | F15: freg
  | F16: freg | F17: freg | F18: freg | F19: freg
  | F20: freg | F21: freg | F22: freg | F23: freg
  | F24: freg | F25: freg | F26: freg | F27: freg
  | F28: freg | F29: freg | F30: freg | F31: freg.

Lemma freg_eq: forall (x y: freg), {x=y} + {x<>y}.