src/HOL/ex/Lagrange.thy
changeset 21404 eb85850d3eb7
parent 20807 bd3b60f9a343
child 22173 7a78b9531b80
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21403:dd58f13a8eb4 21404:eb85850d3eb7
    15 
    15 
    16 The enterprising reader might consider proving all of Lagrange's
    16 The enterprising reader might consider proving all of Lagrange's
    17 theorem.  *}
    17 theorem.  *}
    18 
    18 
    19 definition
    19 definition
    20   sq :: "'a::times => 'a"
    20   sq :: "'a::times => 'a" where
    21   "sq x == x*x"
    21   "sq x == x*x"
    22 
    22 
    23 text {* The following lemma essentially shows that every natural
    23 text {* The following lemma essentially shows that every natural
    24 number is the sum of four squares, provided all prime numbers are.
    24 number is the sum of four squares, provided all prime numbers are.
    25 However, this is an abstract theorem about commutative rings.  It has,
    25 However, this is an abstract theorem about commutative rings.  It has,