Theory: ascii

Parents

• HOL

Type constants

• ascii(Arity = 0)

Term constants

• REP_ascii:ascii -> (bool # bool # bool # bool # bool # bool # bool # bool) ltree {fixity = Prefix}
• ABS_ascii:(bool # bool # bool # bool # bool # bool # bool # bool) ltree -> ascii {fixity = Prefix}
• ASCII:bool -> bool -> bool -> bool -> bool -> bool -> bool -> bool -> ascii {fixity = Prefix}

Axioms

Definitions

ascii_TY_DEF

|- ?rep.
     TYPE_DEFINITION
       (TRP
         (\v tl.
           (?b0 b1 b2 b3 b4 b5 b6 b7. v = (b0,b1,b2,b3,b4,b5,b6,b7)) /\
           (LENGTH tl = 0)))
       rep

ascii_ISO_DEF

|- (!a. ABS_ascii (REP_ascii a) = a) /\
   (!r.
     TRP
       (\v tl.
         (?b0 b1 b2 b3 b4 b5 b6 b7. v = (b0,b1,b2,b3,b4,b5,b6,b7)) /\
         (LENGTH tl = 0))
       r =
     REP_ascii (ABS_ascii r) =
     r)

ASCII_DEF

|- !b0 b1 b2 b3 b4 b5 b6 b7.
     ASCII b0 b1 b2 b3 b4 b5 b6 b7 =
     ABS_ascii (Node (b0,b1,b2,b3,b4,b5,b6,b7) [])

Theorems

ascii_Axiom

|- !f.
     ?!fn.
       !b0 b1 b2 b3 b4 b5 b6 b7.
         fn (ASCII b0 b1 b2 b3 b4 b5 b6 b7) = f b0 b1 b2 b3 b4 b5 b6 b7

ascii_Induct

|- !P.
     (!b0 b1 b2 b3 b4 b5 b6 b7. P (ASCII b0 b1 b2 b3 b4 b5 b6 b7)) ==>
     (!a. P a)

ascii_CASES

|- !a. ?b0 b1 b2 b3 b4 b5 b6 b7. a = ASCII b0 b1 b2 b3 b4 b5 b6 b7

ASCII_11

|- !b0 b1 b2 b3 b4 b5 b6 b7 b0' b1' b2' b3' b4' b5' b6' b7'.
     (ASCII b0 b1 b2 b3 b4 b5 b6 b7 = ASCII b0' b1' b2' b3' b4' b5' b6' b7') =
     (b0 = b0') /\
     (b1 = b1') /\
     (b2 = b2') /\
     (b3 = b3') /\
     (b4 = b4') /\
     (b5 = b5') /\
     (b6 = b6') /\
     (b7 = b7')