src/HOL/NatArith.thy
author oheimb
Wed Jan 31 10:15:55 2001 +0100 (2001-01-31)
changeset 11008 f7333f055ef6
parent 10599 2df753cf86e9
child 11164 03f5dc539fd9
permissions -rw-r--r--
improved theory reference in comment
     1 (*  Title:      HOL/NatArith.thy
     2     ID:         $Id$
     3 
     4 Setup arithmetic proof procedures.
     5 *)
     6 
     7 theory NatArith = Nat
     8 files "arith_data.ML":
     9 
    10 setup arith_setup
    11 
    12 (*elimination of `-' on nat*)
    13 lemma nat_diff_split:
    14     "P(a - b::nat) = ((a<b --> P 0) & (ALL d. a = b + d --> P d))"
    15   by (cases "a < b" rule: case_split) (auto simp add: diff_is_0_eq [THEN iffD2])
    16 
    17 ML {* val nat_diff_split = thm "nat_diff_split" *}
    18 
    19 lemmas [arith_split] = nat_diff_split split_min split_max
    20 
    21 end