src/HOL/Arith.thy
changeset 2099 c5f004bfcbab
parent 1824 44254696843a
child 2681 93ed51a91622
equal deleted inserted replaced
2098:2bfc0675c92f 2099:c5f004bfcbab
    14 consts
    14 consts
    15   pred      :: nat => nat
    15   pred      :: nat => nat
    16   div, mod  :: [nat, nat] => nat  (infixl 70)
    16   div, mod  :: [nat, nat] => nat  (infixl 70)
    17 
    17 
    18 defs
    18 defs
    19   pred_def  "pred(m) == nat_rec 0 (%n r.n) m"
    19   pred_def  "pred(m) == case m of 0 => 0 | Suc n => n"
    20   add_def   "m+n == nat_rec n (%u v. Suc(v)) m"
    20   add_def   "m+n == nat_rec n (%u v. Suc(v)) m"
    21   diff_def  "m-n == nat_rec m (%u v. pred(v)) n"
    21   diff_def  "m-n == nat_rec m (%u v. pred(v)) n"
    22   mult_def  "m*n == nat_rec 0 (%u v. n + v) m"
    22   mult_def  "m*n == nat_rec 0 (%u v. n + v) m"
    23 
    23 
    24   mod_def   "m mod n == wfrec (trancl pred_nat)
    24   mod_def   "m mod n == wfrec (trancl pred_nat)